Theory of relaxation spectra and dielectric relaxation of rigid rodlike particles incorporated in a polymer network

The theory of molecular mobility and relaxation spectra is developed for rodlike particles embedded in a polymer network with allowance for the involvement of the particles in collective network dynamics through topological entanglements with network fragments. A regular cubic coarse-grained network model is used, where the motion of junctions describes the mobility of large fragments (domains) of the initial network with a size equal to the distance between adjacent rodlike particles. The involvement of the rods in collective network dynamics is taken into account by introducing an effective quasi-elastic potential acting between the rods and junctions of the coarse-grained network and preventing long-distance diffusion of the embedded particles. The viscoelastic parameters of the coarse-grained (“renormalized”) network are functions of the viscoelastic characteristics of the initial network. The relaxation time spectra are calculated as well as the frequency dependences of the dielectric loss factor of the embedded particles that possess a permanent dipole moment directed along the major axis of each rod. Depending on the ratio between the viscoelastic characteristics of the rods and the network, the frequency dependence of the dielectric loss factor may have two maxima. The high-frequency maximum corresponds to local orientational movements of particles at fixed junctions of the coarse-grained network, which correspond to the position of the domain centers in the initial network. The low-frequency maximum corresponds to movements of particles involved in large-scale dynamics of network fragments. The dependence of the dielectric loss factor on the ratio between the viscoelastic parameters of the rods and the network is studied.     

The Local and Collective Mobility in Polymer Chains and Networks with Included Rigid Particles Elastically Connected with the Network

Summary: The theory of molecular mobility of a polymer network with included rod-like particles is developed. The case is considered when the length of rods is comparable or greater than the average distance between neighboring cross-links of the primary network. The long-scale dynamics of the network is described by means of a regular cubic “coarse-grained” model. The junctions of this model describe the great network fragments (domains) the sizes of which are near to the average distance between neighboring rods.The quasi-elastic interactions between rods and network fragments lead to a broad relaxation spectrum for included rods as compared with free rods which are characterized by a single relaxation time of rotational diffusion. The frequency dependence of the dielectric loss factor of included rods is calculated for rods with permanent dipole moments directed parallel to the long axes of the rods chaotically distributed in the network. The frequency dependence of dynamic modulus of a polymer network with included rods is obtained. The increment in the dynamic modulus of the relatively short network motions (smaller than the distance between rods) also is taken into account. The broad relaxation spectrum of included rods leads to appearance of several maximums on the frequency dependences of both the dielectric loss factor and dynamical modulus.     

Relaxations in the transition region of crosslinked polyesters. II. The glass transition

The glass-transition region of crosslinked polymers prepared from poly(1,2-propylene phthalate fumarate) and styrene was studied using a torsion pendulum. The glass-transition temperature and the modulus in the rubbery region of these polymers were analyzed in terms of the crosslink density. The styrene concentration at which the maximum crosslink density occurs, as estimated from the viscoelastic data, is found to be in agreement with estimates made by other workers using chemical methods.     

Effect of crosslink on the characteristic length of glass transition of network polymers

The characteristic length of the glass transition temperature was evaluated for crosslinked bulk polystyrenes and poly(methyl methacrylate)s by differential scanning calorimetry. The characteristic length, which corresponds to a length scale of the cooperative rearrangement due to polymer segmental relaxation, was revealed to decrease with increase in the degree of crosslink. The relative values of configurational entropy for crosslinked polymers were evaluated based on a simple polymer network model on a cubic lattice. As a result, the configurational entropy of the smallest cooperatively rearranging region was revealed to decrease with increase in the degree of crosslink, which is responsible for the above behavior of the characteristic length. The effects of crosslink on the characteristic length and the glass transition temperature were found to be stronger for crosslinked poly(methyl methacrylate)s than for crosslinked polystyrenes, which reflects the difference in the structure of crosslink segment. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1958–1966, 2006     

Relationship between structure and rheological properties in the melt of polymers containing spherical inclusions

