Dilatometric fragility and prediction of the viscosity curve of glass-forming liquids

Viscosity and coefficient of thermal expansion (CTE) are both crucial properties in the design of new glasses for various applications. In this work, we extend the application of dilatometry to measure two important parameters governing the viscosity of glass-forming systems, viz., glass transition temperature and fragility index. We also describe a method to determine the dilatometric fictive temperature (T_f,DIL) and present data for five unique glass compositions covering a range of fragilities spanning 38-96, which are subjected to cooling and reheating rates in the range 1-30 K/min. The results show that the glass transition temperature obtained from the dilatometric method at 10 K/min (T_g,DIL) is consistent with both viscosity-based (T_g,vis) and DSC-based measurements (T_g,DSC). It is shown that the fragility of a liquid (m_vis) can be determined by calibrating the dilatometric fragility (m_DIL) with the same empirical model as in the calorimetric approach. Put together, we have developed a reliable method to measure the fragility and predict the viscosity curves of glass-forming liquids over a wide range (eg, 10¹-10¹⁶ Pa·s) without direct viscosity measurements, while simultaneously obtaining the CTE of the glass. However, this method is not suitable for glasses with a strong tendency toward phase separation or crystallization.     

Thermodynamic insight into the evolution of medieval glassworking properties

We present differential scanning calorimetry (DSC) analyses of seven French stained glasses from the 13th to 16th centuries. These glasses illustrate the dramatic compositional change from the antique soda‐rich glasses to potash‐ and lime‐rich compositions, resulting in drastic temperature and viscosity increases. We investigate the influence of chemical composition on glass thermal properties: glass‐transition (T_g), crystallization, and melting temperatures. We find that T_g varies from 533°C (soda type) to 638°C±17°C (potash type) to 685°C±5°C (lime type). The viscous slowdown of the melt as a function of the temperature, close to T_g, was modeled using the Vogel‐Tammann‐Fulcher equation. This enables temperature‐viscosity profile calculations, and suggests that recipes have been empirically optimized to reach similar thermoelastic properties suitable for glassmaking despite changing the nature of raw materials.     

Densities and Viscosities of Oleic Acid at Atmospheric Pressure

The densities of oleic acid were measured over the temperature range from (293 to 459) K at atmospheric pressure using a densimeter based on the modified hydrostatic weighing method. The dynamic viscosities of the same oleic acid sample were measured using a capillary viscometer (VPZ-2 m) in the range from (293 to 363) K at atmospheric pressure. The combined expanded uncertainty of the density, atmospheric pressure, viscosity, and temperature measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 0.15%, 1.0%, 3.5%, and 15 mK, respectively. The values of uncertainty for density and viscosity include the effects of purity and calibration (total expanded uncertainty). These experimental data were used to develop wide-range correlations for the density and viscosity based on theoretically confirmed Arrhenius–Andrade and Vogel-Tamman-Fulcher (VTF) models. The value of the glass temperature ( T _g= 179.78 K.) for the oleic acid was estimated using the VTF parameters derived from the present viscosity measurements. To additionally validate the reliability of the measured density data, the same oleic acid samples were measured using the pycnometric method. The present study showed that the densities measured using the modified hydrostatic weighing densimeter (HWD) agree with the values obtained using the pycnometric method within 0.09% for Sample 1 and 0.25% for Sample 2.     

Molecular weight distribution of polyphenylene sulfide by high temperature gel permeation chromatography

Poly(phenylene sulfide) (PPS) has been characterized using a novel high temperature gel permeation chromatograph (GPC). Samples were injected in slurry form at ambient temperature, and redissolved by an in-line precolumn heater at 250°C. A viscometer consisting of a capillary tube with inlet and outlet taps connected to a sensitive differential pressure transducer was used as sole detector, with deflections converted to concentration using the column calibration. Columns and viscometer were operated at 210°C. Universal calibration was carried out using intrinsic viscosity/molecular weight relations for polystyrene and PPS, determined by light scattering. Satisfactory operation was confirmed by agreement between intrinsic viscosity calculated from GPC with independently measured values, and comparisons with melt flow data. Samples of PPS tested were found to be of relatively narrow distribution, with M_w/M_n typically less than two.     

