The molecular-dynamics simulation of the structure and molecular mobility of an individual macromolecule of a fourth-generation carbosilane dendrimer with terminal cyanobiphenyl groups in a highly diluted chloroform solution in the range 213–323 K is performed. Upon a change in temperature, the dendrimer undergoes structural rearrangement that depends on the ability of terminal segments to penetrate into the dendrimer. At temperatures close to the boiling point of the solvent, aliphatic spacers of terminal segments can penetrate deep into the dendrimer. As temperature decreases, the terminal segments are grouped only on the surface of the molecule; this leads to a 45% increase in the number of solvent molecules in the treelike part of the macromolecule. These results make it possible to give a new interpretation of temperature effects previously observed in NMR experiments for dilute solutions of these macromolecules.

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.

The orientational mobility of segments in dendrimers are studied by the method of Brownian dynamics, and the results are analyzed in terms of an earlier proposed analytical theory. The orientational autocorrelation function for the cosine of an angle of segmental rotation in dendrimers of a given generation P 1 ( t ) is controlled by three relaxation processes with the corresponding relaxation times. Characteristic times and the contribution from the above processes to P 1 ( t ) are calculated. The first process refers to the local mobility of a selected segment; the second process, to the rotations of a dendrimer branch, which originates from the selected segment of a given generation; and the third process, to the rotation of a dendrimer macro-molecule as a whole. The proposed approach makes it possible to estimate the relaxation spectrum of a dendrimer by studying the orientational mobility of segments in different generations. The relaxation times can be used to describe various relaxation processes observed by different experimental methods, such as dielectric relaxation, NMR, dynamic birefringence, and polarized luminescence.

The theory for the deformation of a model macromolecule stretched by its ends under the action of high constant and low periodic forces is constructed. The macromolecule is composed of monomer units in three conformational states. The proposed theory describes the regime of a severe stretching of a macromolecule extended to a length close to its contour length, when its extension proceeds via conformational transitions between different states of monomer units. The structural parameters of the monomer unit are found to correlate with viscoelastic characteristics, which are calculated from the experimental results on the deformation of an individual macromolecule obtained by the frequency atomic force microscopy. For a monomer unit with three conformations, the force dependences of viscoelastic characteristics (effective coefficients of elasticity and friction) can show one or two minima. When the experimental dependences of the above parameters show two minima, the monomer unit can have three or more equilibrium states. With the knowledge of the viscoelastic characteristics of a macromolecule, it is possible to unequivocally estimate all structural parameters of a monomer unit for its three-state conformational model. When the force dependence of viscoelastic characteristics show only one minimum, the monomer unit can have two or more states and analysis of the corresponding viscoelastic characteristics at the minimum makes it possible to select between two- and three-state conformational models. Then, for the three-state model, experimental data allow the prediction of only equilibrium parameters of the monomer unit (position of the minima and energy); dynamic parameters (positions and height of barriers between equilibrium states) remain indeterminate. The proposed theory is used for the interpretation of the viscoelastic characteristics of dextran obtained by single-molecule AFM experiments. The three-state conformational model of a dextran unit is shown to agree better with the experimental data than with the two-state conformational model.

Viscoelastic models for the description of the relaxation characteristics of two identical swollen interpenetrating polymer networks with different topologies moving against the background of an external viscous medium are considered. Two dynamic models that differ in the character of mutual interaction between network junctions are proposed. According to the first model, viscoelastic interaction is assumed to be constant and provided by the entanglements between a junction of one network with eight symmetrically arranged junctions of the other network. The second model involves (i) the predominant interaction between multiple-network junctions most closely located owing to entanglements and (ii) a weaker interaction with more distant junctions of neighboring cells. For the systems composed of two interpenetrating networks, relaxation-time spectra and average inverse relaxation-time spectra are compared with the corresponding spectra and characteristic times for individual noninteracting regular networks. Both models can involve two branches of the relaxation spectrum. One branch is a collective branch corresponding to the motion of the double network, whose parameters are controlled by the constants of elasticity of each of the interacting networks as well as by the effective mutual viscoelastic interactions between networks. This low-frequency branch is characterized by a broad spectrum of relaxation times. The second branch is a high-frequency branch that is primarily provided by mutual local motions of two interacting networks. This branch is characterized by a comparatively narrow relaxation spectrum and depends on quasielastic constants, which describe network entanglements, and on the characteristic elasticity of each network. The second branch does not involve any infinitely long relaxation times for infinitely continuous networks.

