Structure and dynamics of a bisurea-based supramolecular polymer in n-dodecane

The structure and dynamics of a supramolecular polymer formed by a bisurea-type compound, 2,4-bis(2-ethylhexylureido)toluene (EHUT), in an apolar solvent, n-dodecane (C12), were examined in detail. The EHUT/C12 organo-gel system forms long, dynamic chain-like supramolecular polymers, which lead to an entangled network showing remarkable viscoelastic behavior with two major relaxation modes. A slow relaxation mode with an approximately constant relaxation time, tauS, was observed in a flow region and the other, fast, relaxation mode with a time tauF1 (相似文献   

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.     

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(?) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.     

Dielectric relaxation spectroscopy and alignment behavior of a polymer‐dispersed liquid crystal and its component materials

The dielectric properties of a polymer‐dispersed liquid crystal (PDLC), a liquid‐crystal (LC) mixture (BL036), and three polymer matrices of PN314 containing different amounts of BLO36 were determined over a range of frequencies and temperatures and, for the LC and PDLC, over a range of voltages leading to homeotropic alignment of the LC. The overall dielectric relaxation process was a weighted sum of contributions from (1) the primary (δ) process in the LC arising from the motions of the dipoles about the short molecular axis and (2) dipole motions in the polymer matrix. The dielectric spectra were determined as a function of frequency, temperature, and, when appropriate, applied voltage. An equivalent electrical circuit was used as a working model to describe the dielectric behavior of the PDLC in the absence and presence of applied voltages. Agreement between the dielectric data and this model was achieved if a portion of the LC phase at the interface was assumed to be immobile. The director order parameter for the LC component in the PDLC was determined from dielectric measurements as the material was aligned homeotropically in an applied electric field. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1173–1194, 2001     

Dielectric Relaxation of Type‐A Polymers in Melts and Solutions

This article describes the dielectric relaxation behavior of flexible polymer chains having the so‐called type‐A dipoles parallel along the chain backbone. This behavior reflects the global chain motion. Viscoelastically well known features of this motion, such as the power‐law relationship between the relaxation time and molecular weight of entangled linear chains (τ₁ ∝ M^3.5), are also observed dielectrically. More importantly, the dielectric behavior of linear chains having once‐inverted type‐A dipoles enables us to find some detailed dynamic features such as changes in the eigenfunctions f_p of a local correlation function with the chain concentration in solutions. These changes are discussed in relation to motional coupling of concentrated chains. The dielectric properties detect the orientational correlation of two submolecules in the chain at two separate times, while the viscoelastic properties reflect the isochronal orientational anisotropy of individual submolecules. Thus the chain motion is differently averaged in the dielectric and viscoelastic properties, and comparison of these properties enables us to find novel dynamic features. Specifically, this comparison reveals the validity of the tube dilation molecular picture for entangled linear chains and weakening of the short‐time coherence of the submolecule motion due to the constraint release mechanism. Moreover, the dielectric method enables us to investigate the chain dynamics under strong flow and/or in a molecularly narrow space. In particular, the retarded dielectric relaxation found for homopolymers and block copolymers in such narrow spaces (in the microdomains for the latter) indicates important effects of the spatial and thermodynamic constraints on the global chain motion. All the above results in turn demonstrate the importance of the dielectric method in investigations of the polymer dynamics.     

Viscoelastic Effects on the Dynamics of Spinodal Decomposition in Binary Polymer Mixtures

Numerical simulations based on the modified time‐dependent Ginzburg‐Landau (TDGL) equation have been performed on the domain growth dynamics of binary polymer mixtures. An elastic relaxation term was introduced into the equation to take the entanglement effects of the polymer chains into account. A cell dynamical scheme (CDS) is employed in this paper to improve the computing efficiency. The dynamics of the phase separation in polymer blends was investigated through to a very late stage. In the system without viscoelastic effects, there exists an apparent early stage, and in the late stage the modified Lifshitz‐Slyozov law and dynamical scaling law are satisfied very well. In the system with viscoelastic effects, there are some unique characteristics. A morphology with a rough interface between the domains is obtained and suppression of order‐parameter fluctuations is observed. The growth behavior of domains was altered, and there exits an intermediate stage between the early and late stage, in which the growth rate of domains slows down drastically. The intermediate stage was prolonged with enhanced entanglement effects. Entanglement effects also enhance the quench‐depth effects on the correlation and diminish the discrimination of correlation induced by criticality. After the relaxation of entanglements, the growth exponents with the model employed in this paper are independent of entanglements and are essentially consistent with the modified Lifshitz‐Slyozov law. In addition, the pair correlation function and the structure function are shown to exhibit the dynamical scaling law at the late stage.     

