Network architecture and modulus of miscible heteropolymer blends

The architecture and entanglement density of a multicomponent polymer network composed of miscible, flexible chains is related to the corresponding properties and concentrations of the pure components. It is assumed that the coupling frequency between different chain species is proportional to their fractional participation in the blend and that the entanglement ability of polymers can be affected by the presence of heteropolymer neighbors. The theory, equally applicable to temporary and permanent networks, estimates the molecular weight between entanglements and their total number along a chain in the blend. This information is used in establishing a mixing law for the rubbery plateau modulus of a fluid polymer blend and in deriving a relationship for the equilibrium modulus of an interpenetrating polymer network containing trapped entanglements and dangling segments. The theoretical predictions are compared with experimental results from the literature on several miscible polymer blends.     

Polyethylene networks crosslinked in solution: Preparation,elastic behavior,and oriented crystallization. I. Crosslinking in solution

A study has been made of the crosslinking of linear polyethylene in solution. Networks containing a low number of trapped entanglements and elastically ineffective chain ends were prepared by crosslinking high molecular weight linear polyethylene in 1,2,4-trichlorobenzene solutions with dicumyl peroxide at 120°C. No syneresis was observed during crosslinking except at high peroxide concentrations. The networks were characterized by swelling measurements, infrared spectroscopy, and differential scanning calorimetry. The crosslinking efficiency, calculated from swelling, was found to be proportional to the square of the polymer volume fraction. The proportionality constant was 0.8, indicating close to unit efficiency for undiluted polymer. Chemical modification of the polyethylene chains by attachment of peroxide and solvent fragments was of the order of one foreign unit per elastically active network chain, depending on peroxide and polymer concentration. Sol–gel analysis indicated that no chain scission occurred. These results are shown to be consistent with a “cage” mechanism for crosslinking. The possible topological consequence of this mechanism, preferential crosslinking of entanglements, is discussed. The concentration of trapped entanglements was also found to be proportional to the square of the polymer volume fraction. The proportionality constant corresponds to a molecular weight between entanglements of 4000 for the undiluted polymer, which is close to the value of 4200 found for networks prepared from the undiluted polymer. Since the results obtained are based mainly on the use of the swelling equation, different aspects of the applicability of this equation for the evaluation of the crosslinking process are discussed. As regards the reference dimensions, which should be known for a quantitative application of the elastic theory, the results strongly support the use of the dimensions of the network chains after completion of crosslinking.     

Model polyurethane elastomers prepared from noncrystallizable poly(propylene oxide) chains

Elastomers of controlled molecular structure were prepared from hydroxyl-terminated atactic poly(propylene oxide) (PPO) chains having number-average molecular weights M_n in the range 800–4360 g mole^?1. The chains were end-linked into noncrystallizable trifunctional networks using a specially prepared aromatic triisocyanate. The networks thus obtained were studied with regard to their stress–strain isotherms in the unswollen state, in elongation at 25°C, and with regard to their equilibrium swelling in benzene at 61°C. Values of the modulus in the limit at high deformation were in good agreement with corresponding results previously obtained on networks of poly(dimethylsiloxane) (PDMS). This is of considerable importance since use of the widely used “plateau modulus” as a measure of interchain entangling would suggest that the networks of PPO would have a much higher density of such entanglements than would the corresponding networks of PDMS. The close similarity between the moduli of the two types of networks therefore argues against the idea that such entanglements make large contributions to the equilibrium elastomeric properties of a polymer network. These values of the high deformation modulus are also in good agreement with recent molecular theories as applied to the nonaffine deformation of a “phantom” network. The values of the low deformation modulus were considerably smaller than the values predicted for an affine deformation, however, suggesting that the junction points were not firmly embedded in the network structure. This is presumably due to the relatively low degree of chain-junction entangling in the case of relatively short network chains. The swelling equilibrium results were in very good agreement with the new theory of network swelling developed by Flory.     

