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The multilayer polymer system consisting of flexible chains units (subchains). The quasi- elastic constant E describes intrachain interactions provided by the kinematic connections of subchains in chains. The constant E 1 characterizes the chain bending rigidity. The constant E 2 defines the energy
Source publication
Dynamical equations for transverse and longitudinal mean projections of elastic-deformed kinetic chain units (Gaussian subchains) with anisotropic local intra- and interchain orientation interactions of dipolar type and spectra of relaxation times for large-scale motions of the chains in an isotropic and ordered state were obtained. The long-range...
Contexts in source publication
Context 1
... u n is a Cartesian projection of the vector r n ( u n , v n , w n ) directed along a kinetic chain unit, located in the knot n ≡ ( n 1 , n 2 , n 3 ), on the any direction in three-dimensional lattice ( Fig. 1). The first term in Eq. (1) with constant E is the energy of quasi-elastic interactions, which is introduced in terms of the Kargin – Slonimskii – Rouse models [7] and describes intrachain interactions provided by the kinematics connections of flexible units in chains. The second term in the potential (1) with the constant E 1 , as in the Hearst – Harris model [7], characterizes the chain bending rigidity, which is an indicator of orientational interactions of neighboring units in the chain. The third term in Eq. (1) with the constant E 2 describes an energy of local interchain orientational-deformation interactions of the dipolar type. The signs of the parameters of orientational interactions E and E are positive; as a result, the parallel orientations of neighboring units become preferential over the antiparallel orientations. For a calculation and analysis of conformational and dynamical characteristics of the chains in the given model it is comfortable to use dimensionless variables [6, ...
Context 2
... u n , v n and w n are Cartesian projections of the vector r n ( u n , v n , w n ). In Ref. [8], the temperature dependencies of the parameter of the dipolar order for thick films on the base of this model of nematic monodomain have been calculated. These dependencies were compared with the corresponding dependencies obtained in the mean- field approximation for the Ising model for ferromagnetics and the Langevin continuum model for ferroelectric materials as well as with the experimental data on the thermal depolarization in the films based on the vinylidene fluoride-trifluoroethylene copolymer. The order parameter μ = u n / l for the model [8] has been calculated as a function of film thickness (the length of chains) under certain boundary conditions for chain ends. The calculated values of the parameter μ have been compared with the values predicted by the phenomenological theory [9] and with the experimental data obtained from study of the polarization distribution in the ferroelectric films based on vinylidene fluoride [10]. On the other hand, it is known [11] that the PVDF films of finite thickness have a multilayer structure that is not a nematic type. They have the structure with planar orientational order when the chains are almost in the plane ( Fig. 1), and dipolar moments of fluoride groups are directed perpendicular to the plane. The main goal of the current study are (i) to obtain dynamical equations for transverse and longitudinal mean projections of elastic-deformed kinetic chain units (Gaussian subchains) with the anisotropic potential (1) of local intra- and interchain orientation interactions of dipolar type on the base on the three-dimensional multilayer model with planar orientational order to calculate relaxation spectra for large-scale motions of the chains in an isotropic and ordered state and (ii) to compare calculated dependences of relaxation times with the corresponding experimental data obtained by the dipolar polarization method in the investigation of switching times for block (3 d ) and ultrathin (2 d ) Langmuir oriented films based on copolymers of vinylidene fluoride [11]. The other goal of this study is to analyze dependence of the anisotropy of large-scale relaxation properties of the chains in the 3 d -multilayered systems (relative to the axis perpendicular to layers) on the chain bending rigidity, interchain interactions and the scale of its motion. Let us consider mean projections u n / l , v n / l and w n / l of the vector e n r n / l , directed along a kinetic chain, disposed in the site n ≡ ( n 1 , n 2 , n 3 ), on any direction in large system of long chains ( N 1 , N 2 , N 3 1) as dynamical variables for this model. Dynamical equations for these variables may be obtained on the base of generalization of methods of theory for individual isolated chains [7]. They are represented in the ...
Citations
... In the paper, we present computer modeling of a ferroelectric polymer brush attached to a flexible substrate, which models textile and other highly elastic materials. Our approach is based on the lattice models of polymers [9][10][11][12][13][14][15]. Let us note that from mechanical point of view, the similar models of surface meta-materials were considered in Refs. ...
