Maxwell equation and classical theories of glass transition as a basis for direct calculation of viscosity at glass transition temperture

The main relaxation theories of glass transition (Leontovich-Mandelstam and Volkenstein-Ptitsyn) variously formulate the kinetic criteria of glass transition. Both of the approaches are shown to be equivalent in physical sense and provide a single expression that connects the rate of change of a melt temperature and the structure relaxtion time. The theory characterizes the width of a temperature band δT _g in which the glass transition occurs. The values of δT _g can either be obtained from the experiment or be accepted to conform to the value of a temperature step under the change of viscosity by an order of magnitude (direct method for finding by the Volkenstein-Ptitsyn theory). Using the Maxwell equation, a new equation for the calculation of the viscosity for viscoelastic relaxation was suggested, which is based on a shear modulus of glass and the cooling rate. The theory was verified basing on the published data for oxide glass. The average difference between the calculated and measured values of lgη upon glass transition comprises 0 ± 0.30. These results correspond to the cooling rate of 3 K/min and log(η, Pa s) = 12.76 ± 0.26 (for all glass considered). It is shown that the most probable cooling rate which provides the viscosity upon glass transition of ～1012 Pa s is close to 20 K/min (oxide melts). The theory predetermines the dependence of viscosity upon glass transition on the nature of a glass-forming liquid. The disadvantages of other approaches to the problem under consideration are demonstrated.     

Glass transitions of styrene/α-methylstyrene statistical copolymers and of their blends with PPO® resin

The glass transition temperatures (T_g) and specific heat increments (ΔC_p) at T_g of S/AMS statistical copolymers having weight fractions AMS of 0.00, 0.09, 0.17, 0.26, 0.36, and 0.44 are (by DSC) 380.0 (0.280), 384.2 (0.275), 388.8 (0.284), 391.5 (0.275), 398.3 (0.272), and 405.9 (0.27) °K (J·g^? ·deg^?), respectively. The T_g (ΔC_p) for the PPO resin are 492.2 (0.221). The glass transitions of P(S/AMS) (1) + PPO resin (2) blends having w2 = 0.25, 0.50, and 0.75 were also measured. Examination of the copolymer and blend T_g vs. composition data indicates that a relation recently proposed by Couchman gives a somewhat better approximation than the simple Fox relation. However, the nonadjustable k = ΔC_p2/ΔC_p1 constant in the Couchman relation must be replaced by a smaller empirical k to give a true match of calculated to observed T_g.     

ΔCp, Δα and related quantities for epoxy-aromatic amine networks

Summary The parameters of glass transition in several epoxyamine polymer networks were obtained. The changes C_p (T_g) and (T_g) were proved to be correlated with the concentration of crosslinks in these systems. The difference in glass transition parameters for linear and densely crosslinked polymers was analysed in terms of Simha-Boyer (T_g) and Boyer (C_p·T_g) rules and Eyring's hole theory.     

Atomistic molecular simulations of structure and dynamics of crosslinked epoxy resin

Many excellent thermal and mechanical performances of cured epoxy resin products can be related to their specific network structure. In this work, a typical crosslinked epoxy resin was investigated using detailed molecular dynamics (MD) simulations, in a wide temperature range from 250 K to 600 K. A general constant-NPT MD procedure widely used for linear polymers failed to identify the glass transition temperature (T_g) of this crosslinked polymer. This can be attributed to the bigger difference in the time scales and cooling rates between the experiments and simulations, and specially to the highly crosslinked infinite network feature. However, by adopting experimental densities appropriate for the corresponding temperatures, some important structural and dynamic features both below and above T_g were revealed using constant-NVT MD simulations. The polymer system exhibited more local structural features in case of below T_g than above T_g, as suggested by some typical radial distribution functions and torsion angle distributions. Non-bond energy, not any other energy components in the used COMPASS forcefield, played the most important role in glass transition. An abrupt change occurring in the vicinity of T_g was also observed in the plots of the mean squared displacements (MSDs) of the crosslinks against the temperature, indicating the great importance of crosslinks to glass transition. Rotational dynamics of some bonds in epoxy segments were also investigated, which exhibited great diversity along the chains between crosslinks. The reorientation functions of these bond vectors at higher temperatures can be well fitted by Kohlrausch-Williams-Watts (KWW) function.     