The linear viscoelastic behavior of model rubbertoughened polymer melts has been studied. The most significant influence of the dispersed crosslinked rubber phase on the melt rheology of the blends is the existence of a secondary plateau for the storage modulus G′ at low frequencies. This behavior was ascribed to a percolation phenomenon, leading to the formation of a threedimensional network of inclusions, and contributing to the elasticity at low frequencies of the blend. Two different systems were investigated: (a) a polystyrene matrix with crosslinked and structured latex particles and (b) silicon oil matrices with homogeneous crosslinked PMMA particles. An initial shearing history was found to influence the dynamic mechanical properties of the molten blends and in particular to lower the lowfrequency plateau value for G′. During a subsequent annealing, the plateau modulus increases again. These results are in agreement with the assumption of a particle network.     

Viscoelastic characteristics of UV polymerized poly(ethylene glycol) diacrylate networks with varying extents of crosslinking

The viscoelastic relaxation characteristics of ultraviolet crosslinked networks based on poly(ethylene glycol) diacrylate [PEGDA] have been investigated by dynamic mechanical methods. Effective crosslink density in the networks was varied via the use of PEGDA prepolymers of different molecular weight, or by the introduction of controlled amounts of water in the reaction mixture. In all cases examined, fully amorphous networks were obtained. Time–temperature superposition was applied to obtain master curves of storage modulus versus frequency across the glass transition, and these could be satisfactorily described using the Kohlrausch–Williams–Watts relaxation function. The glass transition temperature (T_g), relaxation breadth, and fragility of the segmental relaxation were correlated with the effective crosslink density obtained in the networks. Gas permeation measurements on the PEGDA/water networks indicated only a very modest variation in gas transport properties, despite the sizeable variation in apparent crosslink density achieved in these materials. This result suggests that the controlling structural factor for gas transport in the networks is not simply crosslink density, and that attempts to correlate gas transport to network structure must necessarily consider the broader relationships between crosslink density, segmental mobility, and fractional free volume. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2058–2070, 2006     

Mean field theory for a reversibly crosslinked polymer network

We present a mean field theory for melts and solutions of reversibly crosslinked polymers. In our model, crosslinks are considered as local bonds between two monomers. For a blend of A+B+AB polymers, we assume reversible crosslinks between the copolymers AB with a crosslink strength z and interaction weights ω(A) and ω(B) for monomers of type A and B, respectively. The usual mean field model for polymer blends without reversible crosslinks is recovered if z vanishes. With or without crosslinks, the A+B+AB blend can form a lamellar phase with A and B rich regions. If reversible crosslinks are enabled and ω(A) differs strongly from ω(B), the lamellar nanophase separation of A and B monomers is accompanied by a similar segregation of crosslinked and noncrosslinked polymers. If ω(A) and ω(B) are equal, crosslinked copolymers are well mixed with the homopolymers. For a homopolymer solution with reversible crosslinks between the polymers, our calculations show that polymers and solvent molecules are separated macroscopically if the Flory-Huggins interaction parameter and the crosslink strength are suitably high or if the volume fraction of polymers or the chain length are suitably low.     

Correlation of Cooperatively Localized Rearrangement on the “Fluidized Domain” of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes (I): A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

Based on the structure of glass (or liquid) polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu-tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts (K-W-W) stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.     

聚氨酯的后交联研究进展

通过交联可以将线型聚合物连接成三维网状结构,适度交联后聚氨酯的拉伸强度、模量、耐溶剂性、耐高温性等许多性能都能得到大幅提高,而交联方法、交联的种类及交联密度的大小都是重要的影响因素,因此对交联方法、交联密度的测定、交联密度与聚氨酯性能之间的关系研究对于聚氨酯的质量控制非常重要。本文首先详细介绍了聚氨酯后交联的常用方法,然后对聚氨酯交联密度的测定方法进行了分析比较,在此基础上进一步介绍了国内外关于聚氨酯交联密度与其性能的关系方面的研究进展。     

