Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. IV. States of ease and stress–strain behavior

Linear 1,2-polybutadiene, glass transition temperature (T_g) ?18°C, is crosslinked at ?10°C, to ?20°C by γ irradiation while strained in simple extension, with extension, ratios (λ₀) from 1.2 to 2.7. After release, the sample retracts to a state of ease (λ_s) at room temperature. From equilibrium stress–strain measurements up to a stretch ratio relative to the state of ease (Λ) of 1.2, together with λ₀ and λ_s, the concentration of network strands terminated by trapped entanglements (νN) is calculated. For this purpose, a three-constant Mooney–Rivlin formulation is used, in which the entanglement network is described by Mooney–Rivlin coefficients C_1N and C_2N, whereas the crosslink networks is described by the coefficient C_1x only. The ratio ψ_N = C_2N/(C_1N + C_2N) is estimated from parallel studies of nonlinear stress relaxation of the uncrosslinked polymer, taking into account the thermal history before and during irradiation. For substantial degrees of crosslinking, i.e., for R_0′ = ν_x/ν_N > 0.4 (where ν_N is the concentration of network strands terminated by crosslinks), and for λ₀ < 1.8, C_2N agrees rather well with the value obtained from stress relaxation of the uncrosslinked polymer in the range of time scale where it is nearly independent of time (1.87 X 10⁵ pascals). The corresponding value of ν_N is 2.3 × 10^?4 moles/cm³, in good agreement with that obtained from viscoelastic measurements of the uncrosslinked polymer in the plateau zone (2.5 × 10^?4). However, for R_0′ ? 0.2, smaller values of C_2N and ν_N are obtained, indicating that for low degrees of crosslinking the entanglements are not completely trapped. Also, for higher values of λ₀, C_2N and ν_N turn out to be somewhat smaller. Similar, less extensive results were obtained previously on a 1,2-polybutadiene with somewhat higher vinyl content and a higher T_g. Crosslinked samples of both these polymers were subjected to equilibrium stress–strain measurements in simple elongation from the state of ease at higher strains up to Λ = 1.7. The results agreed closely with calculations from the three-constant Mooney–Rivlin theory.     

Influence of solvent and molecular weight on thickness and surface topography of spin-coated polymer films

The influence of polymer molecular weight, molecular weight distribution, and polymer-solvent interactions on the thickness and topography of spin-coated polymer films was examined. For films prepared from dilute solutions, highly volatile solvents or fair or “poor” solvents for the polymer adversely affect film surfaces causing nonuniformities (waves) to appear. However, if the concentration of these solutions is increased to approximately the concentration at which entanglements are formed, nearly uniform films are produced even if the solvent employed is highly volatile, such as dichloromethane. When toluene is employed as the solvent, which has a relatively low volatility and therefore forms nearly flat film surfaces, films prepared from dilute solution were found to have thicknesses, h, proportional to η Ω^?0.49 for polystyrene and η Ω^?0.49 for poly(methylmethacrylate) where η_o is the zero-shear rate solution viscosity and Ω is the rotational speed at which the films were prepared. These results suggest that the exponents associated with η_o and Ω may be nearly independent of the type of polymer used as long as flat films are produced. Finally, the molecular weight parameter most important in controlling final film thickness for films made from dilute solutions is M_v, the viscosity-average molecular weight.     

Elastic characteristics of branched-network polymers

The computed dependencies of elastic characteristics of branched-network polymers were obtained on the basis of the Takayanagi series model. The moduli ratio (λ) for branched-network and branched polymers increases as a result of an increase of the moduli ratio of network and branched phases (E/E) and the network phase fraction (V_net). The λ-increase as a function of V_net is larger than in the case of the E/E dependence. On the basis of computed dependencies, the experimental results for the radiation crosslinked SBS block copolymer were considered. The experimental results agree with the computed de-pendencies for the hetergeneous branched-network polymers with E/E ≈︁ 20. The influence of entanglements on the elastic characteristics of branched-network polymers is discussed. © 1996 John Wiley & Sons, Inc.     

