Dynamic response of transiently trapped entanglements in polymer networks

The structure and viscoelastic response of polymer networks are highly sensitive to the presence of pendant chains. These imperfections, that are unavoidable produced during a cross-linking reaction, reduce the cross-linking density and affect the damping response of elastomers. In this work the dynamics of pendant chains present in a cross-linked network is investigated using end-linked poly(dimethyl-siloxane) networks with well defined structure. For this purpose, model networks containing 10 and 20 wt% of two different monodisperse pendant chains with molecular weights well above the critical entanglement molecular weight and some of their blends were prepared. It was found that, within this range of concentration of pendant chains, the long-time dynamic response of the networks was nearly insensitive to the content of pendant material but deeply influenced by the average molar mass of these defects. While the equilibrium behavior of the networks can be well described by a mean field theory for rubber elasticity, the long time relaxational dynamics can be rationalized in terms of the Pearson-Helfand picture for the arm retraction process. Within this theoretical picture, the dynamics can be explained in terms of the molecular architecture of the network, the Rouse time and the weight average molar mass of the pendant material.     

Applications of a two-network model for crosslinks and trapped entanglements

The dependence of stress and birefringence on strain in uniaxial extension of crosslinked rubbers can accurately be described by a model in which the properties of a network of crosslinks and a network of trapped entanglements are additive. The crosslink network is neo-Hookean and the entanglement network can conveniently be described by the Mooney-Rivlin equation. When the crosslinks are introduced in a state of strain near the glass transition temperature, the two networks have different reference undeformed states; they can be distinguished by appropriate measurements in the state of ease where their associated stresses are equal and opposite and in the state of deformation where the cross-links were introduced and make no contribution to the stress. When partial relaxation is permitted before crosslinking, trapping probabilities can be calculated for both relaxed and unrelaxed entanglements and compared with the Langley theory. The results are consistent with the terminal mechanism of relaxation in the tube theory of Doi and Edwards.     

The role of entanglements in network formation in unsaturated low density polyethylene

In this study the network formation in a new poly(ethylene-co-1,9-decadiene) polymer was compared with that formed in an ‘ordinary’ low density polyethylene after being crosslinked with a peroxide. The crosslink density was determined by swelling measurements and by strain measurements at different stresses. Above the melting point, physical crosslinking points, in the form of ‘trapped entanglements’, constitute around 60% of the total number of crosslinking points. The chemical crosslinks, which originate from peroxide and from reacted vinyl groups, are in minority. However, although the chemical crosslinks are fewer, they are indeed very important for making the large fraction of physical crosslinks permanent, i.e. that they do not slip under load.     

Elastic moduli of highly stretched tie molecules in solid polyethylene

The elastic properties of interlamellar bridges in semicrystalline polyethylene (PE) were estimated from the molecular-mechanics calculations on the assumption that the energy loading of a chain backbone represents the principal deformation mechanism. The calculations result in the force-length functions featuring abrupt discontinuities due to sequential annihilation of the defects by the conformational transitions. The correlation of the chain elastic moduli E with the concentration of defects in the chain and with the chain extension ratio x were established. The distribution functions ζ(E) of Young's moduli of interlamellar bridges in semicrystalline PE were calculated by using the literature data on the chain length distributions of tie molecules. The impact of the distribution function of moduli ζ(E) on the overall elastic response of solid PE materials was examined, particularly in cases of the stacked lamellae morphology involving so-called hard elastic PE.     

Experimental evidence for trapped chain entanglements: their influence on macroscopic behaviour of networks

The swelling and elastic properties of poly(dimethyl siloxane) networks prepared by end-linking and subsequently swollen in heptane and toluene have been investigated as a function of the volume fraction, v_c, at which networks are generated. Increases in both swelling degree and shear modulus with v_c demonstrate the increase in number of trapped entanglements with v_c. The results may be described by a simple scaling law approach.     

