Solving the initial condition of the string relaxation equation of the string model for glass transition:part-Ⅱ

The string model for the glass transition can quantitatively describe the universal a-relaxation in glassformers. The string relaxation equation （SRE） of the model simplifies the well-known Debye and Rouse-Zimm relaxation equations at high and low enough temperatures, respectively. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the general initial condition of the SRE for stochastically spatially configurative strings is solved exactly based on the obtained special initial condition of the SRE for straight strings in a previous paper （J. L. Zhang et al. 2010 Chin. Phys. B 19, 056403）.

Solving the initial condition of the string relaxation equation of the string model for glass transition:part-I

The string model for the glass transition can quantitatively describe the universal a-relaxation in glassformers, including the average relaxation time, the distribution function of the relaxation time, and the relaxation strength as functions of temperature. The string relaxation equation （SRE） of the model, at high enough temperatures, simplifies to the well-known single particle mean-field Debye relaxation equation, and at low enough temperatures to the well-known Rouse-Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the special initial condition （SIC） of the SRE, i.e. for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics, was solved exactly. It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model, i.e. for stochastically spatially eonfigurating strings, as will be described in separate publications.

Calorimetric Studies on Enthalpy Relaxation in Maltitol Glass Transition Based on Phenomenological Models

To investigate the enthalpy relaxation behavior of maltitol glass system,differential scanning calorimetry（DSC） was used to obtain the specific heat capacity[C p（T）] near the glass transition temperature（T g） at different cooling rates ranged between 1 and 20 K/min.Three phenomenological models of enthalpy relaxation,ToolNarayanaswamy-Moynihan（TNM） model,Adam-Gibbs-Vogel（AGV） model and Gómez Ribelles（GR） model,were used to simulate the experimental data.The models＇ parameters were obtained via a curve-fitting method.The results indicate that TNM and AGV models gave the almost identical prediction powers and can reproduce the curves of experimental C p（T） very well.However,the prediction power of GR model evolved from configurational entropy approach is not so good as those of TNM and AGV models.In particular,the metastable limit state parameter（δ） introduced by Gómez Ribelles has insignificant effect on the enthalpy relaxation of the small molecular hydrogen-bonding glass system.

Effect of melt cooling rate on glass transition kinetics and structural relaxation of Vit1 metallic glass

The thin ribbons and the bulk cylindrical rods with diameters of 2 mm and 10 mm of the Vit1 metallic glass(MG)were prepared by the single roller melt spinning method and the copper mold injection casting method,respectively.The cooling rates of the samples during melt solidification were evaluated.The glass transition behaviors of three groups of MG samples with different solidification cooling rates were studied by differential scanning calorimetry(DSC)at different heating rates.The effects of melt cooling rate on the glass transition kinetic parameters such as apparent activation energy(E)and fragility parameter(m)of the Vit1 MG were studied using the Kissinger and the Vogel-Fulcher-Tammann(VFT)equations.Additionally,the structural relaxation enthalpy(ΔHrel)of three groups of MG samples was quantitatively analyzed by DSC through multi-step temperature rise and fall measurements.Results show that the melt cooling rate(R)has a significant effect on the glass transition kinetics and the structural relaxation of the Vit1 MG.As R decreases in the order of magnitude,the glass transition temperature(Tg),E,m,andΔHrel of the Vit1 MG gradually decreases.Furthermore,in the range of the experimental cooling rates,E,m,andΔHrel all have an approximately linear relationship with lgR.

Ultraslow Relaxation Process of Static Light Scattering Intensity by Boron Oxide above the Glass Transition Temperature

The data describing of the light scattering intensity relaxation above the glass transition temperature by boron oxide obtained by using of the temperature jump methods are presented. It is found that the stabilization of the glass at 220℃ resulted in increasing of the anisotropic intensity at the same time the isotropic intensity is not practically unchangeable. It is shown that after the temperature jump to 330℃the intensity is characterized by the formation of a maximum. This effect is in compliance with the results obtained for the other oxide glasses. It is established that characteristic time of the relaxation of the maximum height is about two orders of magnitude more than the structural relaxation time for this temperature.