Scission of non-interpenetrating macromolecules in transient extensional flows

Solutions of the random coiling polymers; polystyrene, poly (methylmethacrylate), and sodium polystyrene sulfonate (NaPSS), all at concentrations well below the critical value for entanglement, were subjected to transient, high, elongational strain rates by passage from a cylinder through an orifice into a gently diverging section, driven by a piston at constant, high velocity over a short stroke. It is shown that a critical orifice flow velocity V_c. exists for each polymer species, above which scission of polymer molecules occurs creating new molecules. By gel permeation chromatography, the number of additional polymer molecules created per initial polymer molecule, the scission index, was determined as M _n,0/M _n – 1 where M _n is the number average molecular weight, and M _n,0 is the initial value thereof. V_c is found to vary as approximately M . Above V_c the scission index was found to be proportional to M , to the difference: orifice velocity V less V_c, and to the number of passes N of the polymer solution through the orifice. Expansion of NaPSS coils by reducing ionic strength of their aqueous solutions, at constant polymer molecular weight, decreases the scission index, The hypothesis is proposed that intramolecular entanglements are responsible for scission. The random coiling macromolecules in the solution cannot respond to the strain rate (imposed in ca, 100 microseconds) so as to avoid having internal sections, caught by loop entanglement, pulled to nearly full extension and thus broken.     

Strain-induced crystallization,Part III: Theory

A nucleation theory for strain-induced crystallization is formulated to explain and to predict the effects of molecular strain on crystallization kinetics and crystallite size. Unlike any current theories that have based their formulations on some assumed extended-chain line nuclei or folded-chain crystals, the present theory avoids all assumptions concerning the crystal morphology. It is based on experimental findings which indicate limited crystal growth in the strain direction, following a reciprocal dependence of crystal thickness on supercooling ΔT. (ΔT = T, ? T, where the equilibrium melting temperature, T, is a variable dependent on degree of molecular strain prior to strain-induced crystallization.) It is predicted that the logarithm of the nucleation rate, N^o, is dependent on (T)²/T(ΔT) or T/T(ΔT), and that the critical nucleus thickness l^*o is shown to be proportional to T/ΔT. In addition, expressions are also presented, including examples, to show the dependence of N^o, l^*o and T^o_m on degree of molecular strain, ?, or melt entropy reduction, Δs′. Our analysis predicts that, on comparing a polyethylene crystallized in the presence of strain to one crystallized in the absence of strain at 130°C, an increase in “coil” dimension of less than about 50 percent can bring about a 10⁴ fold increase in heterogeneous nucleation rate, a 30–40 percent reduction in critical nucleus thickness and a 10°C increase in equilibrium melting temperature. These results will be discussed and compared with available experimental evidence.     

Numerical and experimental investigation of three-dimensional flow in extrusion dies

The univariant element, Q₁ P₀, and the multivariant elements, QP₀ and R P₀, are compared for the numerical simulation of the flow in extrusion dies. The pressure distribution obtained by using the Q₁ P₀ element was found to be afflicted with the checkerboard pressure mode. On the other hand, the multivariant elements, Q P₀ and R P₀, gave accurate and physically reasonable velocity and pressure distributions. The computed values of the pressure drop across extrusion dies matched well with the pressure drop determined experimentally.     

Lateral strain effects during the large extension of thermoplastics

A noncontacting experimental procedure is used for characterizing lateral strain effects during the large-strain uniaxial stretching of flat sheet-like specimens of polycarbonate, polyetherimide, and poly(butylene terephthalate), both at room and elevated temperatures. It is shown that the in-plane lateral stretch, λ₂, is related to the longitudinal stretch, λ₁, through the relation λ₂ = λ. Depending on the temperature, the “Poisson's ratio” for incremental strains, n, is shown to lie between n = 0.4 and n = 0.5. While the lateral stretch in the thickness direction, λ₃, is smaller than λ₂ at room temperature, it is shown that λ₃ = λ₂ at higher temperatures. Stretch data have been used to infer the volumetric strains in these materials.     

Viscoelasticity of some engineering plastics analyzed with the modified stress-optical rule

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), of poly(ether sulfone) (PES), polysulfone (PSF), and polyethermide (PEI), were measured over the frequency range 1 to 130 Hz. The data were analyzed with a modified stress-optical rule: The Young's modulus was decomposed into two complex functions, E(ω) and E(ω); the modified stress-optical coefficient, C_R and C_G, associated with the rubber (R) and glass (G) components, respectively, were determined. The results for six polymers, including polystyrene, poly(α-methyl styrene), and bisphenol A polycarbonate were compared with each other. One of the coefficients, C_R, equivalent to the stress-optical coefficient in melts, mainly depended on the way in which phenyl groups were connected to the chain. The other, C_G, was in the range of 20 to 40 Brewsters, and did not strongly depend on the details of polymer structure. The component function, E(ω), which was located in the glassy region and originated from the high glassy modulus, was almost the same in shape when plotted against ω with double logarithmic scales. The R component, E(ω), located at the long time end of the glass-to-rubber transition zone, was slightly sensitive to the molecular structure of polymers.     