Importance of tie molecules in preventing polyethylene fracture under long-term loading conditions

Brittle-type slow crack fracture is the dominant mode of failure in polyethylene pipe used for natural gas distribution. Constant tensile load testing of polyethylene pipe sections indicates a link between this mode of failure and environmental stress cracking. Interlamellar fracture can occur in both the presence and absence of an accelerating environment. The fibre deformation process is reviewed, describing the role of amorphous entangled tie molecules in preventing slow crack-type fracture. Relative resistance to slow crack brittle failure is explained in terms of this model for various materials tested.     

Free radicals trapped in polyethylene matrix: 1. Location of the alkyl radicals in irradiated polyethylene

Two types of alkyl radicals were found to be trapped in irradiated crystals grown from polyethylene solution. One of them corresponds to the broad sextet pattern of the e.s.r. spectrum and the other corresponds to the sharp sextet pattern. The free radicals attributed to the broad sextet began to disappear at a lower temperature than the temperature at which the free radicals attributed to the sharp sextet disappeared. When butadiene molecules were brought into contact with the specimen, the decay of the free radicals corresponding to the broad sextet was accelerated. When the specimen was subjected to fuming nitric acid treatment, no broad sextet was observed. The mat of the crystals, was aligned so that the c-axes of its crystallites were perpendicular to its surface. The broad sextet showed no anisotropy when the angle between the direction of applied magnetic field and that of the c-axis of the crystallite was varied. On the other hand, the sharp component of the spectrum showed apparent anisotropy. Consequently, it can be concluded that the broad component comes from the free radicals trapped in the lamellar surface and the sharp component is attributed to the free radicals trapped in the inner part of the crystallite. Hence, the locations of these two types of free radicals have been clarified with much more certainty than before.     

Packing of polyethylene oxide chains in a mixed micelle

The effects of an anionic surfactant, sodium dodecyl sulfate (SDS), on the micellar properties of a nonionic surfactant such as homogeneous heptaethylene glycol n-dodecyl ether (7ED) have been studied by the charge transfer solubilization of 7,7,8,8-tetracyanoquinodimethane, pNa, and electric conductivity measurements. Attention has been paid to changes in packing of polyethylene oxide chains in the mixed micelle and to binding of the counterions onto the micelle surface. All measurements were made on solutions ranging in 7ED concentration from 1 × 10⁻⁶ to 1×10⁻¹ M, while the SDS concentration was maintained constant. It has been shown that the binding of Na⁺ ions to the mixed micelle occurs in the 7ED concentration region where the packing of polyethylene oxide chains in the micelle is loose, while release of Na⁺ ions is observed when the packing is compact. The results of electric conductivity correspond well with those mentioned above. However, in the region of high 7ED concentration, the decreasing mobility of the mixed micelles affects the electric conductivity more than the increasing degree of ionic dissociation of the micelle.     

Modelling of tank electrolysers via Markov chains

The establishment of CSTER-perfect mixer networks via the theory of Markov chains for non-ideal tank electrolysers is described. Such networks, matched to tank electrolysers via experimental exit-age distribution data, can serve (as equivalent models) for the analysis of electrolyser behaviour.Nomenclature A electrode are - c electrolyte concentration;c _i same for inlet conditions;c ₁ same for exit conditions - E exit age - k _M mean mass transport coefficient - P transition probability matrix with elementsp _ij - Q volumetric flow rate of the electrolyte - t time - V effective electrolyser volume - X(t) time-dependent random process - recycle ratio - lumped parameter, equal tok _m A/Q - symbol denoting the state of a Markov chain - dimensionless time, equal toQt/V     

Free radicals trapped in polyethylene matrix: 2. Decay in single crystals and diffusion

The kinetics of the decay of main chain free radicals trapped in polymer matrix in vacuum was investigated. The decay behaviour of alkyl radicals trapped in the lamellar surface of the crystallites of solution grown polyethylene should be different from that of the same radicals trapped in the inner part of the crystallite, and this difference was clearly observed. The analysis of the data of the decay reaction was made, based on three-dimensional diffusion-controlled reaction theory, and reasonable interpretation of the data was made. Alkyl radicals were also observed in an irradiated urea—polyethylene complex and the decay rate of these radicals were very slow in spite of the large mobility. According to these occurrences, it was concluded that the mechanism of three-dimensional diffusion of the free radicals across the chain may occur in the inner part of the crystallites via hydrogen abstraction reactions.     