Dielectric effects of step-increased pressure on the mass- and diffusion-controlled linear chain and network macromolecules growth

The dielectric properties of four stoichiometric liquid mixtures of a diepoxide with two monoamines and two diamines have been studied in real time during the mixture's polymerization isothermally to a linear-chain polymer in two cases and a network polymer in the other two cases, at 1 and 200 bar. The pressure was applied: (a) at the beginning of polymerization, (b) after a small extent of polymerization when the viscosity was low, and (c) after a relatively large extent of polymerization when the viscosity was high. For a fixed polymerization period, pressure increased the dielectric relaxation time much more than any other quantity in all cases, without a change in the distribution of relaxation times. Contributions to the dielectric permittivity and loss from physical and chemical effects have been considered and related to the changes in the dielectric relaxation time, viscosity and polymerization-rate constant as the extent of polymerization increased with time. Pressure is expected to decrease the polymerization rate for all conditions, but the decrease is relatively insignificant at the early stage, when polymerization is mass-controlled. Here other effects override the effect of viscosity increase, and the polymerization rate instead increases. The decrease in the rate becomes significant and predominates only when polymerization becomes diffusion-controlled. Since theories of diffusion-controlled reactions do not consider the mutual slowing of the molecular diffusion and the rate of chemical reactions leading to a macromolecule's growth until its vitrification isothermally, a method for determining the onset of diffusion control was needed. It is shown that this onset can be determined from plotting the rate of polymerization against the dielectric relaxation time. Expressed in terms of the dielectric loss, these plots cross each other. The cross-over point indicates the onset of diffusion control. Thus, the effect of pressure on the dielectric behaviour can be used to determine the change from mass-controlled to diffusion-controlled kinetics.     

Dynamics in water-AOT-n-decane microemulsions with poly(ethylene glycol) probed by dielectric spectroscopy

Water in oil microemulsions, consisting of water, AOT and n-decane, have been used as a model system to investigate the influence of the water soluble polymer PEO on the dynamical behavior of the system. Therefore dielectric relaxation spectroscopy and conductivity, extracted from dielectric spectroscopy, measurements in a wide frequency and temperature range have been applied. The pure microemulsion displays the known phenomenon of percolation that manifests in a steep increase of conductivity at the percolation temperature $T_\text{P}Water in oil microemulsions, consisting of water, AOT and n-decane, have been used as a model system to investigate the influence of the water soluble polymer PEO on the dynamical behavior of the system. Therefore dielectric relaxation spectroscopy and conductivity, extracted from dielectric spectroscopy, measurements in a wide frequency and temperature range have been applied. The pure microemulsion displays the known phenomenon of percolation that manifests in a steep increase of conductivity at the percolation temperature T_\textPT_\text{P}. The percolation temperature has been found to be strongly dependent on droplet volume fraction and droplet size. The latter additionally shows that percolation temperature and surfactant film rigidity are proportional. Far from percolation water-AOT-n-decane microemulsions display two dielectric relaxations. The slower one has a relaxation time of t ? 3·10^-6 \texts\tau \approx 3\cdot 10^{-6}~\text{s} and can be related to an interfacial polarization at the interface of the water core and the AOT shell (core relaxation). The faster one has a relaxation time of t ? 10^-9 \texts\tau \approx 10^{-9}~\text{s} and can be related to the ions in the AOT shell(shell or cluster relaxation). While the first is mainly untouched by the percolation phenomenon, the latter undergoes a slowdown and an increase of relaxation strength, both over about two decades, on approaching the percolation transition. Addition of PEO tremendously shifts the percolation transition to higher temperatures, due to adsorption at the AOT layer which leads to an increase in rigidity. Furthermore a lower phase boundary temperature evolves, below which the microemulsion phase separates. The conductivity of the microemulsion is also slightly increased with polymer. The effect on the dielectric properties is only small, where dielectric relaxation times are reduced by the polymer, while only the relaxation strength of the faster relaxation is influenced and also decreases with polymer. The decreased relaxation time of core relaxation can be either due to changes in the core to shell volume ratio or an increased conductivity of the water core. The decrease in relaxation time and strength of the shell relaxation suggest that the ion mobility in the shell increase, while the dipole moment is reduced. Additionally we applied a cluster relaxation model proposed by Cametti et al. (Phys Rev Lett 75(3):569, 1995) and Bordi et al. (J Phys, Condens Matter 8:A19, 1996) to estimate the cluster size evolution.     

