Structural Relaxation Model Research Articles

Role of fictive temperature distribution involved in CO2 laser polishing of fused silica and its optimization for achieving even heat-affected zones

CO2 laser polishing process is a highly effective way for enhancing the surface quality and laser-induced damage threshold of fused silica optics. Nevertheless, due to the thermal history and spatial gradient of the thermodynamic temperature, the heat-affected zones can be formed unevenly on the surface with an increased fictive temperature, which causes the material densification and residual stress. In this work, a 3D model of structural relaxation coupled with temperature and flow fields was innovatively established to explore the role of fictive temperature distribution involved in CO2 laser polishing of fused silica. The Raman spectrum was applied to verify this model. Subsequently, the impacts of laser beam power, scanning speed, track overlapping, substrate temperature on the fictive temperature were discussed. The results indicate that decreasing the scanning speed and increasing the substrate temperature can decrease the fictive temperature. Additionally, a higher track overlapping can reduce the height of the fictive temperature “tool mark”. Moreover, an optimization strategy based on laser beam scanning speed was proposed based on the uniform distribution of fictive temperature. The depth difference of the heat-affected zones was reduced from 164.26 μm to 31.74 μm. This work could be used to quantitatively predict the 3D fictive temperature distribution and proposed an optimization strategy based on scanning speed to suppress the non-uniformity of fictive temperature distribution, which can provide significant theoretical guidance for CO2 laser polishing technology of fused silica optics.

A thermoviscoelastic model for the one-way and two-way shape memory effects of semi-crystalline polymers

Both one-way and two-way shape memory effects induced by crystallization and melting transitions have been recently demonstrated in several semi-crystalline polymers. The paper proposes a novel thermoviscoelastic phase transition model accounting for the underlying mechanisms of the material. The nonlinear Adam-Gibbs model of structural relaxation and a modified Eying model of viscous flow are incorporated to characterize the thermomechanical behaviors of the amorphous phase. Another main feature of the model lies in the characterization of the formation and melting of the crystalline phase based on a theory of multiple natural configurations. Comparisons with uniaxial shape memory experiments show that the model can well reproduce the stress-strain-temperature responses in different loading conditions.

Network Relaxation and Cooperativity in Ion Conducting Polymers PEO-Li: An Analysis Based on the BSCNF Model

The understanding of fundamental materials properties is indispensable for the development of functional materials. Some years ago, it has been reported that the fragility in poly (ethylene oxide)-based Li+ ion conductors decreases with the Li+ ion content. The behavior was considered as unexpected and the origin unclear. In the present study, it is shown that the Bond Strength-Coordination Number Fluctuation (BSCNF) model of structural relaxation developed by the present authors provides an explanation to the observed behavior. The analysis based on the BSCNF model indicates that the cooperativity, or the number of correlated structural units involved in the network relaxation decreases with the Li+ ion content.

High-precision molding simulation prediction of glass lens profile for a new lanthanide optical glass

Precision glass lens molding (PGLM) is a recently developed method for fabricating glass optical components with high precision in large volumes. Lanthanum optical glasses are extensively used as optical materials owing to their superior optical properties, such as high refractive index, low dispersion, and high transparency. However, the transformation temperature of currently available high refractive index glass is generally above 650 °C and poses a challenge in manufacturing ultra-hard molds, durable coatings, and high-temperature molding equipment using PGLM. In this study, a preparation method for obtaining high refractive index, low -melting -point lanthanide optical glass (B-ZLaT198) used in PGLM was developed to reduce the transformation temperature. The developed method also characterizes the glass refractive indices and thermal-mechanical properties. To achieve the high-precision prediction of a molding shape in a simulation, a viscoelastic constitutive model of glass was established based on a micro-deformation uniaxial compression creep test. Moreover, by solving the Tool-Narayanasway-Moynihan model parameters based on the specific heat capacity fitting of optical glass at different heating and cooling rates, the input parameters of the structural relaxation model (SRM) for simulation prediction of aspheric glass lens profile deviation in the annealing stage were obtained. Finally, the profile deviation of the aspheric lens was predicted using a finite element model simulation. The results showed that the simulation’s predicted profile of an aspheric lens using the SRM model was in good agreement with that of experimental molding profile. In addition, using the SRM provided a higher prediction accuracy than that of the thermal expansion model in the annealing stage. Adopting the SRM was necessary for the annealing simulations of molding pressing and also verified the accuracy of the proposed viscoelastic characterization method for calculating the thermomechanical parameters of optical glasses.