Confinement, composition, and spin-coating effects on the glass transition and stress relaxation of thin films of polystyrene and styrene-containing random copolymers: Sensing by intrinsic fluorescence

The glass transition temperatures (T_gs) of polystyrene (PS) and styrene/methyl methacrylate (S/MMA) random copolymer films are characterized by intrinsic fluorescence, i.e., monomer fluorescence from an excited-state phenyl ring and excimer fluorescence from an excited-state dimer of two phenyl rings. The T_g is determined from the intersection of the rubbery- and glassy-state temperature dependences of the integrated fluorescence intensity measured upon cooling from an equilibrated state. With PS, the effects of nanoconfinement on T_g and the transition strength agree with results from studies using probe fluorescence and ellipsometry. The T_g-nanoconfinement effect is “tuned” by copolymer composition. As S-content is reduced from 100 mol% to 22 mol%, the confinement effect changes from a reduction to an enhancement of T_g relative to bulk T_g. Intrinsic fluorescence is also a powerful tool for characterizing relaxation of residual stresses. Stresses induced by spin coating affect local conformations, which in turn affect excimer and monomer fluorescence and thereby integrated intensity. The heating protocol needed to achieve apparently equilibrated local conformations is determined by equivalence in the integrated intensities obtained upon heating and subsequent cooling. While partial stress relaxation occurs upon heating in the glassy state, full relaxation of local conformations requires that a film be heated above T_g for times that are long relative to the average cooperative segmental relaxation time. For example, in thin and ultrathin films, equilibration is achieved by heating slowly (∼1 K/min) to 15-20 K above T_g. Dilute solution fluorescence of PS and S/MMA copolymers is also characterized and compared to reports in the literature.     

Studies on heat capacity of cellulose and lignin by differential scanning calorimetry

Heat capacities (C_p) of wood cellulose, other natural celluloses having various crystallinities and of lignin are given for temperatures ranging from 330K to 450K using differential scanning calorimetry. The calculation of the C_p of completely crystalline cellulose is based on a two-state model of cellulose which assumes linearity between the crystallinity and C_p. The higher C_p found in the amorphous region compared with the crystalline region, is apparantly due to differences in the frequency of molecular vibration in these two areas. The glass transition of lignin was observed as a sudden increase in C_p at 400K. The precise T_g of lignin was dependent on the sample's origin, characterization, thermal history etc. When annealed at around T_g enthalpy relaxation occurs, and this can be detected as an endothermic peak in the C_p curve at the transition temperature. Moreover, the C_p in the glassy state was found to decrease with both annealing time and temperature, suggesting that rearrangement of the local conformation of lignin molecules occurs in the glassy state temperature range.     

Application of the molecular dynamics method and the excited state model to the investigation of the glass transition in argon

The glass transition in argon at a high cooling rate is simulated. At a temperature of 50 K (considerably below the melting temperature T _f = 83.8 K), the fluctuation volume fraction reaches the constant value f _g ? 0.03–0.05, which is close in the order of magnitude to the criterion for the glass transition in liquids f _g = const 0.02–0.03 within the excited state model. At this temperature, the second maximum of the radial distribution function is split as a result of the glass transition at the temperature T _g = 50 K. The approximate empirical “two-thirds” rule T _g = (2/3)T _f is reasonably satisfied for argon. The data obtained are interpreted in the framework of the excited state model.     

Molecular motions in poly(dimethyl siloxane) oligomers and polymers

The glass transition temperatures of fifteen samples of poly(dimethyl siloxane) polymers and oligomers have been measured by differential scanning calorimetry. Polymers with M_n>2400 exhibit an asymptotic value of T_g(∞)=148K, but for shorter chains the T_g is lower. The thermomechanical behaviour has also been examined using a torsional braid analyser and this has served to confirm the chain length dependence of T_g. A sub-glass transition, located in the temperature range 80–120K for short chain samples, has been attributed to methyl group rotation.     

