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.     

Dielectric relaxations in bilayer structures of comb-like copolymers: Perfluoralkyl and liquid-crystalline side chains

Abstract : A series of comb-like copolymers and homopolymers containing different liquid-crystalline and perfluoralkyl side chains was studied by frequency and temperature dependent dielectric measurements. The structure and the phase behaviour of the systems were characterized by X-ray scattering and differential scanning calorimetry. The dielectric relaxation spectra of these polymers reflect the molecular mobility in bilayer structures formed by the mesogenic or crystalline side chains. By changing temperature it was possible to investigate the molecular motions in the different phases of the copolymers (smectic-crystalline, smectic-isotropic, and isotropic). The homopolymer containing perfluoralkyl side chains and all copolymers show a β-relaxation at low temperatures, which is assigned to local molecular motions. Above the glass transition temperature, all samples exhibit a segmental (α) relaxation with WLF-like temperature dependence in the activation plots. For the polymers forming LC structures only one relaxation process was detected in all phases, i.e. in the smectic, nematic, and isotropic structure or, in case of the copolymers, in the smectic-crystalline and smectic-isotropic double structures. This process was attributed always to the segmental motions, assisted by tumbling motions of the mesogens. The phase transitions are clearly indicated by discontinuities in the dielectric relaxation times and changes in the relaxation strength Δϵ. The dipole reorientations of the mesogens seem to be more restricted by the crystalline layers in the copolymers as by the smectic order of the LC homopolymers.     

Dielectric behavior of some ferrofluids in low-frequency fields

The dielectric behavior of a ferrofluid with magnetite particles dispersed in kerosene was analyzed taking into account the Schwarz model, concerning the low-frequency dielectric behavior in systems consisting of colloidal particles suspended in electrolytes. For this reason, the complex dielectric permittivity and dielectric loss factor, in the frequency range of 10 Hz-500 kHz, at different temperatures between 20 degrees C and 100 degrees C were measured. Based on these experimental results, the experimental dependencies on both temperature of the relaxation time and activation energy of the relaxation process were analyzed. The obtained results show that the Schwarz model can be applied, in order to explain the low-frequency dielectric behavior of a ferrofluid with magnetite particles in kerosene, if the change of counterion concentration at the surface of colloidal particles is taken into account. Consequently, it is shown that the dielectric spectroscopy can be used in order to analyze the presence of particle agglomerations within ferrofluids.     

Collective contributions to the dielectric relaxation of hydrogen-bonded liquids

Dielectric relaxation times are often interpreted in terms of the reorientation of dipolar species or aggregates. The relevant time correlation function contains, however, cross terms between dipole moments of different particles. In the static case, these cross terms are accounted for by the Kirkwood factor g(K). Theories and molecular dynamics simulations suggest that such cross correlations may also affect the time-dependent properties, as reflected in the dielectric spectra. We present an experimental method for detecting effects of such cross correlations in dielectric spectra by a comparative analysis of dielectric and magnetic relaxation data. We demonstrate that such collective contributions can substantially affect dielectric relaxation. Experiments for n-pentanol (g(K)=3.06 at 298 K) and 2,2-dimethyl-3-ethyl-pentane-3-ol (g(K)=0.59) and their solutions in carbon tetrachloride show that in systems with g(K)>1, the cross correlations slow down dielectric relaxation. In systems with g(K)<1, dielectric relaxation is enhanced. The results conform to theoretical predictions by Madden and Kivelson [Adv. Chem. Phys. 56, 467 (1984)] and to results of molecular dynamics simulations. The relaxation enhancement by cross terms in the case of g(K)<1 is difficult to rationalize by conventional models of dielectric relaxation.     

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 aqueous solutions of hydrophilic versus amphiphilic peptides

We report on molecular dynamics simulations of the frequency-dependent dielectric relaxation spectra at room temperature for aqueous solutions of a hydrophilic peptide and an amphiphilic peptide at two concentrations. We find that only the high-concentration amphiphilic peptide solution exhibits an anomalous dielectric increment over that of pure water, while the hydrophilic peptide exhibits a significant dielectric decrement. The dielectric component analysis carried out by decomposing these peptide solutions into peptide, hydration layer, and outer layer(s) of water clearly shows the presence of a unique dipolar component with a relaxation time scale on the order of approximately 25 ps (compared to the bulk water time scale of approximately 11 ps) that originates from the interaction between the hydration layer water and the outer layer(s) of water. Results obtained from the dielectric component analysis further show the emergence of a distinct and much lower frequency relaxation process for the high-concentration amphiphilic peptide compared to the hydrophilic peptide due to strong peptide dipolar couplings to all constituents, accompanied by a slowing of the structural relaxation in all water layers, giving rise to time scales close to approximately 1 ns. We suggest that the molecular origin of the dielectric relaxation anomalies is due to frustration in the water network arising from the amphiphilic chemistry of the peptide that does not allow it to reorient on the picosecond time scale of bulk water motions. This explanation is consistent with the idea of the "slaving" of residue side chain motions to protein surface water, and furthermore offers the possibility that the anomalous dynamics observed from a number of spectroscopies arises at the interface of hydrophobic and hydrophilic domains on the protein surface.     