Deformation zones and entanglements in glassy polymers

Deformation zones are regions of drawn but unfibrillated material which grow from crack tips in thin films of glassy polymers which have a low value of I_e′, the chain contour length between entanglements. The growth of these zones is observed optically and their final structure characterized by transmission electron microscopy. By microdensitometry of the electron image plate the average value of the extension ratio within the deformation zone, λ_DZ, is measured. Such deformation zones have been grown in thin films of four homopolymers and a series of polymer blends. It is found that λ_DZ is approximately 0.6 λ_max, where λ_max is a predicted maximum extension ratio derived from a simple model in which the entanglement points are assumed to act as permanent crosslinks with no chain slippage or scission occurring. This value of λ_DZ is lower than the extension ratios previously measured for crazes grown in the same polymers; typical λ_craze values lie much closer to λ_max. This result can be rationalized by realizing that at least a limited degree of chain scission/slippage must occur during crazing to permit the generation of the void-fibril network. For those polymers where both crazing and deformation zones may form, the latter grow rapidly whereas the formation of crazes requires longer times. This observation also indicates the importance of the kinetic process of chain scission/chain slippage for crazing. Annealing of the polymer films below the glass transition temperature leads to an increased tendency for crazing relative to the growth of deformation zones.     

Trajectory of polyethylene chains in single crystals by low angle neutron scattering

Measurements of coherent neutron diffraction of oriented single crystals of blends of hydrogenous and deuterated polyethylene have been undertaken in order to study the mutual arrangements of the crystalline ‘stems’ of the same molecule. In the appropriate range of diffraction angle, the scatter is fully consistent with thin lamellae, the planes of which contain the stems. The thickness of these lamellae agrees with that expected for neighbouring stems of one molecule being restricted to the same (110) plane. The density of deuterium atoms in the lamellae is consistent with largely adjacent re-entrant folding; for crystals grown at low supercooling there is a possibility of some segregation according to isotope. Outside the above range of diffraction angle, effects are observed which are attributable to the finite lateral dimensions of the proposed lamellae. At the smallest angles of measurement an artifactual signal attributable to voids can be observed, which can be avoided by suitable sample treatment.     

Conformations and mobility of polyethylene and trans-polyacethylene chains confined in α-cyclodextrins channels

Conformational properties and mobility of two polymeric chains containing 30 repeating units of either polyethylene (PE) or trans-polyacethylene (PA) confined into the channel formed by eight α-cyclodextrins (αCDs) are studied by Molecular Dynamics simulations performed at 500 K and compared with the behavior exhibited by the same chains when they stand alone in vacuum. The rotaxane structure (i.e. polymeric chains threaded into the αCDs channel) is stabilized with respect to the separated chain and αCDs mostly because of van der Waals interactions. As it might be expected, large differences are observed in the molecular characteristics of the isolated chains as compared to their confined counterparts. The differences are in the sense of decreasing the conformational mobility in favor of extended conformations in the case of confined chains. Comparison of the results obtained for confined PE and PA chains indicates a noticeably larger mobility of the PA chain. Molecular dimensions obtained for the isolated PE chain agree with the results published in the literature.     

Hindered oscillation and e.s.r. spectra of alkyl free radicals trapped in irradiated polyethylene crystals

Structures of alkyl radicals trapped in solution grown crystals of polyethylene and urea-polyethylene complex were studied in detail. A twisted configuration of methylene group with angle of 4.6° from the regular trans-trans configuration was found for the rigid state configuration of the alkyl radical at 77K. Temperature dependences of hyperfine splitting widths due to the β-protons were observed, and analysed in terms of the hindered oscillation of the β-methylene group. The value of the potential barrier height of hindered oscillation was found to be 900 kcal/mol for polyethylene crystal and 600 kcal/mol for urea-polyethylene complex; indicating that the radical site in urea-polyethylene complex is more mobile than that in polyethylene crystal.     