Molecular dynamics simulation of relationship between local structure and dynamics during glass transition of Mg_7Zn_3 alloy

The rapid solidification process of Mg7Zn3 alloy was simulated by the molecular dynamics method. The relationship between the local structure and the dynamics during the liquid-glass transition was deeply investigated. It was found that the Mg-centered FK polyhedron and the Zn-centered icosahedron play a critical role in the formation of Mg7Zn3 metallic glass. The self-diffusion coefficients of Mg and Zn atoms deviate from the Arrhenius law near the melting temperature and then satisfy the power law. According to the time correlation functions of mean-square displacement, incoherent intermediate scattering function and non-Gaussian parameter, it was found that the β-relaxation in Mg7Zn3 supercooled liquid becomes more and more evident with decreasing temperature, and the α-relaxation time rapidly increases in the VFT law. Moreover, the smaller Zn atom has a faster relaxation behavior than the Mg atom. Some local atomic structures with short-range order have lower mobility, and they play a critical role in the appearance of cage effect in theβ-relaxation regime. The dynamics deviates from the Arrhenius law just at the temperature as the number of local atomic structures begins to rapidly increase. The dynamic glass transition temperature （Tc） is close to the glass transition point in structure （TgStr）.

Solid-state impedance spectroscopy studies of dielectric properties and relaxation processes in Na_(2)O–V_(2)O_(5)–Nb_(2)O_(5)–P_(2)O_(5) glass

Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary mixed glass former(MGF)system 35Na_(2)O–10V_(2)O_(5)–(55-x)P_(2)O_(5)–xNb_(2)O_(5)(x=0–40,mol%).The dielectric parameters,including the dielectric strength and dielectric loss,are determined from the frequency and temperature-dependent complex permittivity data,revealing a significant dependence on the Nb2O5 content.The transition from a predominantly phosphate glass network(x<10,region I)to a mixed niobate–phosphate glass net-work(10≤x≤20,region II)leads to an increase in the dielectric parameters,which correlates with the observed trend in the direct-cur-rent(DC)conductivity.In the predominantly niobate network(x≥25,region III),the highly polarizable nature of Nb5+ions leads to a fur-ther increase in the dielectric permittivity and dielectric strength.This is particularly evident in Nb-40 glass-ceramic,which contains Na_(13)Nb_(35)O_(94) crystalline phase with a tungsten bronze structure and exhibits the highest dielectric permittivity of 61.81 and the lowest loss factor of 0.032 at 303 K and 10 kHz.The relaxation studies,analyzed through modulus formalism and complex impedance data,show that DC conductivity and relaxation processes are governed by the same mechanism,attributed to ionic conductivity.In contrast to glasses with a single peak in frequency dependence of imaginary part of electrical modulus,M″(ω),Nb-40 glass-ceramic exhibits two distinct contributions with similar relaxation times.The high-frequency peak indicates bulk ionic conductivity,while the additional low-fre-quency peak is associated with the grain boundary effect,confirmed by the electrical equivalent circuit(EEC)modelling.The scaling characteristics of permittivity and conductivity spectra,along with the electrical modulus,validate time-temperature superposition and demonstrate a strong correlation with composition and modification of the glass structure upon Nb_(2)O_(5) incorporation.

Phases confirmation of cloudy Silwet L-77 aqueous solution by dielectric relaxation spectroscopy

The phase transition of Silwet L-77(a kind of siloxane surfactant) dilute aqueous solution with temperature was investigated by dielectric relaxation spectroscopy.In the initial heating process,a dielectric relaxation was found at about 10~6 Hz,which was considered as the interface polarization ascribed to the interface between water and liquid phases(W and L_1).With the temperature increasing further,a new dielectric relaxation was observed at about 10~4 Hz,which was assigned to the appearance of liquid crystal phase(L_α).According to the dielectric parameters fitted by Cole-Cole equation,the coexistence temperature of W,L_1 and L_αwas determined at about 37.0℃.