Dielectric relaxation behavior of colloidal suspensions of palladium nanoparticle chains dispersed in PVP/EG solution

Dielectric measurements were carried out on colloidal suspensions of palladium nanoparticle chains dispersed in poly(vinyl pyrrolidone)/ethylene glycol (PVP/EG) solution with different particle volume fractions, and dielectric relaxation with relaxation time distribution and small relaxation amplitude was observed in the frequency range from 10(5) to 10(7) Hz. By means of the method based on logarithmic derivative of the dielectric constant and a numerical Kramers-Kronig transform method, two dielectric relaxations were confirmed and dielectric parameters were determined from the dielectric spectra. The dielectric parameters showed a strong dependence on the volume fraction of palladium nanoparticle chain. Through analyzing limiting conductivity at low frequency, the authors found the conductance percolation phenomenon of the suspensions, and the threshold volume fraction is about 0.18. It was concluded from analyzing the dielectric parameters that the high frequency dielectric relaxation results from interfacial polarization and the low frequency dielectric relaxation is a consequence of counterion polarization. They also found that the dispersion state of the palladium nanoparticle chain in PVP/EG solution is dependent on the particle volume fraction, and this may shed some light on a better application of this kind of materials.     

NMR studies of sorption and adsorption phenomena in colloidal systems

NMR methods provide chemically selective tools, particularly suitable to detect the molecular environment of molecular species in micro-heterogeneous materials. They are consequently applied to solve many questions in colloid science. The present review covers NMR studies of molecular adsorption onto particle surfaces as well as sorption into colloidal particles. Various methods ranging from liquid or solid state spectral analysis over spin relaxation to pulsed field gradient diffusion NMR have been employed in this field, monitoring either the chemical environment or the restricted dynamics of adsorbed or encapsulated guest molecules. Adsorption systems include surfactant layers, stabilizing ligands, small molecules, polymer layers or polyelectrolyte multilayers at the surface of various types of particles. Sorption into colloidal particles and detection of their position in specific compartments of the colloid are particularly relevant in systems employed as colloidal carriers, such as micelles, vesicles, or hollow polymeric capsules. With guest molecules considered as model compounds for drugs these studies have large relevance for the development of nanoparticle drug delivery systems.     

Wide-frequency-range dielectric response of polystyrene latex dispersions

In this work we analyze the dielectric properties of dilute colloidal suspensions of nonconducting spherical particles with a thin electrical double layer from experimental data obtained by performing impedance spectroscopy experiments over a broad frequency range, from 20 Hz to 1 GHz. The electrode polarization correction was made by fitting a circuit model in the complex impedance plane (impedance spectrum) using a constant phase angle (CPA) element to fit the electrode polarization in series with the sample impedance. This simple procedure is found to be effective in eliminating the electrode contribution. The dielectric response shows two different dispersions, the alpha relaxation (counterion relaxation) that occurs at low kilohertz frequencies, and the delta relaxation (Maxwell-Wagner effect) found in the MHz range. These are reasonably well fitted over a broad frequency range by the theoretical expressions given by a simplified standard model (not including anomalous conduction) and a generalized model (including anomalous conduction) for the low-frequency dispersion, plus Maxwell-Wagner-O'Konski theory for the delta relaxation in the mid-frequency range. An analysis was also made of the need to include, for these latices, the effects of ion mobility in the Stern layer in order for the values of the zeta-potential obtained from electrophoretic and dielectric data to be compatible with each other.     

An investigation of patterning anisotropic gels for switchable recordings

A new kind of anisotropic gel has been produced by photopolymerization of liquid crystal (LC) mixtures composed of monoacrylates, diacrylates and non-reactive conventional LC molecules. After polymerization, lightly cross-linked anisotropic polymer networks swollen by the non-reactive molecules are produced. These systems showed a gel-point associated with the onset of the formation of a three dimensional network. Above this point, a rapid increase in the threshold voltage was observed. Various factors, such as the photoinitiator concentration and the monoacrylate and diacrylate concentrations, as well as the intensity of the light used for the polymerization, have a strong influence on the gel-point. The switching kinetics of the materials are also strongly influenced by the aforementioned parameters. Two relaxation processes were found to occur within the gels above the gel-point. Using dielectric spectroscopy, this behaviour was found to be associated with an inhomogeneous phase structure within the gels. Patterned irradiation was used to produce regions with different threshold voltages for switching. In this way, patterns were created in the gels, which become visible, by the application of an electric field. It was demonstrated that this technique can be used to produce switchable gratings, Fresnel lenses, and photographs.     