Kinetics of methyl methacrylate grafting polymerization onto flaky aluminum powder

With ammonium persulfate (APS) as the initiator, the kinetics of methyl methacrylate (MMA) grafting polymerization onto flaky aluminum powder (Al) was studied. It was found that the experimental apparent grafting polymerization rate, R_g = KC × C × C, was basically consistent with the theoretical result based on the theory of stable polymerization and equivalent activity, R_g = KC × C × C_MMA. The activation energy of grafting, homogenous, and total polymerization rate was calculated as 65.1, 35.4, and 37.5 kJ mol^?1, respectively. It could be validated that the relationship among these activation energies accorded with the theoretical result of parallel reactions. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

In situ study of the dynamics of erosion of carbon black agglomerates

With the help of a counter‐rotating transparent rheometer equipped with an optical microscope, the erosion of single, commercial carbon black agglomerates suspended in a polyisobutylene fluid was accurately recorded in situ. We observed that clouds of very small aggregates were leaving the agglomerate at 45 and 225° in the shear gradient–flow direction plane, where the stress is maximum. The distribution of the arrached aggregates is more efficient when the carbon black agglomerate is more asymmetric. A spherical agglomerate of critical radius R₀ will reach a radius R_t at time t following R ? R = at, a being a constant. This implies that the rate at which the number of aggregates is leaving the agglomerate is a constant, independent of the size of the agglomerate. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1627–1629, 2001     

Aniline and some of its derivatives as corrosion inhibitors for nickel in 1 M HCl solution

The inhibiting action of aniline and some of its derivatives (o‐, m‐ and p‐anisidine) towards the corrosion behaviour of nickel in 1 M HCl solution has been studied using weight loss and polarization techniques. These compounds were found to retard the corrosion rate of nickel. At constant temperature, the corrosion rate decreases with increasing inhibitor concentration. On the other hand, at any inhibitor concentration, the increase in temperature leads to an increase in the corrosion rate. The activation energy, ΔE_a, the equilibrium constant, k, as well as the other thermodynamic parameters (ΔG, ΔH and ΔS) for inhibitor process were calculated and analysed. The inhibitor efficiencies calculated from both weight loss and polarization methods are in good agreement and were found to be in the order: p‐anisidine > o‐anisidine > m‐anisidine > aniline. The inhibitive action of these compounds was attributed to the adsorption of molecular species and their inhibitive efficiencies depend on the relative position of the  OCH₃ group in the aniline ring. © 1999 Society of Chemical Industry     

The effect of grafted polymeric lubricant molecular weight on the frictional characteristics of nylon 6,6 fibers

Boundary friction between two crossed nylon 6,6 fibers has been reduced up to 6× by grafting polymeric lubricants to the surface. A modified adhesion model of friction, accommodating multiple materials on the surface, explains the variation in the friction coefficient with the molecular weight of the lubricant. The friction coefficient is proportional to the fraction of the surface covered by the grafted chain, represented by πR/A, where A is the surface area per graft site, and R_G is the radius of gyration of the lubricant. It is also shown that for larger the grafted chains, the appropriate surface area fraction depends on πR/3A. It is argued that if R_G of the grafted lubricant is larger than half the distance between graft sites, the next nearest graft site is used due to steric blocking of the nearest graft site. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 129–136, 1999     

Der Substituenteneinfluß auf IR-Spektrenparameter von 4′-phenylsubstituierten (E)-Styryl-methyl-sulfonen

The Influence of Substituents on the I.R. Spectral Parameters of 4′-Phenylsubstituted (E)-Styryl-methyl-sulphones The positions and integrated intensities of the bands corresponding to characteristic vibrations of eight 4′-phenylsubstituted (E)-styryl-methyl-sulphones were determined and correlated with substituent constants. The results demonstrate a linear dependence of the wavenumbers of vSO₂ and VCC vibrations, respectively, with the electrophilic substituent constants σ. Otherwise the square roots of the integrated intensities A^1/2 (v^sso₂) and σ gave no linear correlation. The influence of the substituents on the i.r. spectral parameters is discussed and compared with π-bond orders and π-electron densities. These magnitudes reflect qualitatively the behaviour of i.r. frequencies and intensities of selected absorption bands.     