Interactions between Hydrophobically Modified Associating Polyacrylamide and Cationic Surfactant at the Water‐Octane Interface: Interfacial Dilational Viscoelasticity and Relaxation Processes

The interfacial dilational viscoelastic properties of hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2‐ethylhexyl acrylate (EHA) (<1.0 mol%) with a hydrolyzed degree of about 1.5–2.0% at the octane‐water interfaces were investigated by means of two methods: the interfacial tension response to sinusoidal area variations (oscillating barriers method) and the relaxation of an applied stress (interfacial tension relaxation method) respectively. The influence of cationic surfactant cetyl trimethylammonium bromide (CTAB) on the dilational viscoelastic properties was studied. The results obtained by oscillating barriers method showed that dilational modulus decreased moderately with the increase of CTAB concentration. The results obtained by interfacial tension relaxation measurements showed that two main relaxation processes exist in the interface at 7,000 ppm polymer concentration: one is the fast process involving the exchange of hydrophobic blocks between the proximal region and distal region in the interface; the other is the slow relaxation process involving conformational changes of polymer chain in the interface. By adding CTAB, the slow process changed obviously due to the strong electrostatic interaction between oppositely charged surfactant and hydrolyzed part of polymer chain. Only when the CTAB concentration was close to the “equal charge point,” the associations formed mainly by the hydrophobic interaction like that in SDS/polymer system appeared and the characteristic time of fast process decreased obviously. The information of relaxation processes obtained from interfacial tension relaxation measurements can explain the results from dilational viscoelasticity measurements very well.     

Dispersions of polymer ionomers: I

The principal subject discussed in the current paper is the effect of ionic functional groups in polymers on the formation of nontraditional polymer materials, polymer blends or polymer dispersions. Ionomers are polymers that have a small amount of ionic groups distributed along a nonionic hydrocarbon chain. Specific interactions between components in a polymer blend can induce miscibility of two or more otherwise immiscible polymers. Such interactions include hydrogen bonding, ion-dipole interactions, acid-base interactions or transition metal complexation. Ion-containing polymers provide a means of modifying properties of polymer dispersions by controlling molecular structure through the utilization of ionic interactions. Ionomers having a relatively small number of ionic groups distributed usually along nonionic organic backbone chains can agglomerate into the following structures: (1) multiplets, consisting of a small number of tightly packed ion pairs; and (2) ionic clusters, larger aggregates than multiplets. Ionomers exhibit unique solid-state properties as a result of strong associations among ionic groups attached to the polymer chains. An important potential application of ionomers is in the area of thermoplastic elastomers, where the associations constitute thermally reversible cross-links. The ionic (anionic, cationic or polar) groups are spaced more or less randomly along the polymer chain. Because in this type of ionomer an anionic group falls along the interior of the chain, it trails two hydrocarbon chain segments, and these must be accommodated sterically within any domain structure into which the ionic group enters. The primary effects of ionic functionalization of a polymer are to increase the glass transition temperature, the melt viscosity and the characteristic relaxation times. The polymer microstructure is also affected, and it is generally agreed that in most ionomers, microphase-separated, ion-rich aggregates form as a result of strong ion-dipole attractions. As a consequence of this new phase, additional relaxation processes are often observed in the viscoelastic behavior of ionomers. Light functionalization of polymers can increase the glass transition temperature and gives rise to two new features in viscoelastic behavior: (1) a rubbery plateau above T(g) and (2) a second loss process at elevated temperatures. The rubbery plateau was due to the formation of a physical network. The major effect of the ionic aggregate was to increase the longer time relaxation processes. This in turn increases the melt viscosity and is responsible for the network-like behavior of ionomers above the glass transition temperature. Ionomers rich in polar groups can fulfill the criteria for the self-assembly formation. The reported phenomenon of surface micelle formation has been found to be very general for these materials.     

Rheological properties of polymer melts

A new method of treating experimental data on the viscous and viscoelastic properties of various polymer melts is suggested. The dependence of the apparent viscosity on the molecular weight, temperature and shear stress can be represented as the product of three independent functions, each of them having a single argument. All three functions are universal, at least in first approximation, and the dependence of the apparent viscosity on the variables indicated is determined by two parameters (glass transition temperature and critical molecular weight), characteristic of each homologous polymer series. The viscoelastic characteristics (dynamic, relaxation, creep, as well as relaxation and retardation spectra) of polymer melts are universal in shape in the linear region and contain only one individual polymer parameter, viz., maximum Newtonian viscosity. It is shown that upon normalization of certain nonlinear characteristics with respect to the maximum Newtonian viscosity, they can also be represented in the universal form.     