The theory of orientational relaxation properties of certain individual segments in a dendrimer macromolecule depending on the generation number and the position of a given segment in the dendrimer was developed. The time dependence for the dipole moment after switching an electric field off and the frequency dependence of the permittivity for this segment were calculated, which are determined by the autocorrelation function P 1 of the average projection of the single element. The dielectric properties of the dendrimer at the random distribution of dipole moments (e.g., as a result of sorption of solvent polar groups on the macromolecule) are considered. The time and frequency dependences of the autocorrelation function P 2 for the mean squared projection of the single element that are detectable by means of some experimental techniques (NMR, luminescence, birefringence, etc.) were studied. The theory qualitatively agrees with both the computer simulation results on the autocorrelation function P 1 for the dendrimer macromolecules and the available experimental data on the dependence of orientational mobility for the terminal segments of the number of generations.

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.

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.

A theory of nuclear magnetic resonance relaxation of13C nuclei and nuclear Overhauser effect (NOE) of polymer networks with included rodlike particles is developed for the case when the length of each rod is comparable or greater than the average distance between neighboring crosslinks. The long-scale dynamics of the network is described by means of a regular cubic “coarse-grained” model. The effects of entanglements of long rods in the network are described by a quasi-elastic potential acting between rods and network fragments. The frequency dependences of 1/T 1C and NOE are calculated for the case when the internuclear vector is directed along each rodlike particle. The frequency dependences of 1/T 1C and NOE for rods included into a polymer network are shifted to high frequencies as compared with these dependences for free rods due to quasi-elastic interactions between rods and network fragments. At strongly different viscoelastic parameters of rods and network fragments, the frequency dependences of 1/T1C and NOE may have two maxima. The high-frequency maximum corresponds to localized motions of rods at immobile network domains. The low-frequency maximum is caused by involving rods in long-scale network motions. The intensity of the low-frequency maximum increases when the degree of interactions between rods and the network increases.

A theory of dielectric properties for dendrimer macromolecules containing polar groups is proposed. A dynamic model of a finite treelike network consisting of Gaussian subchains is proposed. Two existing types of macromolecules with dipole groups are considered: dendrimers consisting of elements with dipole groups and dendrimers containing dipole groups only in the last generation. The time dependence of the dipole moment after the field is switched off and the frequency dependence of the permittivity of dendrimer systems arc plotted for various numbers of generations and various functionalities. The relationship between the relaxation spectrum, on the one hand, and the actually measured time dependence of the dipole moment and frequency dependences of' the permittivity, on the other hand, is established for dendrimer systems. The differences between the dielectric properties of a dendrimer and those of a separate dendrimer branch with a quiescent initial branching junction are considered.

The coarse-grained dynamic model of a treelike network composed of freely jointed rods was used to theoretically study the dynamic properties of a dendrimer macromolecule. A relaxation spectrum was obtained for the model of the dendrimer with arbitrary functionality of junctions and an arbitrary number of generations; the spectrum characterizes both motions inside an extended network and pulsation of the dendrimer as a whole. It was shown that the relaxation-time distribution in the internal and external spectra is similar to that for a dendrimer composed of Gaussian subchains with the same functionality, number of generations, and the constant of external friction between network junctions, provided that the internal-friction term is introduced into its dissipation function.

The coarse-grained dynamic model of a treelike network composed of Gaussian chains was used to theoretically study the dynamic properties of the dendrimer macromolecule. A method was developed which does not require the secular determinant to be solved. The relaxation spectrum was obtained for the dynamic model of a dendrimer with an arbitrary functionality of junctions, taking into account friction due to the environment and friction between network junctions. A relaxation time spectrum was obtained both for motions inside an extended network and those in which the dendrimer pulsates as a whole. Distribution functions were calculated for both relaxation time spectra, and effects associated with mutual friction between network junctions were considered.

Macromolecular Chemistry and PhysicsVolume 203, Issue 7 p. 1040-1040 Book Reviews Molecular Order and Mobility in Polymer Systems Yu.Ya. Gotlib, Yu.Ya. GotlibSearch for more papers by this author Yu.Ya. Gotlib, Yu.Ya. GotlibSearch for more papers by this author First published: 06 May 2002 https://doi.org/10.1002/1521-3935(20020401)203:7<1040::AID-MACP1040>3.0.CO;2-EAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume203, Issue7April 2002Pages 1040-1040 RelatedInformation

The theoretical approach is developed to describe the dynamics of inhomogeneous cross-linked polymers consisting of cross-link agglomerations. An inhomogeneous polymer is treated as an ensemble of noninteracting cross-linked regions (domains) of different sizes. We model an internal architecture of the domains in a rather regular way and assume a power law decay of the relaxation modulus inside the domains, a decay usual for a broad class of cross-linked materials on microscopic scales. Assuming a broad size distribution of the domains in cross-linked polymers due to a random character of cross linking, we demonstrate a stretched exponential time behavior of the relaxation modulus on scales larger than the average size of inhomogeneities in the polymer. We apply this general approach to some special cases of cross-linked polymers, namely to polydisperse polymer networks, to inhomogeneous meshlike networks, and to inhomogeneously cross-linked polymeric gels.