The apparent activation energy and dynamic fragility of ancient ambers

According to the literature, different types of materials have different glass transition temperature (T_g) dependences of apparent activation energy (E_g) and dynamic fragility (m). In previous work we found that for different ambers, there were different glass transition temperatures. These same samples provide an opportunity to study the T_g dependence of E_g and m for amber, which has not been reported previously in the literature. In this work, nine pieces of amber from different locations and having different ages were investigated by differential scanning calorimetry. Six cooling rates were used to provide the different thermal histories, and the corresponding limiting fictive temperatures were determined using Moynihan's area matching method. From the cooling rate dependence of the limiting fictive temperature both the apparent activation energy and dynamic fragility were calculated. We find that as glass transition temperature increases, both the apparent activation energy and dynamic fragility increase. The T_g dependence of m for amber shows a similar trend with temperature as do the metallic glass formers and compares favorably with the m–T_g dependence of other aromatic polymers.     

Polystyrene freeze-dried from dilute solution: Tg depression and residual solvent effects

The calorimetric glass transition temperature, T_g, was measured for both linear and cyclic polystyrenes freeze-dried from dilute solutions of 0.10, 0.05, and 0.02% of polymer by weight in benzene. Upon freeze-drying, T_g was found to be depressed by 4-15 K depending on the sample, solvent concentration, and freezing conditions. Annealing under vacuum at moderate temperatures, from 40 to 140 °C and 0.05 Torr, resulted in the shift of T_g back towards its bulk value and was accompanied by a decrease in sample weight. The data is consistent with the observed weight loss being due to residual solvent. The amount of residual solvent is a strong function of the annealing temperature and the initial freeze-drying solution concentration; exposure to vacuum at temperatures far below T_g is generally insufficient for residual solvent removal.     

Phase transitions and glass transition in a hyperquenched silica‐alumina glass

We investigate phase transitions, glass transition, and dynamic behavior in the hyperquenched 69SiO₂–31Al₂O₃ (mol%) glass (SA glass). Upon reheating, the SA glass exhibits a series of thermal responses. Subsequent to the sub‐T_g enthalpy release, the glass undergoes a large jump in isobaric heat capacity (ΔC_p) during glass transition, implying the fragile nature of the SA glass. The mullite starts to form before the end of glass transition, indicating that the SA glass is extremely unstable against crystallization. After the mullite formation, the remaining glass phase exhibits an increased T_g and a suppressed ΔC_p. The formation of cristobalite at 1553 K indicates the dominance of silica in the remaining glass matrix. The cristobalite gradually re‐melts as the isothermal heat‐treatment temperature is raised from 1823 to 1853 K, which is well below the melting point of cristobalite, while the amount of the mullite remains unchanged.     

Non-isothermal crystallization and thermal transitions of a biodegradable, partially hydrolyzed poly(vinyl alcohol)

A study has been made of the non-isothermal crystallization behavior and thermal transitions of a biodegradable, partially hydrolyzed poly(vinyl alcohol) with 80% degree of saponification (PVA80). Possible sample degradation was first investigated, but no significant degradation or dehydration was detected using FTIR and DSC under the experimental condition. The non-isothermal crystallization of PVA80 was analyzed with Ozawa equation, and the Mo method of combining Ozawa and Avrami equations. Ozawa equation was only applicable in a narrow temperature range from 80 to 100 °C. The deviation from the Ozawa equation is not due to the secondary crystallization or the quasi-isothermal nature of the treatment. It is only a result of the large relative difference of the relative crystallinity values under different cooling rates. The Mo method demonstrated a success in the full temperature range investigated. The isoconversional method developed by Friedman failed to estimate the activation energy for this non-isothermal crystallization. Thermal transitions of PVA80 are associated with its complex hydrogen-bonding interactions. The melt-crystallized PVA80 sample, as that from film casting, followed by annealing at 60 and 80 °C, has a broad melting temperature range measured by DSC and FTIR. It was found that the melting behavior of a semicrystalline polymer can be probed via a non-crystalline hydrogen-bonded CO band using FTIR. The glass transition temperature T_g of PVA80 was raised about 20 °C, after the sample was melt-crystallized. The intensity of the hydrogen-bonded CO band increases when temperature was increased from 110 to 180 °C, due to the promoted hydrogen-bonding interactions between the CO groups in the amorphous phase and the hydroxyl groups from the crystalline phase, which is also the main reason for the increased T_g transition.     

