A simple cubic lattice model of the melt of 3-arm star-branched polymers of various length dissolved in a matrix of long linear chains (n1 = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star-branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star-branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains. 相似文献
We apply the tube model to a specific problem in polymer melt dynamics - the rheology of star polymers as an additive to a monodisperse linear matrix. We find that the tube dilation picture of constraint release may be applied to the relaxation of the star fraction. There are four qualitatively different cases depending on the relative concentrations and relaxation times of the two fractions. Terminal relaxation times and relaxation spectra are calculated for each case and compared with available experimental data. The existence of a modified Rouse relaxation such that G(t)∼t−3/2 is argued. 相似文献
Summary: This paper considers the extension of the parameter‐free tube model of Milner and McLeish for stress relaxation in melts of monodisperse star polymers to star polymers whose arms have a continuous molecular weight distribution such as the Flory distribution in the case of star‐nylons and star‐polyesters. Exact expressions are derived for the relaxation spectrum and the relaxation modulus for star polymers having an arbitrary continuous arm‐length distribution. For a Flory distribution a comparison is made with results of dynamic measurements on a melt of 8‐arm poly(ε‐caprolactone) (PCL) stars. An excellent quantitative agreement over a large frequency range is found, however, only if one treats, in contrast with the original parameter‐free tube model approach, the entanglement molecular weight that determines the relaxation spectrum as a fitting parameter independent of the entanglement molecular weight of the linear PCL. This discrepancy is not in anyway related to the polydispersity in arm‐length, but a consequence of the thermorheological complexity of the PCL stars. A similar discrepancy has been observed for hydrogenated polybutadiene stars, as described by Levine and Milner.
Measured and calculated storage moduli G′ as a function of frequency ω. 相似文献
We show that Shaffer's version of the bond fluctuation model can be used to simulate three‐arm star polymers. We report a simulation study of both single stars and melts of star polymers with arm lengths up to 90 monomer units (approximately twice the entanglement crossover length for linear chains). Center‐of‐mass self‐diffusion of single stars is Rouse‐like (D ˜ N–1). Due to a limited range of molecular weights we cannot distinguish between a power‐law and an exponential dependence of the star‐melt self‐diffusion coefficient on arm length. 相似文献
We report star polymer metal–organic cage (polyMOC) materials whose structures, mechanical properties, functionalities, and dynamics can all be precisely tailored through a simple three‐component assembly strategy. The star polyMOC network is composed of tetra‐arm star polymers functionalized with ligands on the chain ends, small molecule ligands, and palladium ions; polyMOCs are formed via metal–ligand coordination and thermal annealing. The ratio of small molecule ligands to polymer‐bound ligands determines the connectivity of the MOC junctions and the network structure. The use of large M12L24 MOCs enables great flexibility in tuning this ratio, which provides access to a rich spectrum of material properties including tunable moduli and relaxation dynamics. 相似文献
We report star polymer metal–organic cage (polyMOC) materials whose structures, mechanical properties, functionalities, and dynamics can all be precisely tailored through a simple three‐component assembly strategy. The star polyMOC network is composed of tetra‐arm star polymers functionalized with ligands on the chain ends, small molecule ligands, and palladium ions; polyMOCs are formed via metal–ligand coordination and thermal annealing. The ratio of small molecule ligands to polymer‐bound ligands determines the connectivity of the MOC junctions and the network structure. The use of large M12L24 MOCs enables great flexibility in tuning this ratio, which provides access to a rich spectrum of material properties including tunable moduli and relaxation dynamics. 相似文献
The solution rheology of poly(acrylonitrile-co-itaconic acid) (poly(AN-co-IA)) in 1-butyl-3-methylimidazolium chloride ([BMIM]Cl) spanning dilute, semidilute unentangled and entangled regimes were investigated. The exponents in the specific viscosity ηsp ~ overlap parameter c[η] power law were 1, 2 and 4.7 for dilute, semidilute unentangled and entangled regimes, respectively, which were found to be consistent with the scaling prediction for neutral linear polymers in θ-solvent. For dilute solutions (lower than 0.9 wt.%), the linear viscoelastic responses were observed to be in good agreement with the Zimm model (Flory exponent ν = 0.5). While for semidilute unentangled solutions (between 0.9 and 8 wt.%), results obtained had been found to be consistent with Rouse model. Considering Flory exponent ν = 0.5 and the concentration dependences of the specific viscosity and relaxation time, it had been evaluated that poly(AN-co-IA) in [BMIM]Cl behaves as a neutral polymer in θ-solvent. It had also been suggested that according to the unusual deviation of Cox-Merz rule, poly(AN-co-IA)/[BMIM]Cl solutions are typical neutral polymeric liquids for the concentrated solutions but have shown a more complicated behavior at high deformation rates. 相似文献
According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor. 相似文献
