We discuss the relaxation properties of polymer networks possessing either short-scale ordering caused by rigidity of network strands or long-scale liquid crystalline order. The main topics of the paper are the equilibrium and local dynamic properties of a polymer network ordered due to nematic-like interactions of the network segments with included rod-like particles. A simplified three chain network model is used. Lagrange multipliers in the equations of motion of hard rods are replaced by their averaged values. This approximation corresponds to modelling the rod-like particles by elastic Gaussian springs, their mean-square lengths independent of the ordering. 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 ordering of the network segments. Relaxation spectrum of the ordered network splits into two main branches for the parallel and perpendicular components of the chain segments with respect to the director. We calculate the relaxation times of a polymer network as functions of the wave number. The relaxation spectrum of an isotropic network and that of the ordered network with included rods are compared. 相似文献
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. 相似文献
A simplified “three‐chain” network model formed from freely jointed polymer chains consisting of Gaussian elements with fixed mean‐square lengths is proposed for describing local dynamic properties of nematic elastomers. The boundaries of a polymer network are supposed to be fixed when sample volume and shape do not change with ordering. Relaxation times characterising intrachain motions in both isotropic and ordered states are determined by two factors. The first (“dynamic”) factor is related to the friction of chain elements and the second one (“statistical” factor) is determined by statistical mean–square fluctuations of segment projections on the three axes of rectangular frame of reference. The “statistical” factor of relaxation times is calculated here as a function of the order parameter and the parameter characterising the degree of network crosslinking. Statistical factor obtained in the framework of a network model consisting of Gaussian subchains is compared with that calculated here by using freely‐jointed‐rods chain model. Good agreement is shown between statistical factors obtained in the framework of the two chain models considered. This result confirms the validity of describing the dynamics of real rod‐like mesogenic groups in nematic elastomers in terms of a simplified chain model consisting of Gaussian segments with fixed average lengths which do not change with ordering. The influence of “dynamic” factor on the relaxation spectrum of a nematic elastomer is discussed qualitatively. 相似文献
We study theoretically the relaxation properties of polymer networks, whose monomers and junction sites have different friction parameters (ζ and ζjun, respectively). For this, we focus on topologically regular cubic networks built from “bead‐and‐spring” Rouse chains. Setting σ = ζjun/ζ, we determine analytically both the eigenvalues and the eigenmodes of the model for arbitrary values of σ. This allows us to extend previous approaches (Macromolecules 2000 , 33, 6578) which were restricted by the condition σ = 3. We compute the frequency dependent storage, G′(ω), and loss, G″(ω), moduli (which for σ ≫ 3 or σ ≪ 3 display two plateaus and two maxima, respectively) and also the mean‐square displacements of the network junctions and of the beads; these turn out to obey power laws, whose validity ranges depend on σ.
The effect of the linear charge density of natural polyelectrolyte, carrageenan, on the ion binding to carrageenan molecules in relation to the gelation was investigated by using the dielectric relaxation spectroscopy, dc conductivity, optical rotation, and differential scanning calorimetry (DSC). Although carrageenan is an anionic polysaccharide, carrageenan molecules in the helix state at low temperatures can bind not only cation, such as potassium and cesium, but also anion, such as iodide. The dc conductivity steeply decreases just below the coil–helix transition temperature, which indicates the binding of ion to the carrageenan molecules in the helix state due to the increase of the linear charge density compared with that in the coil state. The addition of NaI promotes the helix formation, and prevents from aggregation of helices, which was suggested by the results of the dynamic shear modulus and the DSC, and resulted in an increase of the relaxation amplitude of the lowest frequency relaxation (kHz) attributed to the fluctuation of the tightly bound counter ions along the high charge density region (helix). It is concluded that binding of iodide induces (1) the increase in the amount of tightly bound counterions to carrageenan molecules and (2) the formation of non-aggregated helix. 相似文献
A solution to Fick's equation is presented which accurately predicts the transfer of mass out of a polymeric rod or sheet undergoing relaxation by a solvent permeating it by Case II transport. There is a critical length. Before the solvent permeates to this length the diffusible material can diffuse away from the moving boundary faster than it is becoming available at the boundary. Afterward the reverse is true. Five sets of experimental data from three different sources have been used to test the model. The agreement is excellent. 相似文献
Epoxy polymers with donor–acceptor type side groups were synthesized for application in nonlinear optics. The stability of the Pockels coefficient was measured in thin films after poling. The relaxation times and their temperature dependence seem to be correlated with dielectric measurements. Guest–host systems (polystyrene and polymethylmethacrylate with dimethylaminonitrostilbene) were investigated for comparison. 相似文献
The 87Rb and 133Cs spin-lattice relaxation rates of RbCdCl3 and CsCdCl3 single crystals grown using the slow evaporation method were measured over the temperature range 160-400 K. The changes in the 87Rb spin-lattice relaxation rate near 340, 363, and 395 K correspond to phase transitions of the RbCdCl3 crystal. The jump in T1−1 at 395 K is due to a shortening in the c-direction as a result of a phase transition from a cubic to a tetragonal structure. We suggest that the cubic Rb environment is favored above 395 K due to the fast motions and soft modes, which cause relaxation and average out the quadrupolar splittings. The temperature dependence of the relaxation rate below 340 K in RbCdCl3 can be represented by and is thus in accordance with a Raman process. The 133Cs nuclei in the CsCdCl3 crystal produce only one resonance line, which indicates that the local structure around the Cs atoms is cubic. The temperature dependence of the relaxation rate of the Cs nuclei can also be described with the quadratic equation . In the case of the RbCdCl3 and CsCdCl3 crystals, which are of electric quadrupolar type, their relaxations proceed via Raman processes, whereas in RbMnCl3 and CsMnCl3 crystals, which are of magnetic relaxation type, the relaxations proceed via single phonon processes. Therefore, the relaxation mechanisms of these different types of ABCl3 crystals (quadrupolar and magnetic) are completely different NMR behavior. 相似文献