Glass transformation studies in Ge-Se-Bi system

The thermal behavior of bulk glasses in the Ge₂₀Se_{80 − x} Bi _x (x = 2.5, 4.0, 6.0 at %) system is studied using modulated differential scanning calorimetry (MDSC). All samples have the same thermal history as a result of heating to a temperature above the glass transition point, equilibrating, and then cooling. The total heat flow, modulated heat flow, reversing heat flow, and nonreversing heat flow under heating and cooling schedules are measured. The glass transition temperature T _g , the relaxation enthalpy ΔH, the specific capacity C _p , and the specific heat capacity difference ΔC _p = C _pl − C _pg , which characterize the thermal events in the glass transition region, are also determined. These parameters reveal an increase with x, which can be attributed to the increase in the average coordination number with an increase in the bismuth content (at %) in the composite. The ratio of heat capacities C _pl /C _pg , the width of the glass transition temperature range ΔT _g , and the activation enthalpy for glass transition ΔH _Tg are also studied. The values of the ratio C _pl /C _pg vary in the range between 1.038 and 1.112. The activation energy of crystallization is evaluated using the Kissinger, modified JMA, and Matusita equations, which is found to be in the range of 100.92 kJ/mol. The text was submitted by the authors in English.     

Derivation of accurate glass transition temperatures by differential scanning calorimetry

Glass transition temperatures, T_g, cannot be directly determined from differential scanning calorimetry (d.s.c.) curves because of kinetic effects which are especially serious for well annealed samples. Using an anionic polystyrene as an example it is shown how d.s.c. data can be transformed to enthalpy curves which give T_g with an accuracy of ±1K. As the rate of cooling through the glassy region is lowered T_g is found to decrease by 2.2 K per decade decrease in cooling rate. Quantitative data are given for the specific heat increment at T_g.     

Synthesis and thermal properties of fullerene-containing polymethacrylates

Three poly(methyl methacrylate-co-2-bromoethyl methacrylate) samples were prepared. The bromine groups in the copolymers were converted to azide groups followed by reaction with fullerene (C₆₀) to afford fullerene-containing polymethacrylates. The glass transition temperatures (T_gs) and heat capacity changes (ΔC_p) at T_g of these polymers were measured by differential scanning calorimetry. With increasing fullerene content in the polymethacrylate, the T_g value increases while the ΔC_p value decreases. The incorporation of fullerene improves the thermal stability of the polymethacrylate as shown by thermogravimetric analysis. Received: 25 February 1997/Revised: 12 May 1997/Accepted: 13 May 1997     

Isothermal Cure of an Epoxy System Containing Tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM), a Multifunctional Novolac Glycidyl Ether and 4,4′-Diaminodiphenylsulphone (DDS): Vitrification and Gelation

Times to gelation and vitrification have been determined at different isothermal curing temperatures between 200 and 240°C for an epoxy/amine system containing both tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM) and a multifunctional Novolac glycidyl ether with 4,4′-diaminodiphenylsulphone (DDS). The mixture was rich in epoxy, with an amine/epoxide ratio of 0·64. Gelation occurred around 44% conversion. Vitrification was determined from data curves of glass transition temperature, T_g, versus curing time obtained from differential scanning calorimetry experiments. The minimum and maximum values T_g determined for this epoxy system were T_g0=12°C and T_gmax=242°C. Values of activation energy for the cure reaction were obtained from T_g versus time shift factors, a_T, and gel time measurements. These values were, respectively, 76·2kJmol^-1 and 61·0kJmol^-1. The isothermal time–temperature–transformation (TTT) diagram for this system has been established. Vitrification and gelation curves cross at a cure temperature of 102°C, which corresponds to glass transition temperature of the gel. © of SCI.     