For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive chain network model that allows the spatial fluctuations of sliplink and branch point and the chain sliding along the backbone according to the subchain tension, chemical potential gradients, drag force against medium, and random force. The sliplinks are created and∕or disrupted through the motion of chain ends. The curvilinear hopping of the branch point along the backbone is allowed to occur when all sliplinks on a branched arm are lost. The simulations considering the fluctuation and the hopping of the branch point described well the viscoelastic data for symmetric and asymmetric star polymers with a parameter set common to the linear polymer. On the other hand, the simulations without the branch point motion predicted unreasonably slow relaxation for asymmetric star polymers. For asymmetric star polymers, further tests with and without the branch point hopping revealed that the hopping is much less important compared to the branch point fluctuation when the lengths of the short and long backbone arms are not very different and the waiting time for the branch point hopping (time for removal of all sliplinks on the short arm) is larger than the backbone relaxation time. Although this waiting time changes with the hopping condition, the above results suggest a significance of the branch point fluctuation in the actual relaxation of branch polymers. 相似文献
The rheology of reversible coordination polymer networks in aqueous solution is studied. The polymers are formed by neodymium(III) ions and bifunctional ligands, consisting of two pyridine-2,6-dicarboxylate groups connected at the 4-positions by an ethylene oxide spacer. Neodymium(III) ions can bind three of these terdendate ligand groups. At high concentrations, the polymer networks yield viscoelastic materials, which can be described with the Maxwell model. The scaling of the elastic modulus, relaxation time, and zero-shear viscosity with concentration are in good agreement with the predictions of Cates' model that describes the dynamics of linear equilibrium polymers. This indicates that the networks have only few cross-links and can be described as linear equilibrium polymers. The gels are also thermo-reversible. At high temperatures, fast relaxation was found, resulting in liquidlike behavior. Upon cooling, the viscoelastic properties returned immediately. From the temperature dependence of the relaxation time, an activation energy of 49 kJ/mol was determined for the breaking and reptation of the polymers. 相似文献
A variety of linear and 3-arm star polyethylene (PE) model polymers covering a wide range of molecular weight are synthesized by the living polymerization of butadiene and the subsequent hydrogenation. Several rheological parameters of these model linear and 3-arm star PE samples are analyzed for detecting the long chain branching (LCB) structure. It is found that the analyses based on zero shear viscosity, vGP plot and flow activation energy are very sensitive to the 3-arm star PEs. The information on the presence of LCB can be obtained with these methods even for low molecular weight samples, which can not be determined by GPC-MALLS. However the information about the LCB structure can not be obtained by the rheological methods alone. 相似文献
Functional poly(ethylene oxide) star polymers possessing a tertiary amino group at each arm end were prepared by free-radical copolymerization of poly(ethylene oxide) macromonomers with divinylbenzene (DVB) in water or ethanol. The poly(ethylene oxide) arm was prepared by anionic polymerization using 2-[2-(N,N-dimethylamino)ethoxy]ethanol potassium alkoxide as the initiator. The star polymers had narrow molecular weight distribution. The arm number was controlled by varying the feed ratio [DVB]/[M], the initial concentration of macromonomer [M], and solvent media. The branching factor g' in methanol ([eta]S/[eta]L are the intrinsic viscosities of the star and linear molecules, respectively) exhibited a power-law dependence on the arm number, f, with a negative exponent. This means that the dimensions of a star were in agreement with the Daoud-Cotton scaling model. 相似文献
Miktoarm star copolymers containing two or more arm species were synthesized by atom transfer radical polymerization using a simple and general "arm-first" method, that is, one-pot cross-linking a mixture of different linear macroinitiator (MI) species by a divinyl cross-linker, such as divinylbenzene. Using linear MIs with a high degree of bromine chain-end functionality, including polyacrylate, polystyrene, polymethacrylate and poly(ethylene oxide), resulted in high-yield star polymers (>90%). Characterized by liquid adsorption chromatography techniques, which separated star polymers on the basis of the chemical composition of arms, the obtained star product was proved to be miktoarm star copolymers containing two or more arm species in one molecule, instead of mixture of different homoarm star polymers. Within our investigation, the molar ratios of the arms in the miktoarm star copolymers were always in agreement with the composition of the initial MI mixture, indicating the powerful capacity of this arm-first method for synthesis of miktoarm star copolymers with potentially any molar ratios and species of the arms. By using a mixture containing five types of linear MIs with different chemical compositions, miktoarm star copolymers containing five kinds of arms were synthesized for the first time, which significantly expanded the methodologies for synthesis of miktoarm star copolymers by living polymerization techniques. 相似文献