Evaluation of the polymer-solvent interaction parameter χ for the system cured styrene butadiene rubber and toluene

One of the most popular cured rubbers used in industrial applications is styrene butadiene rubber (SBR) and frequently its network structure is studied by means of swelling techniques in solvent. Normally, toluene is used as solvent in this test. In order to estimate the crosslink density from the equilibrium volume fraction of rubber in the swollen state, the correct evaluation of the Flory-Huggins interaction parameter χ is necessary. This work covers the swelling behavior of cured SBR in toluene. The rubber was vulcanized with different amounts sulfur and accelerator at 433 K in order to obtain several network structures and crosslink densities. Network characterisations of the compounds were made by swelling measurements in the frame of the Flory-Rehner relationship using the molecular weight of the network chain between chemical crosslinks obtained previously by mechanical tests. A relationship between χ and v_r, the polymer volume fraction at equilibrium (maximum) degree of swelling, was established for the cured SBR/toluene system. It was found that χ is not a constant but depends on the crosslink density in the sample. The types of crosslinks in these samples where estimated applying this function to the swelling behavior of the compounds previously treated with the thiol probe method.     

The effect of plasticization on craze microstructure

The structure of crazes in plasticized polystyrene has been studied by means of small-angle x-ray scattering and optical interference microscopy. Addition of plasticizer causes a rapid increase in the mean fibril diameter D and a slow decrease in the craze fibril volume fraction v_f. The crazing stress σ_c was also measured and it was found that the product D σ_c is independent of plasticizer concentration. These results are shown to be consistent with the entanglement model for controlling v_f and the meniscus instability model of craze thickness growth.     

Optical studies of the stress-induced crystallization of rubber

The low-angle light scattering by films of stretched natural and synthetic rubbers was investigated. Intense V_v scattering is found under conditions when crystallization occurs which is characteristic of the scattering from aggregates of dimensions comparable with the wavelength of visible light. These were identified with the γ fibrils described by Andrews. The dependence of scattering was studied as a function of light polarization direction, orientation direction, elongation, temperature, degree of swelling, type of swelling liquid, and degree of crosslinking. It was concluded that the scattering unit consists of an assembly of crystals with their chain axes parallel to the stretching direction, but (in the case of natural rubber at high elongations) with the fibril axis at a slight angle to the stretching direction. The scattering is not affected much by swelling but is decreased upon increasing the temperature. Upon recooling the scattering returns, but does so over several hours, indicating that much of the scattering arises from secondary crystallization.     

Crosslinking,filler, or transition constraint of polymer networks. II

The theory of Part I is developed by application to filler reinforcement of NR and SBR. For unswollen but prestretched networks it quantifies entire stress–strain curves and applies new concepts of extensibility and strain hardening. Constraint of swelling is expressed by a constant φ, termed linkage reinforcement, and by an effective hard fraction C_h per cubic centimeter of compound. For rubber–filler swelling v_c the modified Flory functions F(v_c) in part 1 need 3% correction. Then, relative to gum fix points 1/F₀(v_r): where C_h ≤ 1.15C for filler concentrations C per cubic centimeter of compound. The effective C_h comprises the volume fraction C* of bonded particles and 5–10 Å of surface–bound rubber that has been stretched hard by swelling. When needed, the actual crosslink density and intrinsic linkage reinforcement φ₀ can be obtained by dividing by (1 + 2.5C_φ) where C_φ = (C ln φ)/(1 + 2.5C). The case C_h ≤ 1.15C with Graphon or inert fillers is identified and assessed by equations: Results C_h > 1.15C are invalid, but then C_h ≈ 1.15C* ≈ 1.15C, e.g., for carbon blacks. Even Graphon is distinguished from inert fillers at low concentrations C by substantial constraint reinforcement F₀(v_r)/F(v_c) > 1. For prestressed dry rubber a modulus G, network extensibility α_b ? 1, and upturn coefficient μ_h express the whole curve; G and μ_h show identical constraint strength distributions. Network extensibility α_b ? 1 is the microbreaking strain (prestretch); for pure elastomer it is elongation at break. The relation of stress F to extension ratio α is: where C₂* = 0.7 and j = 0.4 from NR/MPC data. Strain-hardening coefficients h are obtained from μ_h by the theory given in Part I. Hard modulus components G_h = 0.7 ln (h/h₀) vanish as h → h₀ (gum) = 110. After high prestresses the residual ln-(h^*/h₀) due to strong carbon-rubber linkages implies G_h* = 0.42 kg/cm², i.e., ca. 10% of the normal cure crosslinks.     