Thermal properties of poly(vinyl cyclohexane)

Isotactic poly(vinyl cyclohexane) (PVCH) was studied by thermal analysis. The deduced equilibrium melting point, T, is 405°C (678 K). The heat of fusion, Δ H was found to be 50.82 J/g (5.60 kJ/mol) and Δ C_p at T_g, is 0.273 J/(gK) [30.1 J/(molK)]. The glass transition temperature, T_g, of the amorphous PVCH is 80°C (353 K). In semicrystalline samples, T_g increases up to 165°C (438 K) for crystallinities > 40%. Beside crystalline and flexible amorphous, a rigid amorphous phase is postulated in the semicrystalline polymer.     

Factors determining glass transition temperature and relaxation time of poly(vinyl chloride)

Glass transition properties were obtained by measurements of the dilatometric glass transition temperature T_g at elevated pressure by isobaric cooling at a constant rate. The properties include the pressure-volume-temperature (P-V-T) relations of the liquid, the specific heat capacity and the dielectric properties for a single sample of poly(vinyl chloride). From the experimental results, various thermodynamic excess quantities such as the free volumes and the configurational entropy and energies were evaluated as factors determining T_g and the relaxation time τ. Some empirical rules concerning T_g, which have been proposed by Simha and Boyer, and Wunderlich, are also examined. The main conclusions are as follows: (1) the free volume is not an essential factor determining T_g and τ; (2) the Adam-Gibbs parameter is slightly superior to the other excess entropy and energies defined as the difference of the entropy and energies between the liquid and the hypothetical crystal whose thermal expansivity and compressibility are the same as those of the corresponding glasses; and (3) the glass transition may not be treated as a quasi-equilibrium thermodynamic transition to which one of the Ehrenfest relations applies.     

Depolarization current in phenol-formaldehyde resin below the glass transition

A thermally stimulated depolarization (t.s.d.) current study of a novolac phenol-formaldehyde resin performed using electric poling at temperatures T ? T_g (T_g being the glass transition temperature which equals 323 ± 2 K) shows a continuous distribution of polarizability in the range from 295 to 323 K. The efficiency of poling is found to be dependent upon the physical ageing of resin. In addition to the known current peaks P₁ and P₂ which appear at T_m1 = (320 ± 2)K and T_m2 = (334 ± 6)K respectively, a new peak, P₀, is detected at T_m0 = (296 ± 1)K. P₀ appears reversibly with the same magnitude regardless of the electrical history of the resin or the physical ageing. The activation energy determined by the initial rise method and the whole curve integration method is found to be 500 and 570 kJ mol^?1, respectively. It is assumed that P₀ is caused by a discrete phase transition in the resin.     

Fluoride promoted crystallization and mechanical properties of Sr-fluorphlogopite glass

Crystallization, microstructure and mechanical behavior of strontium fluorphlogopite glass-ceramics, SrO·4MgO·Al₂O₃·6SiO₂·2MgF₂, was studied by varying the fluorine content. A number of glass-ceramics of each glass batch with excess MgF₂ [SR0 (0% MgF₂), SR5 (5% MgF₂) and SR10 (10% MgF₂)] were prepared by heating at its respective nucleation temperature followed by at different crystallization temperatures (780–1150 °C). Differential Thermal Analysis (DTA), X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Micro Hardness Indenter were used to study the crystallization, microstructure and mechanical behavior of resulting three glass batches. DTA analysis revealed that the peak crystallization (T_p) and glass transition (T_g) temperatures decreased with increasing fluorine content that also lowers down the activation energy (E) as evident from crystallization kinetics. Hardness and fracture toughness values are higher for less fluorine containing glass-ceramics when they are treated isothermally. However, more fluorine based glass-ceramics is found to be more machinable than the less fluorine one.