Model polyurethane networks prepared from poly(ethylene oxide) and poly(tetramethylene oxide)

Polyurethane elastomers of known degrees of cross-linking were prepared from hydroxylterminated poly(ethylene oxide) (PEO) and poly(tetramethylene oxide) (PTMO) chains having numberaverage molecular weights in the range 880–6820 g mol^?1. The chains were end-linked into “model” trifunctional networks using a specially prepared aromatic triisocyanate. The networks thus obtained were studied with regard to their stress-strain isotherms in both the unswollen and swollen states, in elongation at 25°, and with regard to their equilibrium swelling in benzene at 57.9°. Values of the modulus in the limit at high deformation were in good agreement with corresponding results previously obtained on trifunctional networks of poly(dimethylsiloxane) (PDMS). Since PEO has a much higher value of the plateau modulus in the uncross-linked state, this agreement indicates that inter-chain entanglements do not contribute significantly to the equilibrium modulus of an elastomeric network. These values of the high deformation modulus are also in good agreement with recent molecular theories as applied to the non-affine deformation of a “phantom” network. The swelling equilibrium results were in very good agreement with the new theory of network swelling developed by Flory.     

Moduli of model elastomeric networks prepared from polymer chains having a high plateau modulus,and their interpretation in terms of the constrained-chain model

High-molecular weight polybutadiene chains having approximately 47% cis-1,4 units and 45% trans-1,4 units were crosslinked through their carbon-carbon double bonds using p-bis(dimethylsilyl) benzene as crosslinking agent and chloroplatinic acid as catalyst. This particular polymer was chosen because the high plateau modulus it exhibits in the un-crosslinked state is taken to indicate large numbers of chain entanglements, and stress–strain measurements on such networks have frequently been interpreted with the assumption that the trapping of such entanglements during crosslinking should contribute significantly to their modull. It is shown in the present investigation that such results are equally well interpreted in terms of the new constrained-chain theory of rubbery elasticity. © 1993 John Wiley & Sons, Inc.     

Microscopic theory of rubber elasticity

A microscopic integral equation theory of elasticity in polymer liquids and networks is developed which addresses the nonclassical problem of the consequences of interchain repulsive interactions and packing correlations on mechanical response. The theory predicts strain induced softening, and a nonclassical intermolecular contribution to the linear modulus. The latter is of the same magnitude as the classical single chain entropy contribution at low polymer concentrations, but becomes much more important in the melt state, and dominant as the isotropic-nematic liquid crystal phase transition is approached. Comparison of the calculated stress-strain curve and induced nematic order parameter with computer simulations show good agreement. A nearly quadratic dependence of the linear elastic modulus on segmental concentration is found, as well as a novel fractional power law dependence on degree of polymerization. Quantitative comparison of the theory with experiments on polydimethylsiloxane networks are presented and good agreement is found. However, a nonzero modulus in the long chain limit is not predicted since quenched chemical crosslinks and trapped entanglements are not explicitly taken into account. The theory is generalizable to treat the structure, thermodynamics and mechanical response of nematic elastomers.     

Effect of chain stiffness and entanglements on the elastic behavior of end-linked elastomers

The effect of chain stiffness and entanglements on the elastic behavior and microscopic structure of cross-linked polymer networks was studied using Monte Carlo simulations. We investigated the behavior of entangled and entanglement-free networks at various degrees of chain stiffness and densities. Based on previous results that indicated that trapped entanglements prevent strain-induced order-disorder transitions in semiflexible chain networks, we prepared the entangled networks by end-linking the chains in very dilute conditions so as to minimize the extent of trapped entanglements. We also considered the entanglement-free case by using a "diamond" structure. We found that the presence of even a very small amount of trapped entanglements is enough to prevent a discontinuous strain-induced transition to an ordered phase. In these mildly entangled networks, a nematiclike order is eventually attained at high extensions but the elastic response remains continuous and the cross-links remain uniformly distributed through the simulation box. The entanglement-free diamond networks on the other hand show discontinuities in their stress-strain data. Networks at higher densities exhibit a more stable ordered phase and show an unusual staircaselike stress-strain curve. This is the result of a stepwise extension mechanism in which the chains form ordered domains that exclude the cross-links. Extension is achieved by increasing the number of these ordered domains in the strain direction. Cross-links aggregate in the spaces between these ordered domains and form periodic bands. Each vertical upturn in the stress-strain data corresponds to the existence of an integer number of ordered domains. This stepwise elastic behavior is found to be similar to that exhibited by some tough natural materials.     

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.     

聚丙烯酸酯/环氧树脂互穿网络聚合物的研究Ⅲ.橡胶态弹性模量和互穿缠结

采用一步法（Ｓｉｍｕｌｔａｎｅｏｕｓｌｙ）合成了双组分的聚丙烯酸酯／环氧树脂互穿网络聚合物（ＩＰＮｓ）．选择预溶胀方法制备了聚丙烯酸酯和环氧树脂两种组分网络．测定了各种组分比的ＩＰＮ和不同溶胀度下的组分网络的动态力学性能，从橡胶态弹性理论出发讨论了ＩＰＮ和预溶胀网络之间在橡胶态弹性模量上的关系，并据此指出互穿缠结增加了网络的有效“交联密度”，因此，它对ＩＰＮ的橡胶态弹性模量有较大的贡献．密度测量的结果也提供了另一方面的证据     

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.     