Optical studies of the deformation of model filled rubbers

The strain pattern about a spherical glass bead imbedded in a stretched rubber has been calculated and used to predict the birefringence and light scattering. This is compared with experimental measurements of the retardation pattern observed using a polarization microscope and deduced from the low-angle laser H_v light scattering pattern. The agreement with theory is favorable. The light scattering is suggestive of similar origins of light scattering from crystallizing rubbers and from inhomogeneously crosslinked rubbers.     

Free volumes in simple and polymeric liquids

Values of ε₀ν₀ the vaporization energy and volume in the hypothetical liquid state at 0°K., are derived for some simple polar and nonpolar molecules used as models for vinyl polymers. The following empirical relationship between the free volume fraction, f = (v ? v₀)/v, and the liquid compressibility coefficient β is demonstrated: ?f² ∝? This is applied to several vinyl polymer liquids near their glass transition temperatures, T_g, giving. f_g ? 0.17, if the “hard-core” volume v^* is considered to be independent of pressure and temperature, (i.e., v^* = v₀); or, f_g ?0.12, if the P,T dependence of v^* is considered to be the same as that of the glass. These agree with f_g values derived by Simha and Boyer from thermal expansion coefficients for the two analogous cases. An empirical viscosity-free volume equation of the Doolittle form: η = ATⁿe^b/f is applied to the glass transition, on assuming that this is an isoviscosity state and with the use of reported values for the expansion and compressibility coefficients and dT_g/dP for three polymers: polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). Reasonable values of b/n are thus obtained. This viscosity equation is critically examined in the light of molecular theories of liquid viscosity.     

Viscoelastic properties of crosslinked solutions of poly(β-hydroxyethyl methacrylate) in diethylene glycol. II. Dependence of creep compliance on concentration in the rubbery zone

Creep compliance data, J(t), at 35°C for poly(β-hydroxyethyl monomethacrylate), crosslinked by ethylene glycol dimethacrylate in a range of concentration C from 0.0855 to 2.053 × 10^?4 mole/cm³ and swollen to various degrees in diluents, were examined for time-concentration superposition. From the dependence of time scale shift factors on v₂, the volume fraction of polymer, free volume parameters were calculated for two samples with C = 0.0855 × 10^?4 and 0.136 × 10^?4 mole/cm³, swollen in the range of v₂ from 0.134 to 0.591. Special attention was given to the magnitude of the shift factor on the log J(t) axis and its dependence on concentration, which was found to depend substantially on the crosslinking and the swelling degrees of the samples. This shift was approximately log v₂ for lightly crosslinked samples, swollen to a small degree, measured in the neighborhood of the main transition. For higher degrees of crosslinking and/or swelling, the shift was much less and for the most highly crosslinked networks swollen to equilibrium it was even negative. The correction appears to be very sensitive to the strain of the effective chains and to the location on the time scale with respect to the transition and rubberlike zones of viscoelasic behavior. It was found that the parameters of the WLF equation calculated in our previous study from the time-temperature superposition of the creep curves in the rubber-glass transition are valid also for the rubberlike region.     

Effect oftrans-polyoctenamer on thermal stability of rubbers determined by thermal analysis

An effect of a cyclic low molecular-weight polymertrans-polyoctenamer rubber (TOR) on the thermal stability of diene rubbers and their vulcanizates was investigated. The investigation was carried out in the air and nitrogen atmospheres using thermogravimetry, DSC and simultaneous thermoanalytical methods. The thermal stability indexes:T ₅,T _max and activation energy of degradation (E), as well asT _g andT _m values, have been determined.It was found thattrans-polyoctenamer (TOR) increases of the thermal stability indices of raw diene rubbers and their vulcanizates. The results show that the thermal degradation of diene rubbers occurred at higher temperature if they were blended with TOR. In our opinion, intermolecular structures formed between the cyclic low-molecular weight polymer and some linear rubber molecules may be the reason for the higher thermal stability of these rubber blends.The work was supported by State Committee for Research, Poland. Grant No. 7.T08 E 032-08.     

Mechanochemical energy conversion of neutral polymer gels

Mechanochemical energy conversion exhibited by water-swollen poly(vinyl alcohol) gels has been studied. The effective mechanical work produced as well as the chemical energy converted were measured simultaneously. It is shown theoretically and experimentally that the mechanical work developed during the swelling of the mechanochemical system increases with increase of the external load (m), the degree of cross-linking (DC) and the deswelling ratio (ϕ/ϕ_e, i.e. the ratio of the volume fraction of network polymer (ϕ) to that of the same gel in equilibrium with pure diluent (ϕ_e)). The chemical energy converted was found to be practically independent of m. The efficiency of energy conversion increased with increase of m and DC, and significantly decreased with increase of ϕ/ϕ_e. Comparison is made between theoretical predictions and experimental findings.     