An investigation of patterning anisotropic gels for switchable recordings

A new kind of anisotropic gel has been produced by photopolymerization of liquid crystal (LC) mixtures composed of monoacrylates, diacrylates and non-reactive conventional LC molecules. After polymerization, lightly cross-linked anisotropic polymer networks swollen by the non-reactive molecules are produced. These systems showed a gel-point associated with the onset of the formation of a three dimensional network. Above this point, a rapid increase in the threshold voltage was observed. Various factors, such as the photoinitiator concentration and the monoacrylate and diacrylate concentrations, as well as the intensity of the light used for the polymerization, have a strong influence on the gel-point. The switching kinetics of the materials are also strongly influenced by the aforementioned parameters. Two relaxation processes were found to occur within the gels above the gel-point. Using dielectric spectroscopy, this behaviour was found to be associated with an inhomogeneous phase structure within the gels. Patterned irradiation was used to produce regions with different threshold voltages for switching. In this way, patterns were created in the gels, which become visible, by the application of an electric field. It was demonstrated that this technique can be used to produce switchable gratings, Fresnel lenses, and photographs.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

Dynamic and static light scattering study on the sol-gel transition of resorcinol-formaldehyde aqueous solution

Structure formation during the sol-gel transition of resorcinol-formaldehyde (RF) solutions was traced by dynamic light scattering (DLS) and static light scattering (SLS) techniques. The decay time spectra obtained by DLS revealed that both the growth rates of colloidal particles formed during the early stage of the sol-gel transition and the time required for the colloidal particles to form a firm network structure could be related to the ratio of catalyst to water (C/W) of the starting RF solution. SLS results indicated that the molecular weight of colloidal particles increased with the progress of the sol-gel transition, the rate of which was also affected by the value of C/W. The mesoporosity of RF aerogels, which were prepared by drying RF hydrogels with supercritical carbon dioxide, was confirmed to depend on the size of colloidal particles estimated from the decay time spectrum collected at the last stage of the sol-gel transition.     

Dielectric relaxations of ionic thiol-coated noble metal nanoparticles in aqueous solutions: electrical characterization of the interface

The radiowave dielectric properties of organothiol monolayer-protected Au and Ag metallic nanoparticles have been investigated in the frequency range of 10 kHz to 2 GHz, where a dielectric relaxation, due to the polarization of the ionic atmosphere at the aqueous interface, occurs. The simultaneous measurement of the particle size, by means of dynamic light scattering technique, and of the particle electrical charge, by means of laser microelectrophoresis technique, allow us to describe the whole dielectric behavior at the light of the standard electrokinetic model for charged colloidal particles. Au and Ag metallic nanoparticles experience a large charge renormalization, in agreement with the counterion condensation effect for charged spherical colloidal particles. The value of the effective valence Z(eff) of each nanoparticle investigated has been evaluated thanks to the dielectric parameters of the observed relaxation process and further confirmed by direct current electrical conductivity measurements. All in all, these results provide support for the characterization of the electrical interfacial properties of metallic nanoparticles by means of dielectric relaxation measurements.     

The Local and Collective Mobility in Polymer Chains and Networks with Included Rigid Particles Elastically Connected with the Network

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.     

Studies of molecular relaxation of poly(propylene oxide) solutions by dielectric relaxation and brillouin scattering

Dielectric relaxation and Brillouin scattering are jointly used in studying molecular relaxation in poly(propylene oxide) (PPO) and its solutions in methylcyclohexane. The dielectric method was applied to the more concentrated (100%, 80%, 60%, by volume) solutions over a wide temperature and frequency range (30 Hz to 8 GHz) in order that the variation in activation energy characteristic of a glass-forming substance could be delineated. The present work extends previous work on the undiluted polymer to higher frequencies so that range of 12 decades in the dielectric loss maximum f_max as a function of temperature is now available. The “Antoine” equation is found to represent the behavior of log f_max, of the bulk concentrated solutions very well. The more dilute (40%, 20%) solutions were studied only in the high-frequency (GHz) region since phase separation occurred at low temperatures. Both the temperature and dilution effects were interpreted in terms of free-volume theory. Brillouin scattering spectra were obtained at several scattering angles and a wide range of temperatures. A maximum in the curve of hypersonic attenuation versus temperature was observed in each polymer solution. The attenuation maximum shifts toward lower temperature upon dilution, in agreement with the dielectric relaxation result. The Brillouin scattering follows different activation parameters and evidences a more rapid process than does the dielectric relaxation. It is speculated that it monitors a secondary or subglass relaxation, due perhaps, to damped torsional oscillations.     