Entanglement effects in model polymer networks

Many fundamental questions for the understanding of polymer networks are more suitably addressed by current computer simulations than by experiments. Details of the microscopic topology, such as the elastically active cluster or loop entanglements, can be identified as well as controlled. In particular, it is possible to isolate and quantify their effects on macroscopic observables such as the elastic modulus. The constraints due to connectivity and conserved topology are more clearly present for networks than for melts. Already for strand lengths between crosslinks which are relatively short, the effect of the conserved topology is important. The mode relaxation in a network is significantly different from that of a melt. For weakly crosslinked systems the melt entanglement length is the relevant scaling parameter. The elastic modulus of a long chain network under ideal conditions reaches an asymptotic value which is about 2.2 times smaller than the prediction of an affine model for a network made of strands of the melt entanglement length. An analysis of the stress reveals that in the linear regime the contribution from the excluded volume is dominant compared to that from the connectivity along the strands. For larger elongations, however, the non-linear elastic response is dominated by the chemically and topologically shortest paths through the system, where chemical crosslinks and topological entanglements between meshes of the network play a similarly important role.     

New evidence for molecular entanglements

Torsional creep and creep recovery measurements have been made on a 56% polymer weight solution of an extremely high molecular weight polystyrene (M = 4.4 × 10⁷) in tri-m-tolyl phosphate and on the polymer itself after recovery both from relatively dilute and more concentrated solution in benzene by freeze drying. Although viscoelastic steady state was not achievable, an anomalously shorter rubbery plateau in the response of the bulk polymer relative to its solution was indicated. On the basis of the assumed presence of physical entanglements of the threadlike molecules, which determine the length and height of the rubbery plateau, it was predicted and confirmed that the undiluted polystyrene recovered from dilute solution would have the highest and shortest creep compliance plateau.     

Relation of elastic modulus to crosslink and entanglement concentrations in rubber networks

The theory of rubber elasticity relates the elastic modulus of unfilled amorphous rubber to the concentration of elastically effective strands. A theoretical relation between this concentration and the concentrations of potential entanglements, random tetrafunctional crosslinks, and chain ends was proposed recently. In the present work, the new relation was combined with the theory of rubber elasticity and verified experimentally. Polydimethylsiloxane samples were cured by ⁶⁰Co irradiation and were extensively extracted to determine gel fraction, which was used to calculate concentrations of crosslinking and scission due to irradiation. Equilibrium modulus values determined from creep tests were in excellent agreement with those calculated using the new relation if the average spacing between potential entanglements is 116 (CH₃)₂SiO units. Thus, in typical commercial silicone rubbers, the contribution to the modulus from trapped entanglements is greater than the direct contribution from crosslinks. The new relation allows the calculation of crosslink concentrations from modulus measurements on other unfilled rubbers once the potential entanglement spacing of the polymer is determined.     

Linear viscoelastic studies on a transient network formed by host–guest interaction

A host–guest (HG) polymer was prepared through the radical polymerization of acrylamide monomers (AAm) with a small amount of host‐guest linkers, β‐cyclodextrin‐attached AAm (βCD‐AAm) and adamantane‐attached AAm (Ad‐AAm). The linear viscoelastic and swelling measurements indicated that the resulting HG polymer swollen in water was gel‐like, although the HG polymer is conceptually a linear chain having only temporary crosslinkings. NMR measurements indicated that half of the βCD units incorporated in the HG polymer do not form the inclusion complex with Ad. Rheological analysis of the HG polymer revealed that HG interaction retarded the Rouse modes of networks but did not affect the level of the plateau modulus, which was simply described by the entanglements of AAm chains. This result was confirmed with the reference experiment, in which Ad were capped by competitive βCD molecules. Furthermore, the PAAm polymer with only βCD units (no Ad) was found to exhibit gel‐like behavior. This behavior was attributed to the formation of a small amount of rotaxane structure, which act as permanent crosslinkings, based on 2D NMR data. The HG polymer is basically an entanglement network with temporary sticky points due to the HG interaction, and a few permanent branching points. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1109–1117     