Miscibility and volume changes of mixing in the polystyrene/poly(2-chlorostyrene) blend system

The specific volume-temperature relationships of polystyrene, poly(2-chlorostyrene), and their polymer blends as well as the volume change of mixing Δv_m of the blends were obtained in the liquid state by dilatometry. The equation of state parameter and the molecular parameter of each homopolymer and blends were determined according to the lattice fluid theory of Sanchez and Lacombe. The experimental Δv_m obtained agreed quite well with that predicted from theory, and the enthalpy of mixing ΔH_m was also predicted using the pair molecular parameter. These two values were negative, indicative of miscibility of polystyrene and poly(2-chlorostyrene) in the liquid state. The absolute values of Δv_m and ΔH_m were about twice those for polystyrene and poly(phenylene oxide) blend, suggesting a specific interaction between the two polymers.     

Crosslinking,filler, or transition constraint of polymer networks. I

The basic theory of modulus/swelling is developed to allow for limited extensibility, filler reinforcement or transition effects, and steric hindrance of aligned segments by extended chains or filler particles. Filler forms an effective hard fraction C_h per cubic centimeter of compound with v_c a new (compound) index of swelling. For 1/M_c + σ fix points having ratio φ to gum values 1/F₀(v_r) and with F(v_c) replacing the Flory function F(v_r): where σ denotes entanglement. Linkage reinforcement φ does not vary with sulfur crosslinking of SBR. Vacuoles invalidate φ from mass-increment F₀(v_r)/F(v_r) for inert fillers. Then, or for Graphon, with negligible φ ≈ 1: The effective C_h includes rubber stretched hard on Graphon by swelling or trapped inside hard aggregates. Only the right-hand equation fits normal blacks. In theory, C_h can always be obtained from swollen moduli G by linear slopes (1 + 1.4C_h) relating F(v_c) and (1 ? C)ρRT/G. For filler fractions C ≥ 0 cm^?3 and low strains α = 1.5?2.0 below prestretch the modulus G is given a new basic definition: Here C₂* ≈ 0.7 corresponds to Mooney-Rivlin C₂ and the effective crosslinking 1/[M_c] = (ρRT)^?1G is equal to (1 ? C)(1/M_c + σ) for unswollen prestretched rubber (v_r = 1). For higher strains a hypothesis of strain hardening is proposed. This is distinct and opposite in character to the initial prestretch softening (Mullins effect). Nonlinear effects of crosslinks are expressed by a fractional stress-upturn Ω (1/M_c + σ), effective mesh wieght (1/M_c + σ)^?1 ? Ω, and hard fraction Ω(1/M_c + σ). For μ_h characterizing strain hardening up to the prestretch (α_h ? 1) their contribution is: The sixth-power refinement has J = j(α_b ? 1)^1/2 with j ≈ 0.4. The hard phase is augmented by filler and grows with increasing strain up to the prestretch.     

Diffusion of linear polyisoprene molecules into polyisoprene networks

Diffusion and equilibrium absorption of polyisoprene liquids into crosslinked samples of cis-polyisoprene (natural rubber) have been studied by direct observation of volume swelling. Natural rubber was crosslinked in the form of fine threads, about 40 ± 20 μm in diameter, using a gaseous reaction with SO₂ and H₂S (the Peachey process). An optical microscope was used to observe the relatively rapid absorption of linear high-molecular-weight polyisoprene liquids by these fine threads. From the kinetics of absorption, values of the self-diffusion coefficient D_s of polyisoprene were estimated. They ranged from 10^?16 m²/s to 10^?12 m²/s, depending upon molecular weight, and varied with molecular weight approximately as M^?2 over the entire range employed, from 1,000 to 60,000 g/mol, i.e., both above and below the entanglement molecular weight. Amounts of polymer absorbed at equilibrium varied widely, depending upon the degree of crosslinking of the host material and the molecular weight of the absorbing liquid. They were in reasonable agreement in all cases with simple swelling theory, with the heat of mixing equated to zero.     