FOURIER TRANSFORM INFRARED STUDIES OF POLY (ETHYLENE TEREPHTHALATE) FILM IN THE GLASS TRANSITION REGION

Three specimens from a solution-cast poly (ethylene terephthalate) (PET) film, one being liquid-N_2 quenched from 92℃(Q), one being slowly cooled from 92℃(SC) and one being quenched and sub-T_g annealed at 67℃(AN), have been studied by specimen difference spectra Q-SC and AN-Q and temperature difference spectra T-70 and T_2-T_1 for every 2℃ steps on heating to 90℃ at 2℃ /min. SC and AN showed more gauche conformers than Q. That means that the PET chain has more trans conformers at higher temperatures and some of these are frozen during quenching through T_g. A band at 1340 cm^(-1) has been found to be complex containing overlapping bands reflecting trans in crystalline regions and trans in amorphous regions. The temperature difference spectra on heating through T_g showed that the spectral changes in Q are gradual while a rather abrupt change occurs in AN at 80—82℃ for the bands at 1340, 1042 and 1020 cm^(-1). No new conformational structure or new vibrational mode is involved. A kind of locking mechanism is suggested which hinders the molecular vibrational changes in AN below T_g until a sudden release occurs at T_g. These locking sites can be nothing else than sites of tighter local packing of chain segments. Consequently it is believed that inter-chain van der Waals attraction energy plays a dominating role in the volume relaxation and sub-T_g annealing of quenched amorphous polymers.

Preparation of polymer nanoparticles,and the effect of nanoconfinement on glass transition,structural relaxation and crystallization

In this review the preparation methods of polymer nanoparticles from chemical microemulsion polymerization to physical methods such as spray-drying,freeze-drying,freeze-extracting,fast evaporation and spreading evaporation have been summarized.The influence of nanoconfinement on glass transition temperature(T_(g))variation from significant or slight decrease,no evident T_(g) deviation,to even T_(g) increase,as well as possible explanations of T_(g) deviations were discussed.The influences of nanoconfinement or entanglement on the other properties such as structural relaxation,crystallization in polymer nanoparticle samples were also reviewed in this article.

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore,we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.

A new threshold of uncovering the nature of glass transition:The slow β relaxation in glassy states

The glass transition involves more than one dynamic relaxation mechanisms in supercooled liquids,such as α relaxation,slow β relaxation and fast β relaxation and so on.For the traditional theoretical system,α relaxation is believed mainly responsible for the nature of the glass transition as the beginning of the phenomenon.This idea,however,has been open to a big challenge since recent studies have indicated that slow β relaxation closely relates to α relaxation.Slow β relaxation determines the characteristics of α relaxation and is the precursor and the more microscopic base of glass transition behavior.In order to illuminate the significance of slow β relaxation in the fields of the glass transition and the structure of supercooled liquids,the accomplished progress is summarized from different aspects such as on the correlation between α relaxation and slow β relaxation,on the manner of α-slow β relaxation merging,on the energy landscape,on the excess wing and on the thermodynamically phenomenological models.The tendency of investigation in slow β relaxation is also evaluated.

Measurement scheme to detect α relaxation time of glass-forming liquid

A measurement scheme for detecting theαrelaxation time(τ)of glass-forming liquid is proposed,which is based on the measured ionic conductivity of the liquid doped with probing ions by low-and middle-frequency dielectric spectroscopy and according to the Nernst-Einstein,Stokes-Einstein,and Maxwell equations.The obtainedτvalues of glycerol and propylene carbonate by the scheme are consistent with those obtained by traditional dielectric spectroscopy,which confirms its reliability and accuracy.Moreover,theτof 1,2-propanediol in a larger temperature range is compared with existing data.

A Theoretical Interpretation of Free Volume at Glass Transition

We device a relaxed lattice model （RLM） to study the mechanism of glass transition, which unifies the cage- effects from particle-particle interaction and entropy. By analyzing entropy in RLM with considering the influence of interactions on equilibrium, we demonstrate that glass transition is a second-order phase transition. For a perfect one- dimensional linked particle system like linear polymer under normal pressure, the free volume at glass transition is rigorously deduced out to be 2.6%, which provides a theoretical basis for the iso-free volume of 2.5% given by Willian, Landel and Ferry （WLF） equation. Extending to system with dead particles linked with higher dimensions like branched or cross-linked chains under positive or negative pressure, free volume at glass transition is varied, based on which we construct a phase diagram of glass transition in the space of free volume-dead particle-pressure. This demonstrates that free volume is not the single parameter determining glass transition, while either dead particles like cross-linked points or external force fields like pressure can vary free volume at the glass transition.