Kinetics of polymeric network synthesis via free-radical mechanisms - polymerization and polymer modification

The kinetics of polymeric network formation via free radical mechanisms is an attractive research area because there are many phenomena which are not well understood and in addition, the commercial potential for crosslinked systems is great. Recently, a large research/development program was initiated at the McMaster Institute for Polymer Production Technology (MIPPT) to investigate the fundamentals and applications of polymeric network, in particular, the kinetics of synthesis via free-radical mechanisms and network characterization. The research on crosslinking involved both theoretical developments and experimentation. Herein is provided a comprehensive summary of this work. In the experimental polymerization, two comonomers, methyl methacrylate (MMA) / ethylene glycol dimethacrylate (EGDMA) and acrylamide (AAm) / N,N-methylene bisacrylamide (Bis), as model systems were studied in considerable detail. Measurements included: monomer conversions, radical concentrations, sol/gel fractions, crosslink densities (equilibrium swelling and swollen-state ¹³C-NMR) over the entire range of divinyl monomer levels as a function of polymerization time. In the polymer modification, high density polyethylenes were crosslinked using peroxides and γ-radiation. For this system, crosslinking and chain scission occur simultaneously. In the theoretical studies, it was shown that in general, network formation by free-radical mechanisms is highly irreversible requiring that the classical equilibrium gelation theories after Flory/Stockmayer be generalized. The general model which was developed using the pseudo-kinetic rate constant method predicts the existence of a crosslink density distribution (crosslink density of a primary polymer chain depends on its birth time) with a variance which can vary widely depending on network synthesis conditions.     

Aminolysis of crosslinked polysiloxanes: Tautomeric catalysis by 2-pyridone

Results are presented which extend earlier findings on the transformation of insoluble crosslinked polysiloxanes into soluble linear polymers by selective aminolysis at crosslink sites. The present study provides evidence of a substantial steric effect and catalysis by 2-pyridone. The results with 2-pyridone are attributed to tautomeric catalysis which, to our knowledge, had not been observed before in substitution reactions at silicon. Evidence is also presented that unhindered, difunctional primary amines effect aminolysis with both amine groups to produce insoluble crosslinked polymer, presumably with silylamine functionality at crosslink sites.     

Rheological analysis as a means for determining the silane crosslink network structure and content in crosslinked polymer composites

For evaluating the crosslink content of a polymer, gel content determination is a commonly used method. However, for crosslinked polymer composites containing particulate filler, the gel content may be overestimated due to partly trapping filler inside the gel portion. In this paper, parallel-plate rheology was used, together with the gel determination and FTIR measurement, for determining the silane crosslink network structure and content in crosslinked ethylene–octene copolymer composites. The effects of filler surface property on structure and content of silane crosslink are also discussed. The results show that a correlation plot between gel content, IR absorption index and crosslink density provides useful information on changes in silane network structure and properties of the crosslinked composites. The network structure formed (loose or tight network) shows a strong influence on the final tensile properties of the crosslinked products.     

Effects of phase separation on network and viscoelastic properties in SBS thermoplastic elastomers

Stress relaxation of poly(styrene-b-butadiene-b-styrene) thermoplastic elastomers is studied in dependence of molecular weight and degree of hydrogenation in the temperature range between ?30° and +80 °C. The influence of these parameters on the structure of the physical network and the degree of partial mixing in the domain boundary is investigated by separating the stress-relaxation modulus into a viscoelastic term and an equilibrium network modulus calculated from the relaxation-time spectrum. The temperature dependence of the one-second relaxation modulus is quantitatively described by use of a modified Kerner model for the simulation of the viscoelastic term. The modification allows the estimation of the volume fraction of interfacial material and its correlation to the parameters which govern phase separation.     

