Isochoric Fragility Research Articles

Cooperativity and fragility in furan-based polyesters with different glycolic subunits as compared to their terephthalic counterparts

This works aims to investigate the effect of the molecular groups found in polyester backbones (type of ring in the acidic subunit and length of the glycolic subunit) on the molecular dynamics. The investigation is done on three furan-based polyesters (PEF, PPF and PBF) as compared to their terephthalic counterparts (PET, PTT, and PBT) after full quenching from the molten state. The segmental molecular dynamics is investigated with MT-DSC, FSC and DRS. It is shown that the cooperativity decreases as the length of the glycolic subunit increases in both furan-based and terephthalic polyesters. No direct correlation between the fragility index and the cooperativity is observed in furan-based polyesters containing glycolic subunits of different lengths. The differences in the isochoric fragilities obtained for the furan-based polyesters and their terephthalic counterparts has been assumed to result from the combination of backbone flexibility and packing efficiency of the macromolecular chains in the amorphous phase.

Thermodynamic scaling of relaxation: insights from anharmonic elasticity

Using molecular dynamics simulations of a molecular liquid, we investigate the thermodynamic scaling (TS) of the structural relaxation time in terms of the quantity , where T and ρ are the temperature and density, respectively. The liquid does not exhibit strong virial–energy correlations. We propose a method for evaluating both the characteristic exponent and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions. In particular, we express the TS characteristic exponent in terms of the lattice Grüneisen parameter and the isochoric anharmonicity . An analytic expression of the TS master curve of with as the key adjustable parameter is found. The comparison with the experimental TS master curves and the isochoric fragilities of 34 glassformers is satisfying. In a few cases, where thermodynamic data are available, we test (i) the predicted characteristic exponent and (ii) the isochoric anharmonicity , as drawn by the best fit of the TS of the structural relaxation, against the available thermodynamic data. A linear relation between the isochoric fragility and the isochoric anharmonicity is found and compared favourably with the results of experiments with no adjustable parameters. A relation between the increase of the isochoric vibrational heat capacity due to anharmonicity and the isochoric fragility is derived.

Thermodynamic scaling of vibrational dynamics and relaxation.

We investigate by thorough molecular dynamics simulations the thermodynamic scaling (TS) of a polymer melt. Two distinct models, with strong and weak virial-energy correlations, are considered. Both evidence the joint TS with the same characteristic exponent γts of the fast mobility-the mean square amplitude of the picosecond rattling motion inside the cage-and the much slower structural relaxation and chain reorientation. If the cage effect is appreciable, the TS master curves of the fast mobility are nearly linear, grouping in a bundle of approximately concurrent lines for different fragilities. An expression of the TS master curve of the structural relaxation with one adjustable parameter less than the available three-parameter alternatives is derived. The novel expression fits well with the experimental TS master curves of thirty-four glassformers and, in particular, their slope at the glass transition, i.e., the isochoric fragility. For the glassformer OTP, the isochoric fragility allows to satisfactorily predict the TS master curve of the fast mobility with no adjustments.

In search of correlations between the four-point measure of dynamic heterogeneity and other characteristics of glass-forming liquids under high pressure

In this paper, we examine the linear correlations earlier suggested between the four-point dynamic heterogeneity and the activation volume as well as between the four-point dynamic heterogeneity and the difference between isobaric and isochoric fragilities, which have been previously tested mainly at ambient pressure for different materials near the glass transition. We perform our analyses for twelve glass formers that belong to different material groups such as van der Waals liquids, polymer melts, protic ionic liquids, and strongly hydrogen-bonded liquids. Since our very recent finding [Phys. Rev. Lett. 111 (2013) 125701] shows that the dynamic heterogeneity decreases with increasing pressure along the glass transition line in the phase diagram, which is in contrast to the invariance of the shape of relaxation spectra in isochronal conditions, we exploit experimental data measured at ambient and elevated pressure to test whether the correlations occur over the whole phase diagram area where the supercooled liquid state is achieved. The obtained results are clarified theoretically in the limit of the estimate recently proposed for the degree of the dynamic heterogeneity by Berthier et al. [Science 310 (2005) 1797].

Characteristic Length of the Glass Transition in Isochorically Confined Polymer Glasses.

We report the effect of isochoric confinement on the characteristic length of the glass transition (ξα) for polystyrene (PS) and poly(4-methylstyrene) (P4MS). Utilizing silica-capped PS and P4MS nanoparticles as model systems, ξα values are determined from the thermal fluctuation model and calorimetric data. With decreasing nanoparticle diameter, ξα decreases, suggesting a reduction in the number of segmental units required for cooperative motion at the glass transition under confinement. Furthermore, a direct correlation is observed between ξα and the isochoric fragility (mv) in confined polymers. Due to a nearly constant ratio of the isochoric to isobaric fragility in confined polymer nanoparticles, a correlation between ξα and mv also implies a correlation between ξα and the volume contribution to the temperature dependence of structural relaxation. Lastly, we observe that when the fragility and characteristic length are varied in the same system the relationship between the two properties appears to be more correlated than that of across different bulk glass-formers.