High-temperature coupling of high-speed GPC with continuous viscometry. I. Long-chain branching in polyethylene

The coupling of a high-temperature liquid chromatograph (Waters 150C) with a home-made continuous capillary viscometer is described. This detector is the only one suitable for high-speed GPC when the small volume of the mobile phase prohibits the coupling with a classical viscometer. The pressure drop of the GPC effluent through the capillary is continuously measured along with the refractive index change. This dual detection leads to the determination of the intrinsic viscosity as a function of the elution volume, thus allowing a precise use of Benoit's universal calibration. The accuracy of our system is demonstrated in the case of the characterization of linear and branched polyethylene samples. The results concerning the average molecular weights as well as the branching factors (structure parameter g′ and long-chain branching frequencyλ) are in close agreement with those obtained by the classical way (coupling traditional GPC and discontinuous viscometry). It is well known that an estimate of the λ coefficient is extremely dependent on several hypotheses. However, for a set of commercial low-density polyethylenes, we obtained λ values about 0.5 × 10_?4, with no marked change along the molecular weight range.     

VIscometric behaviour of Kevlar fibre filled liquid crystalline solutions of ethyl cellulose in m-cresol

Liquid crystalline solutions of ethyl cellulose in m-cresol were mixed with Kevlar® fibres, and the viscometric behaviour with respect to temperature of those filled systems was determined with a cone-plate type viscometer. The viscosity of the systems exhibited a maximum and a minimum at temperatures denoted by T_max and T_min' respectively. The effects of fibre on the critical temperatures (T_max and T_min) and critical concentrations (C_a and C_b) and on the viscosity enhancement are discussed. T_max and T_min decreased with fibre concentration for single-phase anisotropic solutions, whereas they increased for the biphasic solution. The critical concentrations increased with fibre concentration and C_b was more sensitive to the fibre than C_a. The viscosity enhancement due to the fibre depended on the phase of solution. In the single-phase (isotropic and anisotropic), the viscosity enhanced with fibre; however, in the biphasic solution, the effect was not simple. The viscosity enhancement for the single-phase anisotropic solutions with fibre was lower than that for the isotropic solutions.     

The Liquidus Temperature of Nuclear Waste Glasses: An International Round-Robin Study

Eight institutions from four countries participated in a round-robin study to determine the precision and bias of a liquidus temperature (T_L) procedure for waste glasses being adopted by ASTM International as ASTM C 1720-11. The participants of the round-robin study were asked to measure three different glasses with one or a combination of the following T_L measurement methods: a gradient temperature (GT) method, a uniform temperature (UT) method, and/or a crystal fraction extrapolation (CF) method. The T_L values reported by different institutions are generally consistent. The precision of T_L measurements with each method was evaluated and is presented herein. The round-robin glasses were all previously studied at Pacific Northwest National Laboratory and included ARG-1 (Glass A), Zr-9 (Glass B), and AmCm2-19 (Glass C), with measured T_L values spanning the temperature range of 960–1240°C. A precision (i.e., standard deviation) for T_L has been obtained from the data, even though the data were not acquired for all three glasses using all three methods from each participating organization. Also, the article provides a brief overview and the importance of the T_L measurement.     

SEC–viscometer detector systems. I. Calibration and determination of mark–houwink constants

Five different types of calibration curve currently used in size exclusion chromatography-differential viscometer (SEC–DV) systems were identified and their use summarized. A simple method of deriving weighting factors for fitting local intrinsic viscosity calibration curves was shown to greatly improve the precision of calculated molecular weight distributions. The problem of reliably extrapolating the fitted curves to allow for differences in sensitivity among detectors has yet to be examined. With regard to Mark—Houwink constants, a method of fitting data from the SEC–DV system to obtain more statistically sound values was derived. For the data used here, the new method involves fitting a plot of logarithm of the local intrinsic viscosity of the sample vs. logarithm of the universal calibration curve parameter, J_i. Results for the data obtained appeared only slightly more precise than those for the traditional method. However, the new method promises improved reliability. © 1993 John Wiley & Sons, Inc.     