Mobility and e.s.r. spectra of alkyl free radicals trapped in irradiated mats of solution-grown polyethylene

E.s.r. studies of alkyl free radicals,a trapped in irradiated mats of solution-grown polyethylene crystals have been studied. The crystal mat was aligned so that the crystallites c-axes were perpendicular to its surface. When the angle between the direction of applied magnetic field and the c-axis of the crystallite was varied, the observed e.s.r. spectra showed apparent anisotropy due to α-proton hyperfine splitting. The principal values and directions of the $\text{A}\text{?}$ tensor due to the α-proton at 77 and 254K were determined using the line shapes of uniaxially-oriented samples. The principal axis directions, A₁ were assigned along the polymer chain axis and A₂ and A₃ were perpendicular to the chain axis. The maximum principal value A₁ did not change with temperature, but the lower principal values, A₂ and A₃ averaged out at high temperatures. Hence, it was concluded that the temperature dependence of the $\text{A}\text{?}$ tensor reflects hindered oscillation around the main chain axis at high temperature. A twisted configuration for the methylene group with 4.5° deviation from the trans-trans configuration was also evident for the rigid state configuration of the alkyl radicals at 77K. Temperature dependences of the hyperfine splitting widths due to β-protons were observed and analysed in terms of hindered oscillations of the β-methylene group.     

X-ray diffraction studies in resins: Effect of entanglements and chain structure

X-ray diffraction halo of alkyd, amino, and epoxy resins were recorded. The effective d obtained from them was used to estimate certain physical parameters like cross-sectional area, number of carbon atoms per chain, and stiffness parameters from the empirical curves of Boyer and Miller. Amino resin was found to behave differently than the rest of the resins which have a benzene ring in their backbone. These ideas find a confirmation from the ultrasonic and dielectric measurements performed on these very samples.     

Continuous distillation of ternary mixtures with C- and S-shaped lines of conjugate tie lines and inverted tie lines

The results of modeling a continuous distillation of ternary mixtures with C- and S-shaped lines of conjugate tie lines and inverted tie lines are analyzed. Characteristic regions for these mixtures are defined in the concentration space. The results of the process are demonstrated to be dependent on the characteristic region to which the feed point belongs.     

Craze microstructure and molecular entanglements in polystyrene-poly(phenylene oxide) blends

Polystyrene and poly(phenylene oxide) are miscible over the entire range of compositions. Thin films of five blends of high molecular weight polystyrene (PS) with high molecular weight poly(phenylene oxide) (PPO), and four blends of low molecular weight PS (whose molecular weight lies below its entanglement molecular weight M_e) with the same PPO have been prepared. Following bonding of these films to copper grids, crazes were grown by uniaxial straining in air. Suitable crazes were then observed by transmission electron microscopy. From microdensitometry of the image plates it is possible to measure the extension ratio λ_craze within crazes in the nine blends. These measured values are compared with predicted values of λ_max, computed from λ_max = I_ed, where I_e is the chain contour length between entanglements and d is the root mean square end-to-end distance for a chain of molecular weight M_e. For the high molecular weight PS blends λ_max depends on the entanglement properties of both PS and PPO chains. For the low molecular weight PS blends, the PS chains cannot form part of the entanglement network and the correct value of λ_max is obtained from appropriate scaling of the pure PPO value. Comparison of λ_craze and λ_max for both types of blends shows excellent agreement, demonstrating the importance of the entanglement network in determining craze parameters and hence the toughness of a given polymer.     

Modelling permeation of modified atmosphere gas mixtures through a low density polyethylene package film

Permeation of individual gases through a low density polyethylene package film with CO₂-N₂ and CO₂-O₂-N₂ mixtures was simulated with a simple mathematical model. Permeabilities of carbon dioxide were of the order of 10 ^?12 m³/s m²atm/m with CO₂-N₂ systems. Including oxygen in the system did not change carbon dioxide permeabilities. Permeabilities of oxygen were of the order of magnitude of 10^?9m³/sm²atm/m with this system. When a CO₂-O₂-N₂ mixture was humidified no substantial change was observed in CO₂ permeability, but the O₂ permeability decreased almost 10 times. These results and the mathematical model presented may help in the modified atmosphere package design to increase the shelf life of produce.