Model Theory of Visco-Elastic Properties and Relaxation Spectra of Two Different Interpenetrating Polymer Networks

Dynamic viscoelastic models of the system of two different interpenetrating polymer networks with different topology and type of interactions were used for calculating spectra of relaxation times of the system under consideration. It was shown, that two branches of the relaxation spectrum appear for two models of interpenetrating networks with different components. One of the branches is the branch of the collective motion of double network consisting of two initial interacting networks. Parameters of this branch of relaxation spectrum are defined by both own elastic constants of each of interacting networks and by effective quasi-elastic interactions between two networks. This branch is the low frequency one and is described by broad relaxation time spectrum. The second branch is the high frequency one and characterizes mutual local motions of two interacting networks. The relaxation spectrum of this branch is comparatively narrow and depends on the quasi-elastic constants and mutual friction which is defined by the entanglements of the networks and by its effective rigidity. The second branch does not contain extremely large relaxation times for infinitely large networks.     

Relaxation spectrum of a polymer network with included particles: A regular cubic network model with mutual friction

A theory of the viscoelastic properties of crosslinked polymers with included particles is developed. The model of a regular cubic coarse-grain network, which suggests the viscoelastic interaction of the particles with the crosslink sites, is used. The particles are assumed to be close to isotropic, and their mobility is described via the introduction of a friction coefficient that is directly proportional to the particle radii. In the framework of this model, the spectrum of relaxation times of the network with included particles consists of two branches: One corresponds to the local displacements of the particles relative to the crosslink sites; the other describes the large-scale collective mobility of the particles along with the network fragments. At all values of the viscoelastic parameters of the model, the relative width of the relaxation-time spectrum for the network with included particles is higher than that for the initial network without included particles. This theoretical result qualitatively explains the experimental data on the mechanical and dielectric relaxations of crosslinked composites, which verify the broadening of the frequency dependences of the elasticity modulus, loss modulus, and dielectric-loss factor for the filled crosslinked polymers relative to these dependences for the initial (unfilled) polymer networks.     

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     

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.     

聚醋酸乙烯酯/聚丙烯酸甲酯互穿网络聚合物的研究 Ⅴ.互穿缠结对相区结构的稳定作用

用定量的甲苯溶胀聚醋酸乙烯酯/聚丙烯酸甲酯互穿网络聚合物(PVAc/PMA IPN),使体系处于分相的热力学条件;或醇解其中的PVAc 网络,即增加两组份的化学不相容性.动态力学谱和透射电镜等结果表明,IPN 和网络Ⅰ的交联密度较高的半 IPN 试样,没有发生进一步的相分离,证明网络互穿缠结是永久性的物理缠结,并且有强迫互容作用的存在.     

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。     

Experimental study of molecular entanglement in polymer networks

Elastomeric molecular networks have been prepared by endlinking polydimethyl siloxane molecules having functional chain ends, both in the presence of an unreactive polymeric diluent and in the undiluted state. Values of tensile (Young) modulus were found to be in good agreement with the simple molecular theory of rubberlike elasticity for networks prepared in a highly diluted state. For concentrated systems the modulus was anomalously high, however. The discrepancy can be attributed to chain entanglements. A second interpenetrating network was introduced into networks formed in the diluted state by replacing the diluent polymer by reactive polymer, which was then gelled in situ. The modulus of these combined networks was much higher than the sum of the moduli of the constituent networks, implying a large contribution from molecular entanglements. © 1994 John Wiley & Sons, Inc.     

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.     

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.     

Rotational and translational relaxation times of quasi-elastic and rigid dumbbells elastically bound to polymer network junctions

The dynamics of a rigid rod located between fixed junctions of a polymer network is studied. Three approaches are used in the solution of this problem. The first is based on the viscoelastic model, where a rigid rod is simulated by an elastic dumbbell with a fixed average length; the second includes solution of equations of motion for projections of the rigid rod using the Lagrangian multipliers under the constraint condition; and the third involves solution of the diffusion equation in the presence of an elastic potential. The second and third approaches allow calculation of orientational relaxation times for rod projections under the action of a strong orienting field. The dependences of the relaxation times of orientational and translational motions of the rod projections on the coordinate axes and the orientational relaxation times of mean-square rod projections on the model parameters (the distances between fixed polymer network junctions, the length of the rigid rod, and the elastic coefficient characterizing the binding between the rod and the network) are found.     