Microwave dielectric spectra and molecular relaxation in formamide-N,N-dimethylformamide binary mixtures

The dielectric dispersion and absorption spectra of formamide (FA), N,N-dimethylformamide (DMF) and their binary mixtures are investigated in the frequency range of 500 MHz to 20 GHz at 30 °C in view of the organic synthesis by microwaves heating using amides solvents. The concentration dependent values of molecular reorientation relaxation times lower than that of the ideal mixing behaviour have been attributed to the cooperative dynamics of H-bonded FA–DMF structures. The molar ratio of stable adduct is 2:1 of FA to the DMF, which is determined from the concentration dependent excess static dielectric constant and the relaxation time plots of these binary mixtures. Electrode polarization effect and ionic conduction in FA and DMF were investigated from their dielectric dispersion spectra in the low frequency region of 20 Hz to 1 MHz.     

Dynamics of the surface layer in cyanobiphenyl-aerosil nanocomposites with a high silica density

Composites were prepared from an aerosil and 4-n-alkyl-4'cyanobiphenyls with five to eight carbon atoms in the alkyl chain. Their high silica density of ∼7 g aerosil in 1 cm³ of liquid crystal (LC) allows the observation of the behaviour of a thin cyanobiphenyl layer (having nearly a monolayer structure) on the silica particles. The systems are investigated by dielectric spectroscopy (10^-2-10⁹ Hz) in a large temperature range (220-370 K). All the composites show a (main) relaxation process at frequencies much lower than the processes observed for the bulk LC that was assigned to the dynamics of the molecules in the surface layer. The temperature dependence of its characteristic frequencies obeys the Vogel-Fulcher-Tammann law, which is found to be typical for glass-forming liquids. The quasi two-dimensional character of the glass transition in the surface layer is discussed for the first time. At the nematic-to-isotropic transition temperature of the bulk, the composites show a continuous decrease of the characteristic frequencies as a function of the alkyl chain length, while the bulk LCs show the well known odd-even behaviour. The magnitude and temperature dependence of the slow relaxation process in the composites (molecules on an outer surface) agree with those of the same molecules confined to the nanopores of molecular sieves (internal surface).     

Electric field induced AC alignment and realignment, a study of a liquid-crystalline copolymer having longitudinally and laterally attached mesogenic groups as side chains monitored through dielectric spectroscopy and optical thermomicroscopy

A study of a liquid crystal side chain copolymer with a siloxane backbone has been carried out using dielectric relaxation spectroscopy and optical microscopy. We have found that this particular copolymer, a mixture of longitudinally and laterally attached mesogens, can be aligned both homeotropically and planarly between two electrodes using a directing AC field of specific frequency by cooling from the melt or more importantly at temperatures below the clearing point (T_c). The switching of the material from homeotropic to planar and the reverse has been studied at temperatures below T_c. It is shown that the kinetics of realignment are strongly dependent on the electrical/thermal history of the sample. The dielectric data allows the state of alignment of the sample to be monitored and the molecular dynamics to be studied. The optical textures of the polymer which were subjected to different AC electric fields have been observed and provide complementary information to the dielectric work on the state of the aligned sample.     

Possible Influence of Layer Deformation and Chiral Segregation on Dielectric Modes in the Dark Conglomerate Liquid Crystal

Dielectric spectroscopy is used to investigate the structure, molecular dynamics, and relaxation phenomena in electric‐field‐induced switchable dark conglomerate (DC) phases in a bent‐core liquid crystal. The DC phases are obtained by applying a high‐frequency ac electric field in the B_1rev phase or by cooling under a dc or an ac field from the isotropic phase. Although the DC phases exhibit good electro‐optic switching properties, the dielectric parameters are different from those observed in typical lamellar SmCP phases and similar to those obtained in a non‐switchable DC phase. We therefore propose that the dielectric response and reduced intensity of the relaxation modes may be a general feature in DC phases and may owe its origin to the deformed layer structure in which certain molecular motions are impeded. Further, we find that in the field‐induced DC phases derived from the isotropic phase, the dielectric modes are affected by chiral segregation promoted by the applied field.