Computer simulation studies of the influence of side alkyl chain on glass transition behavior of carbazole trimer

In this work,all-atom molecular dynamics simulations were employed to study the influence of the side alkyl chain on glass transition behavior of several carbazole trimers(CT) in a temperature range from 423 to 183 K.The glass transition temperatures were obtained from the break in the slope of the volume-temperature curves and found to agree with the experimental values.The short time dynamics of four CT molecules were probed by usingvelocity autocorrelation functions and mean-square displacements.The current studies showed that the dynamics of CT systems can be easily interpreted through the cage effect.Furthermore,the investigation of the torsional autocorrelation function and P_(2-state)/P_(3-state) functions showed that the rotational barriers of side chains can slow down the conformational relaxation and lead to stronger temperature dependence of conformational relaxation.The relaxation time,characteristic time of P_(2-state)(t) and P_(3-state)(t) functions were all found to have Arrhenius-type temperature dependence.

The effect of polyvinylpyrrolidone addition on microstructure,surface aspects,the glass transition temperature and structural strength of honey and coconut sugar powders

Deep knowledge of the microstructure and physicochemical properties of polymeric food systems,such as honey powders(HP)and coconut sugars(CS),has practical importance for industry and end users.This study investigated the effect of polyvinylpyrrolidone(PVP)addition on microstructure,roughness,glass transition,α-relaxation temperatures and structural strength(S)of anhydrous complex carbohydrates mixtures.The addition of PVP slightly increased the glass transition andα-relaxation temperature for HP and CS systems as high molecular weight components.Systems with PVP addition showed“stronger”behaviour according to the S approach.Polarized light,scanning electron and atomic force microscopies showed slight differences in transparency and shapes between controls and systems with PVP addition.Surface morphological changes and roughness were investigated in this study to provide insight into HP and CS particles’structural changes.Moreover,S-involved structural diagrams were built to determine S parameters for controlling the structural transformation of HP and CS systems with and without PVP addition.The results obtained in this work provide new information on polymer-carbohydrate interactions in complex food systems and structural transformations during their production and storage.

DIPOLE POLARIZATION RELAXATION AND MOLECULAR STRUCTURE OF MAIN-AND SIDE-CHAIN LIQUID-CRYSTALLINE POLYMERS

Molecular mobility in thermotropic polyesters and side-chain polymers with different struc-ture of mesogens and spacers has been studied by dielectrical method in dilutesolutions. The results made it possible to establish the multiplicity of dielectric relaxationtransitions which reflects the small- and large-scale types of molecular motion. It was shownthat dielectric relaxation processes occurring in accordance with local mechanism (relaxationtimes 10^(-9)--10^(-7)s. and the activation energy 10--50kJ/mol) are due to the mobility of kineticchain elements of different length within a monomer units. It was found that the dielectricrelaxation process connected with a large-scale form of molecular motion (relaxation times10^(-5)--10^(-6)s. and the activation energy 100kJ/mol) did not depend on the molecular massbut was infiuenced by factors changing the conformational state of the macromolecule. It isestablished tha the cooperative reorientation mobility of associated mesogenic fragments isthe source of the large-scale process.

Stretched Exponential Relaxation in Disordered Complex Systems： Fractal Time Random Walk Model

We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.

Dielectric and ferroelectric properties of Sr_4CaSmTi_3Nb_7O_(30) with tetragonal tungsten bronze structure

Sr4CaSmTi3Nb7O30 ceramics are synthesized and indexed as tetragonal tungsten bronze structure. The dielectric behavior and ferroelectric nature are investigated. Three dielectric anomalies are observed. The phase transition is a displacive phase transition with some diffusive characteristics, which indicates possible compositional variations within the materials on the microscopic scale. The weak distortion disappears in cooling process for differential scanning calorimetry measurement, and the large depression of Curie-Weiss temperature TO indicates the difficulty in forming macroferroelectric domain. The ferroelectric nature in these filled tungsten bronze niobates originates from the off-center displacement of B-site cations, but they are primarily dominated by A-site cation occupation. Both the radius and the valence of A1-site cations play an important role on ferroelectric properties of the filled tungsten bronze compounds. Existence of spontaneous polarization with a remanent polarization of 0.16 μC/cm^2 a coercive field of Ec = 11.74 kV/cm confirms the room-temperature ferroelectric nature of Sr4CaSmTi3Nb7O30 ceramics.