Cure modeling and monitoring of epoxy/amine resin systems. II. Network formation and chemoviscosity modeling

The glass transition temperature (T_g) advancement and the chemoviscosity development under isothermal conditions have been investigated for four epoxy/amine systems, including commercial RTM6 and F934 resins. Differential scanning calorimetry (DSC) was the thermoanalytical technique used to determine the T_g advancement and rheometry the technique for the determination of the chemoviscosity profiles of these resin systems. The complex cure kinetics were correlated to the T_g advancement via an one‐to‐one relationship using Di Benedetto's formula. It was revealed that the three‐dimensional network formation follows a single activated mechanism independent of whether the cure kinetics follow a single or several activation mechanisms. The viscosity profiles showed the typical characteristics of epoxy/amine cure. A modified version of the Williams‐Landel‐Ferry equation (WLF) was adequate to model the viscosity profiles of all the resin systems, in the temperature range 130 to 170°C, with a very good degree of accuracy. The parameters of the WLF equation were found to vary in a systematic manner with cure temperature. Further correlation between T_g and viscosity showed that gelation, defined as the point where viscosity reaches 10⁴ Pas, occurs at a unique T_g value for each resin system, which is independent of the cure conditions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2178–2188, 2000     

Contributions of torsional braid analysis to Tu

The accomplishments of Borden Award Winner John K. Gillham and his colleagues using Torsional Braid Analysis (TBA) and Differential Scanning Calorimetry (DSC) to investigate the T_g and T > T_g or T_u regions of anionic and thermal poly styrenes (PS) are evaluated and related to work on PS and other polymers and to controversies surrounding TBA and the Tu transition. Arguments are presented to refute the contention that T_u by TBA is an artifact produced by the braid and the contention that T_u has a relaxational nature but no thermodynamic basis. Two distinct behavior patterns are found for T_u vs log M?_n plots: quasi-static methods such as DSC on fused films show T_u to level off above M_c and approach an asymptotic value of ～435K; dynamic methods involving melt flow show that T_u increases without limit above M_c because of entanglements. A compilation is presented of 25 investigations of T_u on polybutadiene, poly(methyl methacrylate) (PMMA), PS, plasticized PS, and atactic polypropylene, involving twenty experimental techniques. The behavior of zero shear melt viscosity for PS is summarized. Gillham's work has not only led to clarification of many isolated papers in the literature but has also inspired various parallel experimental and literature studies on T_u. We conclude that T_u is a molecular level transition which, like T_g, exhibits both kinetic (relaxational) and thermodynamic aspects. It is shown that heat capacity should be a more sensitive method than dilatometry for studying the T_u transition.     

Preparation of transparent Bi2O3-ZnO-B2O3 glass by conventional sintering at low temperatures

Glass components fabricated by the sintering route have wide-ranging applications. However, one issue is that the crystallization tendency of glass powders often leads to residual pore-glass interfaces and crystal-glass interfaces, thereby causing strong light scattering and rendering the sintered glass opaque. This issue is particularly pronounced in glasses with a low glass transition temperature (T_g) due to their weak bonding and thus high crystallization tendency. In the present study, a Bi₂O₃-ZnO-B₂O₃ glass with a low T_g of 364°C was fabricated using the conventional sintering method to explore whether transparent glass materials can be obtained. The temperature range of crystallization of the glass powders was analyzed using differential scanning calorimetry. X-ray diffraction was employed to analyze the crystalline phases formed in the sintered glasses. The microstructure of the sintered glasses was examined using scanning electron microscopy. The optical transmittance of the sintered glasses was measured using ultraviolet-visible spectroscopy. The results show that transparent sintered glasses with the highest transmittance of 54% at the wavelength of 650 nm can be obtained by using a coarser initial particle size, lower forming pressure, and an appropriate sintering temperature/time (430°C/30 min). It is suggested that this combination of processing parameters can suppress glass crystallization while maintaining a low glass viscosity during sintering.     

Polystyrene crosslinked with oligomeric and polymeric poly(dimethyl siloxane) derivatives. Thermal and dynamic mechanical studies

Styrene has been copolymerized with various bifunctional poly(dimethyl siloxane) cross-linkers having molar masses in the range 200–35,000. Calorimetric and rheological measurements show that the crosslinkers change T_g, T_ll, and T_exo, as well as melt viscosity and elasticity of polystyrene. These changes are strongly dependent on the molar mass of the crosslinker. Increasing the length of the siloxane crosslinker lowers T_g and melt viscosity, if the molar mass of the crosslinker is in a range 200–2000. Copolymerizing styrene with a bifunctional poly(dimethyl siloxane) having molar mass near 35,000 leads to a phase-separated polymer where polystyrene phase largely retains its original properties.     

