Elastic behavior,birefringence, and swelling of amorphous polyethylene networks

Polyethylene networks were prepared by γ-irradiation of linear polyethylene, both molten and crystalline. The elastic and photoelastic properties of the networks were studied at high temperatures, i.e., in the molten state. The equilibrium swelling was also measured in several solvents. Values of the crosslinking efficiency G of γ-radiation, the molecular, weight M_e between entanglements, the optical anisotropy α of the equivalent random link, and the polymer-solvent interaction parameter μ are deduced. Samples prepared by irradiation in the amorphous state showed markedly non-Gaussian elastic behavior. The presence of a large non-Gaussian term in the optical anisotropy is also deduced. The value of α obtained for swollen samples, which showed substantially Gaussian elastic behavior, was 3.9 × 10^?24 cm.³, about one-half of that obtained for dry samples. It corresponds to an equivalent random link of only about 5 CH₂ units, on the basis of Denbigh's values for bond polarizabilities. The samples prepared by irradiation in the crystalline state showed lower values for α, which also depended upon the degree of crosslinking. This is attributed to the nonrandom chain configurations prevailing at the time of crosslinking. The same samples were found to show more nearly Gaussian elastic behavior, which is attributed to the same cause.     

Formation and elasticity of layer networks

Layer network formation of poly(styrene‐alt‐n‐octadecylmaleimide) in dodecane is investigated. It is shown that the polymer in the bulk exhibits lamellar structures of alternated alkane side‐chain and main‐chain layers. Adding dodecane into the polymer separates the polymer layers, increases the mean distance between the layers, and results in a less orderly layered structure. Crystallization of the alkane side chains introduces linkages to staple the layers together and builds up a layer network. Dimensional analysis predicts that the modulus (G) of the layer network is simply related to the long period (L) of the layer network through a cubic power law, i.e., G ∼ L⁻³. This prediction is indeed observed experimentally. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 667–677, 1999     

Synthesis,structure, and swelling behavior of two-component copolymer networks

A two-component copolymer network comprising polystyrene (PS) and poly(dimethylsiloxane) (PDMS) as copolymer components was prepared by cross-linking PS with telechelic PDMS with a new method. The microphase structure of the dry PS/PDMS network was found to be irregular from DSC and small angle X-ray scattering measurements. The swelling behavior was observed in three kinds of mixed solvents which were chosen so as to contrast with one another in respect of solubility of the component polymers. The observed swelling degree depended on the solvent composition in a manner peculiar to the respective mixed solvent systems. The Flory swelling equation extended to the two-component polymer network qualitatively reproduced the experimental swelling behavior.     

Polyelectrolyte gel transitions: experimental aspects of charge inhomogeneity in the swelling and segmental attractions in the shrinking

This paper aims to provide a systematic discussion based on our experimental results both previously published and unpublished, to promote better understanding of volume-phase transitions in polyelectrolyte gels. Special attention was paid to the distribution of network charges as well as to the attractive interaction among polymer segments. From looking at how these effects appear in the swelling curves, an exploration of the nature of polyelectrolyte gel transitions was attempted. Two sorts of polyelectrolyte gels, temperature-responsive ionic gels based on N-isopropylacrylamide (NIPA) and cationic poly(ethyleneimine) (PEI) gels, were mainly employed with various modifications. The charge inhomogeneity within the gel phase was created by surfactant binding, immobilized enzyme reaction and physical entrapment of polyions. The attractive interactions holding the gel in a collapsed state were studied in comparison with phase separations of the corresponding linear polyelectrolyte. The main conclusions are summarized as follows: (i) The charge inhomogeneity exhibits a large influence on the volume transition in ionic gels. (ii) Hydrogen bonding and hydrophobic association, other than electrostatic attraction, can be considered to play an important role in the segmental association. (iii) Stably associated segments via one or more of these attractive interactions causes a large hysteresis in the swelling process, in which the repulsive interaction among the fixed charges on the network is dominant as shown in the Katchalsky's model. (iv) A distribution of "neutral but hydrophilic" moieties (e.g., ion pair or salt-linkage formed between the opposite charged groups) within the gel shows a marked effect on the temperature-induced volume collapse, the aspect of which is similar to that observed in the gels with a charge inhomogeneity.     

Water swelling of polyester networks

The water equilibrium concentration in styrene crosslinked polyesters increases with the temperature; this behaviour has been interpreted in terms of material expansion induced by temperature. We have verified this hypothesis by swelling measurements in water and gravimetric experiments at various temperatures between 30°C and 90°C. Samples were propylene glycol/neopentyl glycol - maleate / isophthalate copolymers crosslinked by styrene.     