Simulation of phase behavior and mechanical properties of ideal interpenetrating networks

In this work microphase separation in ideal interpenetrating networks as well as its influence on the mechanical properties of the networks has been studied. Structures with long-range order in such networks have not been found to be formed; the reason for this is apparently the weak bonding (physical entanglements) between the subnetworks. The dynamics of the relaxation of interpenetrating networks with highly incompatible subnetworks has been studied and it has been found that the slow rearrangement of phase boundaries during the stretching process has a significant influence on it. Using the analysis of subchains conformations, it has been found that the increase in the stiffness of interpenetrating networks with incompatible subchains occurs due to the irregular tension of subchains related to the presence of big aggregates in the system.     

Relaxation Spectra and Viscoelastic Behavior of a Model Hydrophobically Modified Alkali-Soluble Emulsion (HASE) Polymer in Salt/SDS Solutions

The viscoelastic behavior of a semidilute hydrophobically modified alkali-soluble emulsion (HASE)-C20 polymer in NaCl and NaCl/SDS (sodium dodecyl sulfate) solutions was determined using a Rheometric fluids rheometer and the data were converted to relaxation spectra. The dynamic moduli can be fitted with a multiple modes Maxwell model. In the presence of increasing amounts of NaCl, the moduli decrease, where G', decreases more rapidly than G". However, in the presence of SDS and 0.4 M NaCl, the dynamic moduli increase to a maximum at a critical concentration and decrease thereafter. The relaxation spectra suggest that the structure of the polymer network is complex and it contains two to six relaxation times, depending on the NaCl or SDS/0.4 M NaCl concentrations. With increasing NaCl concentrations, the fastest peak shifts to longer times while the slowest peak decreases. This corresponds to the destruction of the network as the polymer backbone collapses to form clusters with a larger aggregation number. For HASE in SDS/0.4 M NaCl solutions, the lifetime of both the hydrophobic junction (fastest peak) and network relaxation (slowest peak) shift to longer times, which suggests the strengthening of active junctions by bound SDS molecules. However, beyond a critical SDS concentration, the relaxation time of the polymer and hydrophobic junction decreases to an asymptotic value. Copyright 2000 Academic Press.     

AN EPOXY/(METHYL METHACRYLATE)INTERPENETRATING POLYMER NETWORK FOR NONLINEAR OPTICS*

An interpenetrating polymer networks (IPN) consisting of an epoxy-based polymer network and apolymethyl methacrylate network were synthesized and characterized. The IPN showed only one T_g, andhence a homogeneous-phase morphology was suggested. The second-order nonlinear optical coefficient (d_(33))of the IPN was measured to be 1.72×10~(-7) esu. The study of NLO temporal stability at room temperature andelevated temperature (100℃) indicated that the IPN exhibits a high stability in the dipole orientation due tothe permanent entanglements of two component networks in the IPN system. Long-term stability of secondharmonic coefficients was observed at room temperature for more than 1000 h.     

Effects of Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included rod‐like Particles: Mean‐Field Approximation

Summary: Equilibrium and local dynamic properties of ordered polymer networks with included rod‐like particles are considered using a simplified network model. Lagrange multipliers in the equations of motion of rigid rods are replaced by their averaged values. This approximation corresponds to modelling rod‐like particles by elastic Gaussian springs with mean‐square lengths independent of the orientational order. Nematic‐like interactions between network segments and rods are taken into account in terms of the Maier‐Saupe mean‐field approximation. Nematic ordering of rods induces network segments ordering and changes the relaxation spectrum of the network. The relaxation spectrum of the ordered network splits into two main branches for parallel and perpendicular components of chain segments with respect to the director. Relaxation times of a polymer network are calculated as functions of the wave number for the corresponding normal mode and of the order parameter taking into account both the dynamic factor (determined by friction effects) and the statistical factor (related to mean‐square fluctuations of segment projections). We compare the relaxation spectra of ordered unstretched polymer networks with fixed boundaries with those for polymer networks at free boundaries. A polymer network with free boundaries is stretched along the director. This produces additional fine structure of the two main branches in the relaxation spectrum.