Numerical simulation of the structural relaxation characteristics of K-LCV161 glass

Only a few glass structure relaxation parameters are applicable for finite element simulation. The structural relaxation characteristics of K-LCV161 glass were described using the Tool–Narayanaswamy–Moynihan (TNM) model in multiple differential scanning calorimetry(DSC) experiments. First, the proposed method of narrowing the fitting parameter range was based on the influence of TNM model parameters on DSC curve. The position of the DSC curve peak is affected by changing Δh*/R and A, the height of the DSC curve peak is affected by changing x and β. The least squares fitting method to solve the TNM model parameters was then systematically presented systematically presented, and the following results were obtained: ∆h*/R = 52,394.91 K, A = 6.15e−31 s, x = 0.77, β=0.70. Finally, the volume change of K-LCV161 glass during cooling was predicted by using the thermal expansion and structural relaxation models, and the difference between these two models was approximately 23%.

Kinetic Model of Structural Relaxation in Diblock Copolymer Film

A relaxation model for the structure ripening under annealing of a microphase-separated polymer film has been developed. Equations have been derived that describe the appearance and annihilation of defects in the kinetically controlled mode based on the experimental data on the hexagonal structure evolution. Using that equations, the time dependences of the defect-free area size have been analyzed. It has been found that the predominance of the defect annihilation upon their triple contact leads to the power-law dependence of the orientation correlation length ξor ~ t1/4, which is observed experimentally at high annealing temperatures. A more detailed analysis of the evolution of two types of defects (dislocations and disclinations) shows that this dependence can also be realized in a model that takes into account the annihilation of disclination pairs and quadruples providing that dislocations influence this process. The results demonstrate that macrokinetic models can describe structural rearrangements in block copolymer films.

A Nonequilibrium Model for Particle Networking/Jamming and Time-Dependent Dynamic Rheology of Filled Polymers.

We describe an approach for modeling the filler network formation kinetics of particle-reinforced rubbery polymers—commonly called filler flocculation—that was developed by employing parallels between deformation effects in jammed particle systems and the influence of temperature on glass-forming materials. Experimental dynamic viscosity results were obtained concerning the strain-induced particle network breakdown and subsequent time-dependent reformation behavior for uncross-linked elastomers reinforced with carbon black and silica nanoparticles. Using a relaxation time function that depends on both actual dynamic strain amplitude and fictive (structural) strain, the model effectively represented the experimental data for three different levels of dynamic strain down-jump with a single set of parameters. This fictive strain model for filler networking is analogous to the established Tool–Narayanaswamy–Moynihan model for structural relaxation (physical aging) of nonequilibrium glasses. Compared to carbon black, precipitated silica particles without silane surface modification exhibited a greater overall extent of filler networking and showed more self-limiting behavior in terms of network formation kinetics in filled ethylene-propylene-diene rubber (EPDM). The EPDM compounds with silica or carbon black filler were stable during the dynamic shearing and recovery experiments at 160 °C, whereas irreversible dynamic modulus increases were noted when the polymer matrix was styrene-butadiene rubber (SBR), presumably due to branching/cross-linking of SBR in the rheometer. Care must be taken when measuring and interpreting the time-dependent filler networking in unsaturated elastomers at high temperatures.