Thermoelasticity of networks in swelling equilibrium

A theoretical analysis of the thermoelastic behavior of polymeric networks in swelling equilibrium with excess diluent, using both the kinetic theory of elasticity and the Flory-Huggins theory of mixing, is presented. Our calculations are restricted to the special case of diluents composed of a single constituent. The results are used to obtain the ratio of the energy component of the force f_e to the total force f of rubber networks swollen in excess n-decane, and we find f_e/f to be 0.17, which compares favorably with the value 0.18 reported for the unswollen network. Furthermore, f_e/f is independent of elongation, in accordance with theory. The kinetic theory of elasticity is reasonably well obeyed in this highly swollen system although there remains a small contribution to the force from the C₂ term of the Mooney-Rivlin phenomenological elasticity equation. It is not believed that this has an appreciable effect on f_e/f.     

Emission of occluded volatiles during deformation of polycarbonate due to strain-enhanced diffusion

Measurements of the emission of purposely entrained volatiles (Ar and D₂O) during the loading and unloading of a bisphenol-A polycarbonate in vacuum are made by quadrupole mass spectrometry. Transient loading events are accompanied by dramatic increases in emission, reflecting a similar rise in the diffusion constant of the measured species. We attribute this change to an increase in size of molecular voids in the polymer network, which accompany the increase in sample volume under load. The results are interpreted in terms of the Dolittle relation in which the diffusion constant depends exponentially upon v^*/v_f0, the ratio between an activation volume for diffusion and the average size of the relevant voids in the polymer network. Our data suggests that v^*/v_f0 is unusually low in the D₂O-polycarbonate system, which we attribute to a relatively large value of v_f0; this would be consistent with the relatively long distance between flexible links in the polycarbonate structure. © 1994 John Wiley & Sons, Inc.     

The elastic free energy and the elastic equation of state: Elongation and swelling of polydimethylsiloxane networks

The elastic free energy for a tetrafunctional network is here expressed as where λ₁, etc., are the principal extension ratios relative to the state of reference (wherein 〈r²〉 = 〈r²〉₀), and C₁, C₂, and m are arbitrary parameters. The free energy of a swollen system is taken to be the sum G = G_mix + G_el of G_el and the free energy of mixing \documentclass{article}\pagestyle{empty}\begin{document}$ G_{{\rm mix}} = RT\left[ {n_1 \ln v_1 + n_2 \ln v_2 + \bar \chi n_1 v_2 } \right] $\end{document}. Stress-strain relations and the chemical potential μ₁ are derived from G as functions of the elasticity parameters C₁, C₂, and m, and of the thermodynamic interaction parameter χ or of \documentclass{article}\pagestyle{empty}\begin{document}$\chi = \bar \chi + n_1 v_2^{ - 1} \partial \bar \chi /\partial n_1 $\end{document}. The dilation of the semi-open system subject to deformation when exposed to diluent at fixed activity is derived as the sum of the dilation at fixed composition and the dilation due to absorption of diluent. Experiments are reported on the dependence of the equilibrium retractive force on elongation for cross-linked polydimethylsiloxanes (PDMS) exposed to benzene or hexamethyldisiloxane vapor at regulated activities. Volume fractions of samples covered the range v₂ = 1.00 to v₂ ≈ 0.30. With the choice of m = ½ the elastic behavior of a given polymer is well represented by one combination of values for C₁ and C₂ at all dilutions by either diluent. The dependence of the Mooney-Rivlin (C₂) term on volume is thus established, at least for PDMS, and the scope of the semi-empirical free energy expression and its consequents is greatly enlarged. Values of χ deduced from the equilibrium swelling of the unstrained networks exposed to benzene at various activities are in excellent agreement with those obtained previously from vapor pressures and osmotic pressures on linear PDMS. The results of Allen, Kirkham, Padget, and Price on the elastic behavior of natural rubber are discussed, with particular reference to the coefficients of dilation with elongation which they determined at fixed composition. The present results lend strong support to the principle of additivity of the free energies attributable to the network and to the bulk liquid system, respectively. This principle is fundamental to the analysis of rubber elasticity.     

Characterization of moisture-cured polyurethane films

A series of polyurethanes (PU) prepolymers with NCO/OH ratios of 2.1:1 and 1.9:1 were prepared by reacting hydrogenated methylene di-p-phenyl diisocyanate (HMDI) with triol mixtures of TP740 (molecular weight 740) and TP1540 (molecular weight 1540). Stress–strain (S/S) and swelling equilibrium measurements were performed using thin-film samples prepared by moisture-curing the prepolymer at room temperature. The swollen PU networks gave an S/S curve which is fully described by rubber elasticity theory. The Mooney-Rivlin constant C₁ (swollen) was found to increase directly while the molecular weight between crosslinks M_c decreases as the number of branches per cubic centimeter is increased. The solvent—polymer interaction parameter χ determined in benzene was 0.077 + 0.97_vr, where v_r is the volume fraction of rubber in the swollen network. The crosslink density v′, and M_c were calculated from the relations v′ = pNB and M_c = 0.667 B^?1, where B denotes moles of branches per gram, and were found to be in good agreement with v′ and M_c established from S/S and swelling-equilibrium measurements. In calculating v′ and M_c, the water-PU crosslinking reaction at room temperature was assumed to occur mainly through the formation of a urea linkage.     

Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor(X) was introduced, the theoretical model could fit the tensile stress-strain data of mono-and bi-modal foam matrix well(Adj. R-Square = 0.9989, 0.9983). Parameters related to the polymer network, namely, average molecular weight(Mc) and volume fraction(ф) of chain segments between adjacent cross-linking points(network strands), were calculated by probabilistic method from the number-average molecular weight(Mn), vinyl content(w Vi) of the primary polysiloxanes and percent conversion(q) of vinyl groups. The primary and infinite strain amplification factors(X0, X∞) and decay exponent(z), introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams', we introduced another item, strain hysteresis item(H, related with the foam porosity and cell structure), into the statistical model as well. With the same above values of Mc,ф, X0 and X∞, the model could also fit the compressive stress-strain data of mono-and bi-modal foams well(Adj. R-Square = 0.9948,0.9985). Interestingly, the strain hysteresis items of the mono-and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.     

Low-frequency losses in rubbers cross-linked in the presence of diluent

Measurements of the complex shear compliance have been made from 0.1 to 7 cycles/sec. and from ?5° to 45°C. on several samples of natural rubber cross-linked by dicumyl peroxide in the presence of a diluent oil (volume fraction of rubber, v₂, = 0.63 and 0.76) which was subsequently extracted. The properties of the extracted vulcanizates were compared with those having the oil still present and with those of conventional undiluted vulcanizates. Measurements of the diffusion coefficient of radioactively tagged n-hexadecane in trace amounts through the polymer structure were also made both before and after extraction of the oil. The diffusion coefficient was higher in the presence of the oil by an amount consistent with the Fujita theory for concentration dependence of diffusion rate based on free volume considerations. The low-frequency mechanical losses (reduced to 25°C. by the method of reduced variables), as measured by the loss tangent, were shifted to higher frequencies by the presence of oil to a much larger degree than would be expected from the difference in local mobility gauged by the diffusion coefficient. The equilibrium modulus, derived by extrapolation to zero frequency, was diminished by the presence of oil to a greater extent than the factor of v₂^? expected from the simple theory of rubberlike elasticity. The low-frequency losses in the extracted vulcanizates were smaller than those in conventional vulcanizates with comparable degrees of cross-linking; the differences are attributed to differences in network topology.     

Effect of interference between anisotropic scattering entities on light scattering from polymer films. II. The correlation function approach

A theory is developed by use of the correlation function approach for calculating both the H_v and V_v intensity of scattered light for a concentrated assembly of spherulities. The scattering becomes a function of the radial and tangential polarizabilities of the spherulite α_r and α_t, the polarizability α_m of the medium, surrounding the spherulites, and the volume fraction ?_s of spherulites. The “effective polarizability of the surroundings” α_s, which appeared in previous theories, becomes function of these variables. The theory can explain, for example, why the V_v scattered intensity passes through a maximum during the course of crystallization.     

Modeling of chromatographic retention of the selected antiarrhythmics and structurally related compounds in the hydrophilic interactions under the TLC and HPLC conditions

Abstract

High-performance liquid chromatography (HPLC) plays an important role in testing the pharmaceutically active compounds. In despite of the advantages of HPLC, thin-layer chromatography (TLC) retains its applicability to the different experimental tasks. The experimental conditions which allow hydrophilic interactions in the chromatographic system were tested in the HPLC and TLC systems for ivabradine, its related compounds, diltiazem and verapamil. Under the TLC conditions, retention behavior of the investigated compounds was tested on silica gel modified with cyanopropyl ligands as stationary phase and acetonitrile?+?methanol containing 25% v/v formic acid. Under the HPLC conditions, we used silica gel modified with cyanopropyl ligands as a column packing and the acetonitrile + 0.25% aqueous solution of formic acid as mobile phase. Retention behavior of the investigated analytes depending on the changing volume fractions of the mobile phase modifier was characterized both for TLC and HPLC data sets by the Soczewiński–Wachtmeister equation. Linear relationships were established between the retention coefficients characterizing the retention mechanism (R_M⁰/m, logk₀/m) and molecular properties of the investigated compounds. The Quantitative Structure Retention Relationship (QSRR) modeling was performed with the use of the stepwise multiple linear regression, in order to select molecular properties which influence retention.