Formation,structure and properties of polymer networks: theory and modelling

The application of a Monte-Carlo (MC) algorithm to account fully for loop formation in RA₂ + R′B₃ and RA₂ + R′B₄ polymerisations is described. The resulting interpretation of experimental elastic moduli of polyurethane networks prepared at different dilutions shows it is essential to account for elastic losses in loop structures of all sizes. An important parameter, x, is introduced, namely the average fractional loss of elasticity per larger loop structure relative to the loss per smallest loop structure. Values of x vary between 0.50 and 0.60, depending on junction point functionality, reactant or network chain stiffness and number of skeletal bonds per smallest loop structure. Application of the MC calculations to the formation and resulting structure of poly(dimethyl siloxane) networks again predicts significant reductions in modulus due to loop structures. However, comparison with experimental modulus data shows that the reductions in modulus due to loops are outweighed by increases due to chain entanglements.     

聚醋酸乙烯酯/聚丙烯酸甲酯互穿网络聚合物的研究——4.橡胶态模量和网络间的互穿缠结

用动态粘弹谱仪测定了分步法互穿网络聚合物,聚醋酸乙烯酯/聚丙烯酸甲酯(PVAc/PMA-IPN)的橡胶态模量。实验值与从方程E_R=φ_Ⅰ~1/3·E_(R,Ⅰ)~0+φ_(Ⅱ)E_(R,Ⅱ)~0所得理论值的比较,表明网络问有明显的互穿缠结,网络Ⅰ交联程度对其的影响大于网络Ⅱ。并结合实验结果对Binder-Frisch理论中,ΔS_(ent)∝N_(c,Ⅰ)~(-1)·N_(c,Ⅱ)~(-1/2)关系的合理性进行了讨论。     

Modification of cellulose nanocrystal-reinforced composite hydrogels: effects of co-crosslinked and drying treatment

The synthesis platform of composite hydrogels containing rigid reinforcing filler cellulose nanocrystals (CNCs) and polymer matrix polyacrylamide (PAM) has been proposed (Yang et al. in Cellulose 20:227–237, 2013). The features of CNCs as multifunctional crosslinkers and flexible polymer chain entanglements contributed to the unique arrangement of CNC/PAM clusters with reversible network structures. In this article, the chemical crosslinking agent N,N′-methylene-bisacrylamide (BIS) was added to obtain the dual crosslinked networks, and the mechanical properties of the resulting co-crosslinked hydrogels were examined by tailoring the CNC and BIS concentrations. The results indicated that the homogeneous dispersion of CNCs throughout the polymer matrix was disturbed in the presence of BIS, and the covalent crosslinkers led to weakness and brittleness of the hydrogels. Some new entanglements within the networks were formed after a simple drying treatment, which was verified by the greater tensile strength compared with the as-prepared ones. The mechanism for the formation of these new entanglements was ascribed to the irreversible rearrangement of the CNC/PAM network structure, whereas for co-crosslinked hydrogels no strength increment was observed after the drying treatment.     

The effects of polydispersity,entanglements, and crosslinks on pulsed-gradient NMR diffusion experiments in polymer melts

We have used the pulsed-gradient spin-echo NMR method to measure diffusion in a highly polydisperse polymer, a hydroxyl-terminated polybutadiene. We have modelled the expected spin-echo attenuation assuming that the low-molecular-weight fractions are unentangled and constitute a Rouse-like diluent to the entangled larger molecules. Fitting this simulation to our data is consistent with the model and permits the extraction of the range of diffusivities and a semiquantitative value for the molecular weight above which entanglements inhibit diffusion. The model is extended to include a monodisperse diluent present additionally, e.g., a curing agent. This extension is tentatively applied to polybutadiene resins undergoing curing and shows that the diffusivity of the remaining unreacted curing agent is little affected by network formation, whereas the retardation of the unreacted polymer molecules is clearly evident.     

Radiation crosslinking of elastomers. I. Polybutadienes

The chemical and physical crosslink densities of irradiated polybutadiene were determined using a precise and consistent method. This method included the use of a statistical theory of crosslinking modified to include chain reactions and the use of Langley's theory for calculating the number of trapped chain entanglements. The number of crosslinks formed per unit radiation dose, G(X), was measured for a series of polybutadienes containing various isomeric forms of unsaturation. The physical crosslink density and the molecular weight between entanglements were determined from measurements of the compression modulus of swollen samples.