Correlation of swelling and crosslinking density with the composition of the reacting mixture employed in radical crosslinking copolymerization

This article reports the scaling laws relating the synthesis conditions with the crosslinking density (ν_e) and swelling degree (S) of poly(N‐vinylimidazole) hydrogels (PVI) prepared by radical crosslinking copolymerization in aqueous solution, with N,N′‐methylene bisacrylamide (BA) as crosslinker. Multiple linear regression of ν_e versus BA concentration ([BA]) and total comonomers concentration (C_T) in double log scale render the scaling law ν_e ～ C × [BA]^1.04 as comparable to that predicted by the model of polymer network with pendant vinyl groups (ν_e ～ C_T × [BA]), and showing inverse dependence on C_T to that expected, following from stoichiometry, for an ideal network (ν_e ～ 2[BA]/C_T). S scales with ν_e through a solvent‐dependent exponent ranging from ?0.46 to ?0.54, only slightly over the value predicted by the Flory–Rehner theory (?0.6) or the blob's model by de Gennes (?0.5 to ?0.8). Finally, the scaling law of S with the composition of the reacting mixture is also solvent‐dependent and it seems to result not only from the dependence of ν_e on C_T and [BA] but also from that of v_2r, the polymer volume fraction in the reference state, and χ, the polymer–solvent interaction parameter. Models used seem to overestimate the contribution of entanglements to the effective crosslinking density of PVI. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 263–269, 2007     

Some solution properties of fractionated water-soluble hydroxypropylcellulose

A solution-fractionation technique has been developed for water-soluble (molar substitution, MS, ca. 4) hydroxypropylcellulose (HPC), utilizing mixtures of anhydrous ethanol (solvent) and n-heptane (nonsolvent) of varying composition. Solubility is primarily an inverse function of chain length, species of highest molecular weight being soluble only in solvent mixtures richest in ethanol. Fractionation data indicate HPC substitution is fairly uniform, although there is a tendency for shorter chains to be more highly substituted than long ones. Some control over the degree of variation is possible by changes in processing conditions. Molecular weight and molecular weight distribution reflect the properties of the cellulose employed in sample preparation and the use or omission of deliberate degradation for viscosity control. A sample of HPC ([η] = 4.2; MS = 4.4) was separated into seven fractions of approximately equal weight and the average molecular weight (M_w), root mean square radius of gyration, and second virial coefficient of each of these fractions in ethanol were determined by light scattering, while molecular weight distributions were investigated by gel permeation chromatography in tetrahydrofuran. The relation between intrinsic viscosity and degree of polymerization (DP) was found to be [η] = 7.2×10^?3DP . A comparison of hydrodynamic and configurational parameters for HPC in ethanol with those for hydroxyethylcellulose (HEC) in water indicates these two polymers behave very similarly in solution. In both systems the ratio of the mean square end-to-end unperturbed molecular chain length (R ) to DP diminishes with increasing molecular weight, reaching a minimum at a DP _w of approximately 3000. The ratio [(R )/(R )], where (R )^½ is the root mean square end-to-end distance for 1,4′-polysaccharides assuming free rotation of the chain units, also diminishes with increasing molecular weight, reaching a limiting value of 3.5. This relatively high ratio indicates considerable rigidity in the coiled molecule and is believed to be at least partially the result of intramolecular hydrogen bonding.     

The viscoelastic properties of rubber–resin blends. III. The effect of resin concentration

The viscoelastic properties of a rubber–resin blend, which influences performance of the blend as a pressure-sensitive adhesive, depend upon the structure of the resin as well as its molecular weight. The effect of the concentration of a compatible resin in the blend was examined using a mechanical spectrometer. Four types of resins were used. These are the rosin esters, polyterpenes, pure monomer resins such as polystyrene and poly(vinyl cyclohexane), and petroleum stream resins. Each was examined in blends with both natural rubber and styrene–butadiene rubber over a range of concentrations. It is shown that the temperature of the tan δ peak for compatible systems can be predicted by the Fox equation, T = W₁T + W₂T, where W₁ and W₂ are the weight fractions of the resin and rubber, respectively, and the T_g's are the tan δ peak temperatures in K. The plateau modulus G for a blend can be identified as the G′ value in the rubbery plateau at the point where tan δ is at a minimum. The relationship between G and G, the plateau modulus for the undiluted elastomer, is shown to be proportional to the volume fraction of the elastomer raised to the 2.3–2.4 power for natural rubber with six different compatible resins. The exponent for styrene–butadiene rubber is 2.5–2.6 with four different resins. Using these relationships, both the tan δ peak temperature and plateau modulus can be predicted for a rubber–resin system from data on the unmodified elastomer and on one typical rubber–resin blend.     