Physical Ageing of Silicate Glasses at Room Temperature: General Regularities as a Basis for the Theory and the Possibility of a priori Calculation of the Ageing Rate

A review has been presented of the poorly known data on the ageing of thermometric, optical, and other glasses at observation durations as long as 40 years. The correct mathematical processing of the data is carried out. It is shown that the volume relaxation is described by a simple exponential function with the characteristic time varying from three weeks to fifteen years. The process can be complicated by a superposition of slower or faster processes whose characteristic times can differ from the characteristic time of the dominant process by 1.5–2 orders of magnitude. The compositions of the studied glasses (from borosilicate crowns to flints) and their viscosities in the annealing range are given. It is demonstrated that the main characteristic ageing time (in years) and the structural temperature T _13.5 (corresponding to a viscosity of 10^13.5 P) are related by the expression log = 0.0260T _13.5 – 20.414, which makes it possible to calculate from T _13.5 with an error of no more than 20%. The expression is theoretically justified under the assumption that the cooperative -relaxation processes occur without -relaxation. The possible relation between the ageing and annealing processes is revealed. This relation follows from the splitting of the stretched exponent relaxation function (which is valid at T _g/T 1) into Debye components at the ratios T _g/T 2.5–2.8, which, for silicate glasses, correspond to room temperature.     

Resin,cure, and polymer properties of photopolymerizable resins containing bio-derived isosorbide

We have developed photocurable bio-derived isosorbide (meth)acrylates for use in photoinitiated additive manufacturing (AM). We have shown that the viscosity of isosorbide-based resins obeyed logarithmic rule of mixtures, and the viscosity values were significantly lower than that of commercial stereolithography (SLA) resins as well as various other urethane (meth)acrylates and bisphenol A (meth)acrylates-containing blends. Using isobornyl acrylate or 4-acryloylmorpholine as reactive diluents, we were able to reduce the brittleness of the isosorbide-based polymers and retain high glass transition temperatures (T_g) of up to 231°C. The isosorbide-based resins were still somewhat brittle but had both greater T_g and strength relative to analogous bisphenol A dimethacrylate resins. Addition of oligomeric urethane (meth)acrylate crosslinkers further improved the mechanical properties of the polymers, whereby the strength approximately doubled to 55 MPa at 25°C, while maintaining high thermal properties, T_g > 190°C, and low viscosities, <140 cP, that are desirable for photoinduced AM applications. Furthermore, we were able to print this resin using SLA which produced specimens with similar moduls, but reduced strength relative to photocured resins and a commercial high temperature SLA resin.     

Structural relaxation in chalcogenide glasses

The structural relaxation of chalcogenide glasses is discussed within Tool–Narayanaswamy–Moynihan (TNM) formalism. The TNM parameters for more than 70 different glassy compositions are compared on the basis of the relaxation rate defined as R_f(ΔT) = −(dT_f/dlogt)_i at the inflection point of the isothermal relaxation curve plotted on a logarithmic timescale. The R_f(ΔT) depends on the TNM parameter ß and the parameter σ, combining the nonlinearity parameter x, the effective activation energy h^* or the fragility m. It is shown that R_f(10) estimated at 10 K below T_g is useful for the prediction of structural relaxation kinetics in different amorphous materials. The chalcogenide glasses are, for example, compared with oxide glasses and organic polymers. For all these materials, the R_f(10) versus σ plot shows a well-defined pattern that is thoroughly discussed.     