Intramolecular photo‐driven electron transfer in the series of DMABN related compounds with para‐substituted acceptors. Study of the rate constants by Marcus theory

AbstractA series of DMABN‐related compounds with two‐band fluorescence was studied by steady‐state absorption and fluorescence spectroscopy, time‐resolved absorption spectroscopy upon excitation with a 30‐fs laser pulse, and by TDDFT and xMCQDPT2 quantum chemical methods. The efficiency of the intramolecular electron transfer was found to depend on the excitation wavelength in MeCN. The reaction is described by a two‐state scheme (LE↔CT); the Stevens‐Ban method gives underestimated values for the reaction enthalpy ΔH (SB). The spectral luminescence and kinetic parameters, rate constants, and barriers for the forward (k1, Ea) and reverse (k−1, Ed) electron transfer were calculated. The Marcus plot for k1 versus the driving force (−ΔG) and the total reorganization energy (λ) were calculated for six compounds. It was shown that without a barrier, the 1/k1 value (267 fs) is close to the mean solvation time in MeCN (260 fs), ie, the reaction rate is completely determined by the solvent. The results of conformational analysis for all studied compounds are consistent with the twisted intramolecular charge transfer model of structural relaxation.

Multi-objective optimization of glass multi-station bending machining for smartphone curved screen

Glass multi-station bending machining (GMBM) is a high-precision and efficient glass processing technique for smartphone curved screen in 3C industry. In this paper, simulation model of the GMBM of smartphone curved screen was researched by using MSC Marc software. The stress relaxation and structural relaxation models of glass material were used in the numerical model to accurately predict the forming process of the glass component. The effects of process parameters of GMBM, namely heating rate (HR), holding time, bending temperature (BT), bending pressure and cooling rate (CR), on the product quality characteristics (residual stress and shape deviation) and energy efficiency were analyzed based on orthogonal experiments. It can be found that the BT, CR and HR have extremely important effects on product residual stress, shape deviation and energy efficiency. Furthermore, a multi-objective optimization method based on NSGA-III (a non-dominant sorting genetic algorithms based on reference points) was applied to efficiently solve the optimization problem between glass product quality and energy efficiency. The optimal parameter schemes with high quality and low energy efficiency were obtained by the Pareto front of multi-objective, and the average prediction errors of the numerical results by the optimized schemes are no more than 20% through confirm experiments. The optimized schemes improve the stability of the process of GMBM, which can deal with the challenge of green manufacturing.

Pressure relaxation and diffusion of vacancies in rapidly grown helium crystals

An experimental study of the features of pressure relaxation in rapidly grown crystals of a diluted solid solution 3He–4He, at temperatures above 1.3 K, was performed. A cylindrical cell with capacitive pressure sensors at the ends was used for measurements. It was found that, when the helium crystals were grown at cooling rates ≳4 mK/s, the difference in pressure ΔP registered by the sensors at 1.3 K reached 2.4 bars. The ΔP value decreased with subsequent stepwise increase in temperature, but reached zero only after thorough annealing at the premelting temperatures. The kinetics of pressure changes at the sample ends at different temperatures was recorded. The results obtained were interpreted within the framework of the structural relaxation model based on the monovacancy diffusion mechanism. The proposed model made it possible to explain the dependence of ΔP on the time and temperature recorded in the experiment, as well as to determine the activation energy of the structural relaxation process and the diffusion coefficient of vacancies. The details of the vacancy model are described in the Appendix.

Prediction of heating rate controlled viscous flow activation energy during spark plasma sintering of amorphous alloy powders

The viscous flow behavior of Fe-based amorphous alloy powder during isochronal spark plasma sintering was analyzed under the integrated theoretical background of the Arrhenius and directional structural relaxation models. A relationship between viscous flow activation energy and heating rate was derived. An extension of the pertinent analysis to Ti-based amorphous alloys confirmed the broad applicability of such a relationship for predicting the activation energy for sintering below the glass transition temperature (Tg) of the amorphous alloy powders.

Communication: Non-Newtonian rheology of inorganic glass-forming liquids: Universal patterns and outstanding questions.

All families of inorganic glass-forming liquids display non-Newtonian rheological behavior in the form of shear thinning at high shear rates. Experimental evidence is presented to demonstrate the existence of remarkable universality in this behavior, irrespective of chemical composition, structure, topology, and viscosity. However, contrary to intuition, in all cases the characteristic shear rates that mark the onset of shear thinning in these liquids are orders of magnitude slower than the global shear relaxation rates. Attempt is made to reconcile such differences within the framework of the cooperative structural relaxation model of glass-forming liquids.