The elasticity of nematic networks

Nematic rubbers are composed of crosslinked polymer chains with stiff rods either incorporated into their backbones or pendant as side chains. When nematic effects axe strong, such rubbers exhibit discontinuous stress-strain relationships and spontaneous shape changes. We model such a rubber using Gaussian elasticity theory, including the nematic interaction via a mean field. Results are presented for the cases of uniaxial extension and compression. Under uniaxial extension the rubber can undergo a first order phase transition to a uniaxial nematic phase. Under uniaxial compression first or second order transitions are possible to genuinely biaxial nematic states with biaxial strains. When nematic effects are very small (i.e. T >> T_c where T_c is the nematic-isotropic phase transition temperature of the rubber) we postulate that the model is a good approximation to a conventional, non-nematic elastomer, and fit our model to data from an isoprene rubber.     

Entanglements and elasticity in polybutadiene networks

Polybutadiene networks were prepared by peroxide crosslinking of monodisperse 1,4-polybutadienes both in solution and in bulk. The effect of the entangled sol fraction on the elastic modulus of high-molecular-weight polybutadiene was observed in stress relaxation measurements. Sol fraction was shown to make a large contribution to the Mooney–Rivlin 2C₂ term. This effect was also observed on the molecular level in NMR spin-spin relaxation measurements. For networks crosslinked in bulk the stress relaxation measurements suggest the presence of trapped entanglements. The 2C₂ term is insensitive to sol extraction in these networks. NMR spin-lattice relaxation measurements in the rotating frame at 4.68 kHz verify the presence of additional effective crosslinks in these networks.     

Non-gaussian elasticity of composite and interpenetrating networks

The elastic behavior of composite and interpenetrating network structures composed of non-Gaussian chains is investigated. The chain probability density given by Nagai is employed utilizing only the leading correction terms for finite chain extensibility. The independent-network hypothesis, proven valid in Gaussian statistics, is shown to be erroneous in non-Gaussian systems. Further, it is found that composite networks composed of monodisperse chains are elastically isotropic, whereas a most probable contourlength distribution yields a large anisotropy but in the direction opposite to that observed experimentally for rubber. On the other hand, retention of the independent-network hypothesis coupled with a most probable distribution successfully accounts for much of the observed anisotropy. Interpenetrating networks are shown to be substantially anisotropic when a most probable contour-length distribution is employed.     

Effect of initial monomer concentration on the equilibrium swelling and elasticity of hydrogels

The linear swelling ratio α and the effective network chain length N of a series of poly(N,N-dimethylacrylamide) (PDMAAm) hydrogels were investigated as a function of the gel preparation concentration . PDMAAm hydrogels were prepared at a fixed cross-linker ratio but at various initial monomer concentrations. It was found that α is not a monotonic function of . As is increased, α first decreases up to about and remains constant in a narrow range of , but then it increases continuously. The -dependence of α is due to the variation of the network chain length N depending on the gel preparation concentration. In the range of below 0.1, N follows the scaling relationship , while at higher concentrations, N varies only slightly with . The increase of α with N obeys the relation , as predicted by the Flory-Rehner theory.     

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.     

Nonhomogeneous state of stress,strain, and swelling in amorphous polymer networks

The total free energy of an amorphous, crosslinked polymer is given as ΔA = ΔA_mix + ΔA_el, where ΔA_mix indicates the free energy of mixing of the crosslinked polymer and the solvent to which the network is exposed throughout the deformation process; ΔA_el indicates the elastic free energy of the network as a function of strain, including the effect of dilation with the solvent. The explicit forms of the mixing and the elastic free energies are obtained from the molecular theory of rubber elasticity. Recent developments in this field allow accurate representation of the behavior of swollen networks under strain. Expressions for the stress in terms of strain and swelling ratio are obtained from the free energy. Formulation of boundary-value problems are discussed. Bending of a cuboid subject to the action of a swelling agent is analyzed as an example. Material parameters are chosen for a crosslinked amorphous network. The distribution of stresses, strains, and solvent in the bent cuboid are calculated numerically. The magnitude of moments applied at the two ends are calculated for different degrees of flexure. Results are compared with those obtained for the same network in the dry state.     