RHEOLOGICAL CHARACTERIZATION OF NON-NEWTONIAN FLUIDS WITH A NOVEL VISCOMETER

A hydrostatic head viscometer and its novel viscosity equation were developed to determine flow characteristics of Newtonian and non-Newtonian fluids. The objective of this research is to test capabilities of the hydrostatic head viscometer and its novel non-Newtonian viscosity equation by characterizing rheological behaviors of well-known polyethylene oxide aqueous solutions as non-Newtonian fluids with 60 wt.% sucrose aqueous solution as a reference/calibration fluid. Non-Newtonian characteristics of 0.3–0.7 wt.% polyethylene oxide aqueous solutions were extensively investigated with the hydrostatic head viscometer and its non-Newtonian viscosity equation over a 294–306 K temperature range, a 0.14–40 Reynolds number range, and a 55–784 s^?1 shear rate range at atmospheric pressure. Dynamic viscosity values of 60 wt.% sucrose aqueous solution were determined with the calibrated hydrostatic head viscometer and its Newtonian viscosity equation over a 3–5 Reynolds number range at 299.15 K and atmospheric pressure and compared with the literature dynamic viscosity value.     

High Glass Transition Temperature Barium Silicophosphate Glasses Designed with Topological Constraint Theory

Alkali‐free glasses have attracted tremendous attentions for their high glass transition temperature (T_g). Such a feature broadens their potential applications, especially in the area of high‐density and high‐power laser glasses. BaO–P₂O₅ glasses, as one of the major matrix materials due to its high‐T_g, can be applied in high‐power laser glasses. Introducing SiO₂ is an effective method to improve the thermal, refractive index, and mechanical properties of phosphate glasses. Herein, we studied the barium silicophosphate glasses with MAS NMR and the T_g was successfully calculated by the topological constraint theory. The designed glass (20BaO–26.7SiO₂–53.3P₂O₅, mol%) with a high T_g (789K) was prepared and it also exhibited high refractive index and high Vickers hardness, suggesting the barium silicophosphate glasses have widespread applications in high‐power laser glasses and optical fibers.     

Viscosity of polystyrene near the glass transition

A quantitative explanation is given for the apparent viscosity increase with increasing capillary shear rate for polystyrene at temperatures approaching the glass transition, T_g. Possible shifts in T_g as a function of the parameters shear rate, frequency, and pressure are interrelated to viscosity changes. Experimentally, the Instron capillary rheometer and the Weissenberg rheogoniometer provided a means for uncoupling the variables for individual consideration. Calculated and experimental data for the apparent viscosity as a function of the given parameters are presented and discussed. The explanation of the apparent viscosity increase in capillary flow can be quantitatively explained through the pressure dependence of T_g. Brief mention is made of the pressure effects on the Bagley and Rabinowitsch corrections normally made in capillary measurements.     

Physical and Mechanical Behavior of Polymer Glasses. VI. the Role of Free Volume

Abstract

For various polymer glasses, the temperature-induced recovery of residual deformation was studied. The ratio between the low-temperature and high-temperature recovery components is controlled by the difference between deformation temperature and glass transition temperature T _g of polymer samples independently of their chemical structure. This ratio correlates with polymer macroscopic mechanical characteristics such as elastic modulus and yield stress. Experimental results were treated in terms of the dynamics of segmental mobility within different structural sublevels with different packing densities. To correlate this mechanical response with the structural state of glassy polymers, positron annihilation lifetime spectroscopy (PALS) was used. For different polymer glasses, the microscopic segmental mobility and resultant macroscopic mechanical properties were shown to be controlled only by the development of the adequate free volume content which depends on the difference between testing temperature and T _g . These results allowed us to propose the general correlation between microstructure, microscopic molecular mobility, and Macroscopic mechanical behavior of polymer glasses.     

Glass formation and electrical conductivity of glasses in the Na<Subscript>2</Subscript>Se-P<Subscript>2</Subscript>Se<Subscript>5</Subscript> system in a wide temperature range

The glass formation region in the Na₂Se-P₂Se₅ system and the temperature-concentration dependences of the electrical conductivity of glasses have been investigated over a wide range of temperatures. The densities and glass transition temperatures T _g of glasses have been determined. A comparison of the electrical conductivity of glasses in the Na₂Se-P₂Se₅ and Na₂O-P₂O₅ systems has demonstrated that the conductivity of selenium-containing glasses (at 25°C) is approximately three orders of magnitude higher than the electrical conductivity of oxide glasses. The assumption has been made that an increase in the electrical conductivity of glasses with selenium is caused by the increase in the degree of dissociation of Na⁺[Se⁻PSe_3/2] polar structural chemical units and the higher mobility of sodium ions in the oxygen-free matrix.