Cell of a three‐chain network model with included rods.     

Two tube models of rubber elasticity

Polymer entanglements lead to complicated topological constraints and interactions between neighboring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they effectively confine each individual chain in a tube-like geometry. In polymer networks, due to crosslinks preventing the global reptation and constraint release, entanglements acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. In this article we discuss two different models of rubber elasticity, both utilizing the reptation ideas. First, we apply the classical ideas of reptation statistics to calculate the effective rubber-elastic free energy of an entangled rubbery network. In the second approach, we examine the classical Rouse dynamics of chains with quenched constraints at their ends by crosslinks, and along the primitive path by entanglements. We then proceed to average a microscopic stress tensor for the network system and present it in a manageable form in the equilibrium t → ∞ limit. Particular attention is paid to the treatment of compressibility and hydrostatic pressure in a sample with open boundaries. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2679–2697, 2006     

Equilibrium conformations of polymer chains Part II. Conformons in networks

With regard to the ideal network it is shown that the concept ofN non-interacting polymer chains can be transformed in a problem of non interacting excitations (called conformons) for rubber elasticity. Modelling the interaction on permanent crosslinks as a scattering problem and taking the finite chain length into account, an interpretation of the second Mooney coefficient can be given. There is some evidence that the junctions move by constrained self diffusion.Dedicated to Prof. Dr. W. Ruland on the occasion of his 60th birthday.     

Some properties of intermediate regions in interpenetrating polymeric networks

The molecular mobility in an interpenetrating polymeric network (IPN) based on crosslinked polyurethane (1) and styrene–divinylbenzene copolymer (2) was studied by broad-line NMR spectroscopy and reversed gas chromatography. NMR and infrared investigations show the absence of chemical interaction between the two constituent networks. For an IPN in the temperature range ?196 to 120°C transition regions corresponding to the individual networks and to an intermediate region were found, the latter being characterized by an additional transition at 25–60°C (NMR spectroscopy) and 44–78°C (gas chromatography). The existence of an intermediate region, presumably of loosely packed structure, leads to a shift in the beginning of the temperature transition in IPN to lower temperature and to a decrease in activation energies of relaxation in comparison with the individual networks. The activation energies in IPN are decreased with increasing weight fraction of the second network.     

Stress relaxation of monodisperse poly-α-methylstyrene

The viscoelastic properties of monodisperse poly-α-methylstyrenes of molecular weights of 4 × 10⁴ to 50 × 10⁴ were studied by the tensile stress-relaxation method. The relaxation-time spectra as well as the steady-flow viscosity, the steady-state compliance, the maximum relaxation time, and the modulus associated with the maximum relaxation time were determined. The molecular weight dependences of these quantities were compared with the theory of Rouse and Bueche as modified by Ferry, Landel, and Williams, as well as with data on other polymers reported in the literature.     

On the application of the modeling of the relaxation spectrum to the prediction of linear viscoelastic properties of surfactant systems

 In this work, the linear viscoelastic properties of cetyl-trimethylammonium tosilate–water system are predicted by the modeling of the relaxation spectrum. The modeled spectrum of relaxation times is of the “wedge-box” type where the “wedge” portion is located at the short-time scale of relaxation times and the “box” part covers the long-time scale. The linear viscoelastic properties are calculated through the exact relationships with the suggested spectrum. Agreement between the calculated expressions and experimental data of the moduli and the stress relaxation function is found. Comparison is also made with predictions of the empirical expressions of the Cole–Cole and the Williams–Watts models. Received: 17 December 1996 Accepted: 1 July 1997