Thermodynamics of swelling in unfilled and filler-loaded networks

Within the framework of the van der Waals-network model a consistent interpretation of swelling and simple extension in differently crosslinked networks is presented. It is observed that the excess parameters in the Staverman-Koningsveld-Kleintjens version do not depend on the degree of crosslinking. Swelling of filler-loaded rubbers shows universal features because of not depending on the type and the properties of the filler. By introducing the Einstein-Smallwood modification in an adequate manner one understands this phenomenon without any further parameter adjustments. It is the consequence of having quasi-permanent filler-to-matrix contacts that are not modified in presence of solvent molecules. The excess-parameters in the swollen matrix are not affected. The entropy elastic stress due to the swelling induced deformation of the matrix is apparently too small as to enforce chain-slippage. The strength of the adhesion of the polymer inhibits filler-to-solvent contacts. These results defend the mean-field treatment of the boundary problem as presented by Einstein-Smallwood, and allows a valuable proof of the thermodynamics of swelling in networks.Dedicated to Prof. H. H. Kausch on the occasion of his 60th birthday     

Characterization of polyethylene networks based on the jointed description of melting,swelling and deformation

Investigations of melting, equilibrium swelling and the stress-strain behavior of radiation crosslinked polyethylene are reported. The results are jointly described where by a novel phenomenological treatment of the swelling of van der Waals networks was needed implicating a discussion as to how the modulus is related to the concentration of the cross-linkages. This concentration is obtained from the analysis of the melting process by application of the thermodynamics of eutectoid copolymers, which is also shown to deliver structural parameters which are in good accord with X-ray data.     

Templation,Water Content,and Zeta Potential of Polyelectrolyte Nanoassemblies: a Comparison Between Polyelectrolyte Multilayers and Brushes

This feature article deals with the self assembly and physical chemistry of polyelectrolytes: multilayers and brushes. The article highlights the interesting behavior of polyelectrolytes in nanoscale assemblies, giving more insight into the complexity of the formation of the assemblies. The water content of multilayers and brushes is studied during the assembly and in different ionic strengths. Similarities are found in the behavior of the brushes and multilayers with ionic strength, with regard to changes in the thickness and the water content. An invariance of the zeta potential with ionic strength is also observed for both systems, which can be explained as a result of conformational changes of the polymer chains. Finally, the combination of brushes and multilayers for surface modification is presented.     

Neutron scattering and swelling properties of end-linked polydimethylsiloxane networks

Small angle neutron scattering measurements were performed on polydimethylsiloxane-toluene solutions and gels at different degrees of swelling. The scattering signal of the gel was decomposed into a solution-like part and a static part. The thermodynamic information obtained from the solution-like part of the signal is compared with macroscopic swelling pressure observations.     

Computer simulation of polymer networks: swelling by binary Lennard-Jones mixtures

The swelling of regular, tightly meshed model networks is investigated by a molecular-dynamics-Monte Carlo hybrid technique. The chemical equilibrium between two simulation boxes representing the gel phase and a solvent bath, respectively, is obtained by subjecting the Lennard-Jones particles of a binary mixture, serving as explicit solvent, to the particle transfer step of Gibbs ensemble-Monte Carlo. The swelling behavior, especially preferential absorption of a single component, whose dependence on temperature, pressure, and fluid composition is studied, also depends significantly on the size of the central simulation cell. These finite-size effects correlate well with those exhibited by the density of solvent-free (dry) networks. A theoretical expression, whose derivation is based on network elasticity (of dry networks) yields finite-size scaling behavior in good accord with simulation results for both dry networks and gels in contact with solvent baths. This expression can be used to extrapolate the swelling behavior of simulated finite systems to infinite system size.     

Effect of the functionality of junctions on the elasticity of polymacromonomer networks: Computer simulation

The elastic properties of polymer networks formed via the radical polymerization of macromonomers with two polymerizable end groups are studied via computer simulation. It is shown that variation in the average functionality of network junctions, f _avg, in a wide range (∼5–55) leads to a significant change in the shear modulus of the network. According to experiments with real networks (gels of poly(ethylene oxide) macromonomers), the shear modulus increases as f _avg increases. This effect is not due only to a decrease in the fluctuations of positions of network junctions. The main cause of the increase in the modulus is that the modulus component due to interaction between polymer chains (entanglements) increases as the functionality of junctions in the investigated networks increases. The conclusion is made that these networks gain entanglements during the formation of network junctions with high functionality rather than inherit them from the solution of macromonomer chains.     

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.     

Polybutadiene model networks —synthesis,mechanical characterization and comparison with rubber elasticity models

Model networks of defined crosslink density are prepared via nonradical statistical crosslinking of polybutadiene in bulk and concentrated solution using a masked bistriazolinedione as crosslinker. The kinetics of crosslinking is monitored by FT-IR-spectroscopy. The reaction follows pseudo-1st-order reaction kinetics. The activation parameter of the crosslinking reaction is estimated from crosslinking at various temperatures. Networks of deuterated polybutadiene are prepared by this reaction in a wide range of crosslink densities. The stress strain behavior is analyzed according to the Junction Constraint-Theory of rubber elasticity (JCT) and to the approach introduced by Graessley accounting for trapped topological constraints. The analysis clearly demonstrates that trapped entanglements contribute to the mechanically effective cycle rank, i.e., to the modulus in this system in the small and large strain limit.