Chain structure,phase morphology,and toughness relationships in polymers and blends

We present chain structure, phase morphology, and toughness relationships in thermoplastic polymers and polymer/rubber blends. In neat polymers, molecular aspects of craze/yield behavior are controlled by two chain parameters: entanglement density ν_e and characteristic ratio C_∞. The crazing stress is proportional to ν, and the yield stress is proportional to C_∞. The dispersed rubber toughens a polymer/rubber blend mainly by promoting energy dissipation of the matrix. The toughening efficiency correlates with the rubber phase morphology and the chain structure of the matrix.     

Surface activity and micellar behavior of dimethylamino‐ and trimethylammonium‐ tipped oxyethylene–oxybutylene diblock copolymers in aqueous media

Surface activity and micellar behavior in aqueous media in the temperature range 20–50°C of the two block copolymers, Me₂N(CH₂)₂OE₃₉B₁₈, (DE₄₀B₁₈) and I^?Me₃N⁺(CH₂)₂OE₃₉B₁₈, (TE₄₀B₁₈) in the premicellar and postmicellar regions have been studied by surface tensiometry, viscometry, and densitometry. Where E represents an oxyethylene unit while B an oxybutylene unit. Various fundamental parameters such as, surface excess concentrations (Γ_m), area per molecule (a) at air/water interface and standard Gibbs free energy for adsorption, ΔG have been investigated for the premicellar region at several temperatures. The thermodynamic parameters of micellization such as, critical micelle concentrations, CMC, enthalpy of micellization, ΔH, standard free energy of micellization ΔG, and entropy of micellization ΔS have also been calculated from surface tension measurements. Dilute solution viscosities have been used to estimate the intrinsic viscosities, solute‐solvent interaction parameter and hydration of micelle. Partial specific volume and density of the micelle were obtained from the density measurements at various temperatures. The effect of modifying the end group of the hydrophilic block was investigated by comparing the behavior of trimethylammonium‐ and dimethylamino‐tipped copolymers, designated TE₄₀B₁₈, and DE₄₀B₁₈, respectively. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Simultaneous sorption and diffusion of a 4-aminoazobenzene derivative and its conjugate acid in cellulose membrane carrying sulfonic acid groups

An azo dye, 2-methyl-N,N-bis(2-hydroxyethyl)-4-aminoazobenzene (nonionic dye) and its conjugate acid (cationic dye) are simultaneously adsorbed by the cellulose membranes carrying sulfonic acid groups from a slightly acidic aqueous solution. Sorption equilibria of the nonionic and the cationic dye are described in terms of the Henry's partition and the ionic exchange mechanism, respectively, in the latter case, the ion exchange constants obtained for the membrane with sulfonic acid group content (SAG) = 261 meq/kg at 30°C are K = 1.43 × 10^?5 and K = 0.542, respectively, where Na, H, and DH refer to sodium, hydrogen, and cationic dye ions. The diffusion coefficients of the nonionic dye (D_N) and the cationic dye (D_C) in the membranes were estimated from the permeation data of the dyes through the membrane. Both D_N and D_C decrease with increasing SAG. The ratio D_N/D_C ranged in 2.2–10, the ratio increases with the SAG.     

Optothermal properties of fibers. IV. Optical properties of nylon 66 fibers as a function of quenching process

In this work, optical properties of samples of nylon 66 fibers were quenched in coarse-grained ice after annealing in the temperature range 80–180°C for 1–10 h. Two independent techniques were used to study optical parameters in these fibers. The first technique is the application of the diffraction technique to study the effect of quenching on the swelling factors of these fibers for some different liquids at room temperature of 25 ± 1°C. The second method dealt with the application of multiple-beam Fizeau fringes in transmission to estimate the refractive indices and birefringence of the skin and core of these fibers. The obtained results were utilized to calculate the polarizability per unit volume, isotropic refractive indices, and the Cauchy's dispersion constants. The relationship between n, n, n, Δn_s, Δn_c, Δn_a, n_(iso)s, n_(iso)c, and n_(iso)a different annealing times and temperatures is given for these fibers. Microinterferograms and curves are also given. © 1996 John Wiley & Sons, Inc.