Magneto‐sensitive Elastomers in a Homogeneous Magnetic Field: A Regular Rectangular Lattice Model

A theory of mechanical behaviour of the magneto‐sensitive elastomers is developed in the framework of a linear elasticity approach. Using a regular rectangular lattice model, different spatial distributions of magnetic particles within a polymer matrix are considered: isotropic, chain‐like and plane‐like. It is shown that interaction between the magnetic particles results in the contraction of an elastomer along the homogeneous magnetic field. With increasing magnetic field the shear modulus, G, for the shear deformation perpendicular to the magnetic field increases for all spatial distributions of magnetic particles. At the same time, with increasing magnetic field the Young's modulus, E, for tensile deformation along the magnetic field decreases for both chain‐like and isotropic distributions of magnetic particles and increases for the plane‐like distribution of magnetic particles.

     

Theory of light-induced deformation of azobenzene elastomers: influence of network structure

Azobenzene elastomers have been extensively explored in the last decade as photo-deformable smart materials which are able to transform light energy into mechanical stress. Presently, there is a great need for theoretical approaches to accurately predict the quantitative response of these materials based on their microscopic structure. Recently, we proposed a theory of light-induced deformation of azobenzene elastomers using a simple regular cubic network model [V. Toshchevikov, M. Saphiannikova, and G. Heinrich, J. Phys. Chem. B 116, 913 (2012)]. In the present study, we extend the previous theory using more realistic network models which take into account the random orientation of end-to-end vectors of network strands as well as the molecular weight distribution of the strands. Interaction of the chromophores with the linearly polarized light is described by an effective orientation potential which orients the chromophores perpendicular to the polarization direction. We show that both monodisperse and polydisperse azobenzene elastomers can demonstrate either a uniaxial expansion or contraction along the polarization direction. The sign of deformation (expansion/contraction) depends on the orientation distribution of chromophores with respect to the main chains which is defined by the chemical structure and by the lengths of spacers. The degree of cross-linking and the polydispersity of network strands do not affect the sign of deformation but influence the magnitude of light-induced deformation. We demonstrate that photo-mechanical properties of mono- and poly-disperse azobenzene elastomers with random spatial distribution of network strands can be described in a very good approximation by a regular cubic network model with an appropriately chosen length of the strands.     

Dynamics of Polymer Networks with Strong Differences in the Viscous Characteristics of their Crosslinks and Strands

We study theoretically the relaxation properties of polymer networks, whose monomers and junction sites have different friction parameters (ζ and ζ_jun, respectively). For this, we focus on topologically regular cubic networks built from “bead‐and‐spring” Rouse chains. Setting σ = ζ_jun/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.

     

Dynamic Mechanical Analysis and Molecular Mobility of the R-BAPB Type Polyimide

Summary: Dynamic mechanical experiments are performed to study molecular mobility of the R-BAPB type polyimide based on 1,3-bis-(3,3′,4,4′-dicarboxyphenoxy)benzene (R) and 4,4′-bis-(4-aminophenoxy)biphenyl (BAPB) with a molecular weight M_w ∼ 80 000 g/mol. Frequency dependences of the storage and the loss tensile moduli are measured within the temperature domain 199°C ≤ T ≤ 211°C that includes the glass transition temperature of the compound, T_g = 206°C. It is shown that the time-temperature superposition principle holds for the R-BAPB type polyimide. A theoretical analysis of the master curves constructed at T_ref = 204°C is performed on the basis of the piecewise-power-type distribution function of the relaxation times. Relaxation times for typical scales of motion inside polyimide macromolecules are calculated and the molecular weights of the characteristic kinetic units (the Kuhn segment and the chain fragment between entanglements) are estimated.     

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.     

Shear Dynamic Moduli of Stretched Polymer Chains and Networks: Modified Rouse Model

The dynamic mechanical properties of polymer chains and networks under large static strains are studied. Polymer chains are modeled as sequences of Gaussian subchains whose elasticity constants are different for motions parallel ( ) and perpendicular ( ) to the stretching force, f , and are functions of the elongation ratio (a modified Rouse model). The frequency‐dependent storage and loss shear moduli are shown to be different for different geometries under small oscillating shear deformation. Three principal geometries under shear deformation denoted by D‐, V‐ and G‐geometry (see the image) are considered. Static elongation leads to the broadening of the frequency dependencies of the loss moduli for all considered geometries. The predicted storage and loss moduli are in a good agreement with experimental data.