Statistical and local relaxation properties of two-dimensional finite polymer systems (domains) are considered. The domains consist of a large number of semirigid chains with the finite contour length at free, half-free and fixed boundary conditions for chain ends. The intermolecular orientational order at short distances between chains in the thick domains is similar to the order in infinite two-dimensional systems. The correlations of orientation between sufficiently distant elements of different chains decay by the exponential law, but the effective constant of interchain interactions in the domain is proportional to the molecular weight of the chain. At the given intra-and interchain interactions an elongtation of the chains leads to a local ordering of chains in the domain (at free boundary conditions) or, on the contrary, to the decreasing of the parameter of short-range orientational order (at fixed and half-free boundary conditions). Independently of type of boundary conditions the parameter of large-range orientational order tends to zero with increasing of the chain contour length.Dynamical equations and relaxation spectrums for times of local motions are obtained. From time correlation functions of local relaxation the times of nano-scaled mobility of chains were calculated in depending on the bending rigidity of chains, the parameter of interchain interactions, and the contour length of chains. At the given intra-and interchain interactions an elongtation of chains forming the domain leads to to the slowing-down of local mobility of chains in the domain. The comparison with experimental date obtained by dielectric relaxation and polarized luminescence methods on investigation of nano-scaled mobility in the dilute melts of comb-shaped polymers has been carried out.

The Kerr effect in unstrained (isotropic) and preliminarily strained (anisotropic) polymer networks is theoretically studied within the framework of a model of a three-chain network with freely jointed chains between junctions. Also considered is the Kerr effect for macromolecules with a zero constant dipole moment, where the optically anisotropic chain segments are oriented in the external electric field due to the field-induced dipole moments. Dependence of the average difference ≡ <a∥- a⊥ of the chain segment polarizabilities in two principal directions (a∥ and a⊥-along and across the field, respectively) on the field strength is calculated. The birefringence parameters of preliminarily strained polymer networks exposed to strong electric fields can be used to evaluate the density of crosslinks. The electrooptical parameters of the polymer networks are compared to those of polymer solutions (melts), provided that the chain segments in both systems have identical chemical structures and equal molecular weights.

The Ngai model of cooperative dynamics is employed to describe the spin-lattice relaxation in a network polymer, A modified equation for the orientational correlation function of the vector connecting nuclei is proposed. The frequency and temperature dependences of the inverse spin-lattice relaxation time 1/T-1, are calculated. As the coupling parameter n (i.e,, the parameter characterizing the cooperativity of macromolecular dynamics) increases, the spectrum of relaxation times widens and its maximum shifts. The theory is compared with experimental data on the temperature dependence of 1/T-1 for fluorine nuclei in a cross-linked poly(heptafluorobutyl acrylate) with different content of the cross-linking agent.

The effective potential energy of intra-and interchain orientational interactions of two-dimensional ordered both infinite system and finite domain (Fig. 1.), like the corresponding Hamiltonian of anisotropic“quasi-lattice“ version of the classical plane-rotator Vaks-Larkin (1965) model, has the form 1 $$V_{ef} \{ \varphi _{n{\text{,}}m} \} = - K_l \mathop \Sigma \limits_{n{\text{,}}m} \cos (\varphi _{n{\text{,}}m} - \varphi _{n{\text{ - 1,}}m} ) - K_t \mathop \Sigma \limits_{n{\text{,}}m} \cos (\varphi _{n{\text{,}}m} - \varphi _{n{\text{,}}m - {\text{1}}} )$$

A theory of the Kerr effect (electro-optical birefringence) for polymer networks has been developed. The optical birefringence of polymers in the external electric field E is connected with orientation of optically anisotropic chain segments. The orientation of the segment due to induced dipole moment has been considered. The polarizability tensor of segment was assumed to be axial symmetrical with respect to axis of segment. The comparison of electro-optical properties of isotropic polymer networks with those of mechanically deformed networks has been made. The uniaxial mechanical deformed samples (both stretched and compressed) have been considered. Our theory corresponds to an experiment when the boundaries of the deformed sample are fixed so that the volume and the form of the sample remain constant after applying of the electric field (electrostriction effect is not taken into account). The particular case, when external electric field is directed parallel to the direction of mechanical deformation, has been studied.