Percolation simulation of the network degradation during ultrasonic devulcanization

The percolation model of network degradation during rubber devulcanization is presented. The model is based on a random crosslink scission and molecular chain breakup. The obtained results indicate that the primary model parameter characterizing the network degradation is the ratio of the probabilities of backbone breakup to crosslink scission. The predicted dependences of the gel fraction of devulcanized rubber on crosslink density are in excellent agreement with experimental data for styrene-butadiene rubber and ground rubber tire. The estimated critical exponents indicate that the process of devulcanization for the vulcanizate without filler appears to belong to the universality class of standard 3D bond percolation while devulcanization for the vulcanizate with filler appears to belong to its own new universality class. © 1996 John Wiley & Sons, Inc.     

Swelling studies of crosslinked poly(p-phenylene terephthalamide) copolymers in sulfuric acid

In an attempt to improve the mechanical properties of extended chain polymers such as poly(p-phenylene terephthalamide) (PPTA), a crosslinkable terephthalic acid derivative (XTA) has been developed which can be incorporated into copolymers in various concentrations and activated after polymerization. The crosslinking of PPTA-co-XTA copolymer particles was investigated through a series of swelling experiments in concentrated H₂SO₄. The data show a systematic decrease in equilibrium swelling with increasing XTA content, indicating the XTA units are in fact acting as crosslink sites. Values for crosslink density were calculated from the Flory-Rehner theory of polymer swelling and compared with previous findings on crosslinked rigid polymer network systems. The effective number of crosslinks per XTA unit (efficiency) predicted by the Flory-Rehner theory increases and then decreases with % XTA. The decrease in crosslinking efficiency at high XTA concentrations is consistent with differential scanning calorimetry data which show the enthalpy of XTA reaction decreasing slightly with % XTA. The deviations at low % XTA may represent a failure of the Flory-Rehner theory to properly describe the rubbery elasticity of extended chain polymers. © 1994 John Wiley & Sons, Inc.     

Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)

The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010     

Long‐time relaxations in rubber‐modified polymer systems

Linear and nonlinear viscoelastic properties were measured in the molten state for several model ABS polymers with different rubber particle contents. Linear viscoelastic functions for ABS polymers can be separated in two parts. One is a relaxation associated with the entanglement of matrix SAN chains and the other comes from the particle‐particle interactions of rubber particles. This relaxation depends strongly on the degree of dispersion of rubber particles. The second‐plateau modulus appeared at low frequency with samples in which rubber particles agglomerate. While, the second‐plateau modulus was not observed with samples in which rubber particles are finely dispersed. Matching of AN content between grafted and matrix SAN and optimum graft density form a finely dispersed system. Large deformation relaxation measurements revealed that the damping of ABS polymers having a good dispersion of particles become stronger with an increase in rubber content. This strong damping can be explained by a layered structure. The very long relaxation was found for higher rubber content, when the neighboring grafted SAN chains contact with each other.     

Chain dynamics of end-group modified polystyrenes as studied by fluorescence depolarization

Polystyrenes, both linear and crosslinked with various crosslink densities, having modified end-group structures, were synthesized with the objective of studying chain-end mobility in the glassy state. One end of each polymer chain of these polystyrenes was modified with a fluorescent molecule. These polymers containing fluorescent probes in specific environments have been used in studies of segmental motion using fluorescence depolarization. The mobility has been studied below the glass-transition temperature as a function of temperature and crosslink density. The experimental data show that chain-end mobility is not of major importance in connection with the β-transition.     

Strain-induced post-curing of acrylate networks

The mechanical properties and network structure of photocurable polymers are strongly dependent on processing conditions. Here it is reported that highly crosslinked acrylate systems undergo unexpected additional post-curing during DMTA measurements, resulting in an increase in glass-transition temperature (T_g). A detailed study of the conditions under which this increase in T_g takes place unequivocally shows that a small (0.1%) oscillatory strain applied above T_g is responsible for additional cross-linking reactions. The effect of strain-induced post-curing is confirmed by applying post-curing treatments under oscillatory shear strain in rheological tests. Different acrylate systems were characterized and the results show that the strain induced post-curing depends on the network structure of the polymer. In polymer networks with an initial high crosslink density the effect is pronounced while in polymers with an initial lower crosslink density no shift in T_g is observed.