... Within the framework of lattice multiparticle models of polymers [9][10][11][12][13][14], N 1 N 2 N 3 rigid kinetic elements of length l called rotators form a "quasi-lattice" ! n n 1 ; n 2 ; n 3 ð Þ , where indices n 1 , n 2 , n 3 take the following values: n 1 D 1; . . . ...
We carried out the computer simulation of the dependences of mechanical properties of a system consisting of flexible substrate and ferroelectric polymer coating on the degree of bending deformations and on temperature within hybrid discrete-continual model. The substrate is modeled as an elastic medium subjected to the Hooke law. For the description of interaction in the polymer coating, we proposed a discrete model based on Stockmayer potential. We demonstrated that the structural transition from the ordered ferroelectric state into depolarized one occurred with the increase of deformations, and the influence of the surface coating on the properties changes became negligible.
... Within the framework of multiparticle models of polymers [12][13][14][15][16][17] Energetic-type parameter K 1 along "longitudinal" curvilinear direction n 1 of quasi-lattice describes the longitudinal orientational interactions and determines mean cosine of the angle between neighbour kinematic units [12][13][14]. Energetic-type parameters K 2 and K 3 characterize orientational interactions of neighbour kinematic units in transversal interactions n 2 and n 3 of quasi-lattice [13,14]. ...
For a hybrid discrete-continual model describing a system which consists of a substrate and polymer coating, we provide computer simulation of its mechanical properties for various levels of deformations. For the substrate, we apply the elastic model with the Hooke law while for the polymeric coating, we use a discrete model. Here we use the Stockmayer potential which is a Lennard-Jones potential with additional term which describes the dipole interactions between neighbour segments of polymer chains, that is Keesom energy. Using Monte-Carlo method with Metropolis algorithm for a given temperature the equilibrium state is determined. We obtain dependencies of the energy, force, bending moment and Young's modulus for various levels of deformations and for different values of temperature. We show that for the increase of the deformations level the influence of surface coating on the considered material parameters is less pronounced. We provide comparison of obtained results with experimental data on deformations of crystalline polymers (gutta-percha, etc.)
Computer simulation of repolarization and inverse piezoeffect is realized by Monte-Carlo method in polymer ferroelectric materials, observed in AC electric field with different frequencies and amplitudes. For describing the interactions between the segments of polymer chains, Lennard-Jones potential was used with additional term describing exchange short-range orientational interactions. We investigate the influence of temperature and parameters of external electric field on the hysteresis curve area, which determines the absorption coefficient. It is shown that for ferroelectric systems there is a frequency of the external field, which accounts for the maximum absorptivity.
The influence of free surface on structural phase transitions from an ordered to a disordered state in thin ferroelectric films is investigated. The dependence of the order parameter on the distance from the free surface is calculated. It is shown that the effective thickness of the surface layer depends on the temperature of the film. Nearby the phase transition point, its thickness increases indefinitely.
The formation of polymer coating on a solid substrate is investigated by means of computer simulation (Monte-Carlo method). The sticking coefficient depending on different factors affecting the adhesion of monomer units is calculated. Mechanical properties are stimulated on the base of the hybrid discrete-continuous model, which describes the system consisting of flexible substrate and polymer coating. At different temperatures and intermolecular interactions constants, the dependencies of Young modulus on the deformation degree are calculated. Ferroelectric properties of the polymer coating depending on frequency and amplitude of external electric field, temperature and interchain interactions are investigated.
Composite system “polymer + metal” has been simulated by means of the Monte-Carlo method taking into account the influence of a double electric layer. Structural phase transitions in the polymer system are investigated. Dependences of the parameter of long-range orientation order on the reduced temperature at presence and absence of the metal are calculated. Influence of the metal surface and the quality of its treatment on the orientation order in the polymer coatings has been analyzed.
The orientational order and dynamic properties of macromolecules have been studied in two- and three-dimensional systems of polymer chains that are orientationally ordered on the level of elastically strained kinetic units (Gaussian subchains) with anisotropic local intra- and interchain interactions of the dipole type. The values of the order parameter as a function of the film thickness for the corresponding type of boundary conditions imposed on the ends of the film have been calculated, and a comparison with the phenomenological theory and experimental data on polarization distribution in ferroelectric films based on vinylidene fluoride has been performed. Equations of motion have been obtained for transverse and longitudinal mean projections of kinetic units and relaxation time spectra for large-scale motions of chains in the state with a planar order. The long-range order in three-dimensional layers leads to anisotropy of mean-square sizes and, therefore, to relaxation properties of chains in their orientational motions (with respect to the direction of ordering).