Viscoelastic response of elastomers in large deformations

A simple nonlinear theory of viscoelasticity has been developed for application to elastomers. The interpretation of nonlinear viscoelastic responses based on Gibbs-DiMarzio theory has been identified at a molecular level and hence structural understanding has been established. The introduced model is applied to strain imposed conditions. From this, a relaxation process has been revealed for the resultant stress, where a dependence of relaxation time on the state of strain has been established.     

Use of a cooperative-motion domain model to analyze brillouin light scattering measurements of the dynamic modulus in triblock copolymers

The use of the relaxation function is widespread in the study of polymer dynamics. Since the popular empirical KWW relaxation function consistently underestimates dielectric loss at high frequency, several models dealing explicitly with intermolecular cooperativity have been proposed as alternatives. In this article, the domain model proposed by Matsuoka, previously used only to analyze dielectric relaxation results, is used to analyze Brillouin light scattering results from polystyrene–polybutadiene–polystyrene triblock copolymers. A single relaxation time analysis and the KWW model are both compared to the domain model. Neither of these models fits the Brillouin data well. The single relaxation time analysis gives a physically unrealistic results; the KWW analysis fits the data at low frequency, but fails in the high-frequency region by underestimating the attenuation. The domain model fits the Brillouin data well over the entire temperature/frequency range. The results show that in order to understand the full range of dynamics in these materials and in polymeric materials in general, the KWW model is insufficient due to its underestimation of attenuation at high frequency. A model including cooperative motion is crucial to fully understand polymer dynamics. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2170–2178, 2000     

Similarity of the relaxation modulus of polydisperse polymers

A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.     

Dielectric relaxation in proteins: a continuum electrostatics model incorporating dielectric heterogeneity of the protein and time‐dependent charges

A boundary element formulation of continuum electrostatics is used to examine time‐independent dielectric relaxation and screening in two proteins, and time‐dependent relaxation in two simpler solutes. Cytochrome c oxidation is modeled by inserting partial charges on the heme, using one to three dielectric regions in the protein. It was suggested recently that for charge insertion on a protein‐bound ligand, all or part of the ligand should be treated as a cavity within the protein medium. Here, the effect of an internal cavity surrounding the central heme atoms is examined, considering separately the static and relaxation (or reorganization) free energies. The former is the free energy to remove the redox electron while maintaining the rest of the structure and charge distribution fixed; the latter is the free energy associated with the relaxation into the product state after the corresponding constraints are released. The effect of the cavity is found to be small for the static free energy, while for the relaxation free energy it is large, as polarization of groups immediately around the heme dominates the relaxation. If the protein surface groups are treated as a distinct medium with a dielectric of 25 (as suggested by recent molecular dynamics simulations), the relaxation free energy decreases significantly (from −37.0 to −43.9 kcal/mol), compared to a model where the whole protein has a dielectric constant of two. Therefore, with this model, although polarization of groups immediately around the heme still dominates the relaxation, polar groups near the protein surface also contribute significantly, and solvent negligibly. The screening of an applied field within myoglobin is calculated, with the protein surrounded by either a low‐dielectric or a high‐dielectric glass. In the vicinity of the CO ligand, the screening is approximately isotropic with a low‐dielectric glass. It is anisotropic with a high‐dielectric glass, but the applied and local fields are still approximately parallel. This has implications for experiments that probe dielectric screening in proteins with the newly developed technique of vibrational Stark spectroscopy: with a high‐dielectric glass, a single, rotationally averaged screening factor can be used, the local field being about 1.65 times the applied field. Finally, we calculate the time‐dependent relaxation in response to instantaneous charge insertion within a spherical cavity in a Debye solvent, and to photoexcitation of a tryptophan solute, illustrating the extension of the boundary element formulation to time‐dependent problems. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 290–305, 2001     

Response times and voltages for PDLC light shutters

The response times and operating voltages of light shutters formed from polymer dispersed liquid crystals (PDLCs) have been studied experimentally and the results compared with calculations based on non-sperhically shaped nematic droplet models. The experiments were performed on light shutters with elongated and uniformly aligned droplets where the relaxation time and voltage response were measured. It is shown that the droplet shape can be a dominant factor, particularly for the relaxation time, and the data are compared with equations derived in terms of the aspect ratio of the droplet l = a/b, where a and b are the lengths of the semi-major and semi-minor axes, respectively, of the elongated droplet. It is further demonstrated that the electric field inside the droplet can be considerably smaller than the applied field, due to the conductivity and dielectric properties of the polymer and liquid crystal materials. These data are used to obtain values for the ratio of the conductivities of the polymer binder and liquid crystal droplet, as well as the anisotropy of the conductivity in the liquid crystal.     

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.