Decoding flow unit evolution upon annealing from fracture morphology in metallic glasses

The intrinsic correlation between the fracture morphology evolution and the structural heterogeneity of flow units in a typical Zr52.5Ti5Cu17.9Ni14.6Al10 (vit105) metallic glass (MG) upon annealing was investigated. By systematically tuning the annealing time at temperature below the glass transition temperature, a series of dimple-like fracture morphology were obtained, which is the unique fingerprint-like pattern for every annealing state. Based on the structural relaxation model of flow units, the evolution of the typical dimple sizes, the largest and smallest dimple size, with annealing were well fitted. Then the evolution of flow unit density was estimated from the fracture morphology evolution, which displays the same evolution trend with that measured from thermal relaxation. A stochastic dynamic model considering the interaction of activated flow units was proposed to analyze the effect of the initial flow unit density and the flow unit interaction intensity on the dynamic evolution of dimple distribution. Our work may provide a novel scheme to investigate the structural fingerprint information on flow units from fracture morphology, and enlighten the microscopic structural origin of the ductile-to-brittle transition during structural relaxation in MGs.

Thermo-mechanical constitutive equations for glass and its numerical formulation for warpage analysis of silicon-glass multilayered structure

Thin multilayered structures with glass substrates are widely used in electronic devices. When layers having different thermal or mechanical properties are subjected to processes with temperature variations, warpage and residual stresses may develop incurred by the mismatch of volume change, possibly leading to the failure of the device. In order to analyze the thermo-mechanical behavior of glass including the warpage in multilayered structures with glass substrates, the thermo-mechanical constitutive equations of glass are developed here by coupling the stress relaxation (for mechanical behavior) and structural relaxation models (for thermal behavior). The constitutive equations for structural relaxation are generalized for the case with temperature dependent thermal expansion coefficients, while considering both formulations based on the specific volume and the fictive temperature. Besides, the numerical formulations of the constitutive equations for finite element analysis are derived for three-dimensional and plane stress conditions. The developed constitutive model is validated with experiments for the warpage of silicon-glass multilayered structures undergoing thermal cycles.

Numerical Evaluation on the Curve Deviation of the Molded Glass Lens

The compression molding of precision glass lens is a near net-shape forming process for optical components fabrication. The final profile curve accuracy is one of the most crucial criterions for evaluating the quality of the molded lens. In this research, our purpose was focused on the evaluation of the molded lens curve deviation. By incorporating stress relaxation and structural relaxation model of glass, numerical simulations of the whole molding process for fabricating a planoconvex lens were conducted by utilizing the commercial software msc Marc. The relationship of the three variables, i.e., the lens curve deviation, the mold curve deviation, the gap between the lens and the lower mold, was discussed and the evolution plots with time of the three variables were obtained. Details of the thermal boundary conditions were discussed by considering the contact heat transfer behavior. Then the essentiality of a small gap between the molds and the molded lens after releasing the upper mold was demonstrated. In details, the sensitivity analysis of the processing parameters was conducted, such as the releasing temperature, the cooling rate in the annealing and fast cooling stage, respectively, and the magnitude of the hold-up force. The results showed that the glass lens curve deviation was not sensitive to the choices of the releasing temperature and the cooling rate. What's more, the results indicated that the curve deviation decreased with the hold-up force increasing. Finally, with all the details considered, the final simulation results were presented accurately with good reason.

Quantitatively measurement and analysis of residual stresses in molded aspherical glass lenses

Residual stresses are important criteria for evaluating precision compression molded glass lenses. In this research, residual stresses inside a molded aspherical glass lens were investigated using both experimental and numerical methods. Specifically, residual stresses were calculated from optical measurements obtained by the use of a circular polariscope. From the measurements, both the magnitude and distribution of residual stresses in the aspherical glass lens were obtained. The residual stresses were also calculated using the structural relaxation model implemented in the finite element method software, and the results were compared to the measurements in experiments that were performed using matching molding conditions. In addition, residual stresses under different cooling rates were investigated in simulation and the impact of the cooling rate on the aspherical surface deviation was also discussed.

Temperature gradient in sample and its effect on enthalpy relaxation model fitting of polystyrene

A method to calculate the temperature profile in the polymer samples in differential scanning calorimetry (DSC) measurements by combining the Fourier's law of heat conduction and structural relaxation model is proposed. It is assumed that the temperature at the bottom of the sample is consistent with the program temperature but temperature lag exists between the top and bottom of the sample because that the thermal transfer paths to the two surfaces of the sample are different. The fitting quality of the apparent heat capacity data of polystyrene (PS) samples with different thicknesses using one set of Tool–Narayanaswamy–Moynihan (TNM) parameters are excellent, which conforms the method for temperature profile calculation. It was found that the temperature gradient has slight effect on the best fit TNM model parameters of PS samples with different thicknesses. The investigation on enthalpy relaxation of PS with different thermal histories showed that the temperature gradient existing in the sample only has slight effect on the thermal history dependence of TNM model parameters, which may originate mainly from the flaw of the model itself.

Analysis of annealing processes of glass sheets based on structural relaxation model

Since the high resolution glass panel became the main stream of the display industry, the dimensional change of the glass after a thermal process applied during the panel production, in particular shrinkage has become a major technical hurdle for glass substrate and panel producers to overcome together. The shrinkage might incur failure in the layers deposited on the glass substrate and ultimately degrade the optical property. A common practice to control the shrinkage is to introduce an annealing process to the glass substrate between the glass production and the deposition process. In an effort to develop a way of optimizing the annealing process, a numerical method to analyze the shrinkage during the annealing and subsequent deposition processes was developed in this work based on the structural relaxation model of the glass substrate. Then, the developed method was tried out to optimize annealing processes such that there would be little shrinkage in various subsequent deposition processes.

Stochastic Model for Volume Relaxation in Glass Forming Materials: Local Specific Volume Model

A stochastic model for structural relaxation in glassy materials is developed, where the rate of relaxation in a mesoscopic domain depends upon the state in that meso-domain. Because the meso-domains have nanometer dimensions, fluctuations are included. The model predicts the volume relaxation for arbitrary thermal histories at ambient pressure in the glass transition region, where the local rate of relaxation is given by a single relaxation time that depends on the local density and temperature. Using a single set of parameters, the stochastic model accurately predicts the entire Kovacs poly(vinyl acetate) volume relaxation data set. The meso-domain size was determined to be 2.8 nm, consistent with NMR and other measurements. This model indicates that the origin of the wide relaxation spectra observed experimentally is a single Debye process that experiences significant fluctuations in its state. The stochastic model also naturally predicts the small amount of thermorheological complexity that is observe...

Modelling the spatio-temporal cell dynamics reveals novel insights on cell differentiation and proliferation in the small intestinal crypt.

We developed a slow structural relaxation model to describe cellular dynamics in the crypt of the mouse small intestine. Cells are arranged in a three dimensional spiral the size of which dynamically changes according to cell production demands of adjacent villi. Cell differentiation and proliferation is regulated through Wnt and Notch signals, the strength of which depends on the local cell composition. The highest level of Wnt activity is associated with maintaining equipotent stem cells (SC), Paneth cells and common goblet-Paneth cell progenitors (CGPCPs) intermingling at the crypt bottom. Low levels of Wnt signalling area are associated with stem cells giving rise to secretory cells (CGPCPs, enteroendocrine or Tuft cells) and proliferative absorptive progenitors. Deciding between these two fates, secretory and stem/absorptive cells, depends on Notch signalling. Our model predicts that Notch signalling inhibits secretory fate if more than 50% of cells they are in contact with belong to the secretory lineage. CGPCPs under high Wnt signalling will differentiate into Paneth cells while those migrating out from the crypt bottom differentiate into goblet cells. We have assumed that mature Paneth cells migrating upwards undergo anoikis. Structural relaxation explains the localisation of Paneth cells to the crypt bottom in the absence of active forces. The predicted crypt generation time from one SC is 4–5 days with 10–12 days needed to reach a structural steady state. Our predictions are consistent with experimental observations made under altered Wnt and Notch signalling. Mutations affecting stem cells located at the crypt floor have a 50% chance of being propagated throughout the crypt while mutations in cells above are rarely propagated. The predicted recovery time of an injured crypt losing half of its cells is approximately 2 days.