Size of the cooperative rearranging regions vs. fragility in complex glassy systems: Influence of the structure and the molecular interactions

By using Donth's model, the size of the Cooperative Rearranging Regions (CRR) at the glass transition was determined from TM-DSC measurements on two glassy biopolymers with different molecular structures (amylose and amylopectin) as well as on starch, which is the mixture of amylose and amylopectin as it is obtained during its biosynthesis. For these materials, the ΔCp values at Tg and the values of the fragility index (m) were determined by conventional DSC. The fragility concept was then analyzed by taking into account the existence of two contributions: misoV (the so-called isochoric fragility, which is a pure thermal contribution) and mΔv (which incorporates the effects due to volume and density fluctuations). Whenever the molecular structure of a glass-forming liquid involves non-linear sequences of rigid and sterically hindered repeating units with high densities of hydrogen bonds, the fragility is found to be governed only by the temperature; the contribution of the volume (density and pressure contribution) has a quasi-nil effect.

Fragility of an Isochorically Confined Polymer Glass.

We report the effect of isochoric confinement on the dynamic fragility of a polymeric glass-former, that is, polystyrene (PS). Utilizing silica-capped PS nanospheres as a model system, the fictive temperature (Tf) and the isochoric heat capacity (Cv) are measured as a function of diameter via differential scanning calorimetry. By examining Tf as a function of cooling rate for each sample, the isochoric fragility (mv) is obtained, which decreases significantly as the diameter of the nanospheres is reduced from 260 to 129 nm. Hence, the temperature dependence of structural relaxation near the glass transition is weakened with isochoric confinement.

Fragility and glass transition temperature of polymer confined under isobaric and isochoric conditions

It is now well established that the glass transition temperature (Tg) of polymers can deviate substantially from the bulk with nanoscale confinement. Understanding the impact of confinement on the Tg of polymers is important but it does not provide information about the temperature dependence of the cooperative segmental dynamics near the Tg, a phenomenon commonly referred to as the dynamic fragility. Here, we measure the dynamic fragility index (m) as well as the Tg of confined poly(4-methylstyrene) (P4MS) under isobaric and isochoric conditions. We accomplish this via variable cooling rate differential scanning calorimetry (DSC) studies on aqueous-suspended and silica-capped P4MS nanoparticles. We observe that both the isobaric (mp) and isochoric (mv) fragilities decrease with confinement. However, Tg decreases and remains constant with isobaric and isochoric confinement, respectively. The importance of interfaces in the observed trends as well as comparisons to prior studies is discussed.

Universality of the onset of activated transport in Lennard-Jones liquids with tunable coordination: Implications for the effects of pressure and directional bonding on the crossover to activated transport, configurational entropy, and fragility of glassforming liquids

We establish, via classical density functional theory, that the crossover to activated transport in liquids takes place when the depth of the metastable minimum in the free energy corresponding to long-lived aperiodic structures reaches a certain near universal value. We show that the particle vibrational displacement is strongly correlated with this depth in a broad range of pressure and temperature, thus providing basis for a Lindemann-like criterion for the onset of activated transport in liquids. The configurational entropy at the crossover temperature T(cr), too, is found to be nearly system-independent, consistent with the random first order transition theory. We show that to reproduce existing data for the pressure dependence of T(cr), the liquid must increase its coordination with pressure. Upon increasing pressure at fixed coordination, the liquid's fragility is predicted to exhibit re-entrant behavior. This prediction is consistent with glycerol data but is in contrast with data in several organic liquids and polymers, whose fragility monotonically decreases with pressure in the so far accessed pressure range. Allowing for increase in coordination with pressure mitigates the disagreement, owing to the resulting decrease in the thermal expansivity. Finally, we rationalize the correlation between the isobaric and isochoric fragilities put forth by Casalini and Roland [Phys. Rev. E 72, 031503 (2005)] and make predictions on the limiting behavior of the fragility at high pressure.

Correlation of cooperatively localized rearrangement on the “fluidized domain” in glass substances (or polymers) to their fragility III: Theory of dynamic fragility at isochoric state

A set of universal equations on the reduced stress relaxation modulus with K-W-W stretched exponential function has been derived from the dynamics of α and β structural relaxation processes. In the present work, the K-W-W decay function is used to define the three types of relaxations (single α, single β relaxation and α-β co-relaxation), then their average times of relaxation are theoretically calculated from the reduced shear stress relaxation modulus and the relaxation time spectrum function H(τ). When the average time of co-relaxation, the reference temperatures (ficitive T f and glass transition T g ) and the isostructural parameter achieved from the conditions of isostructural glass state are introduced into the reduced shear stress relaxation modulus (G T ) under the equilibrium state, a set of correlations between isochoric fragility index (m να , m νβ and m ναβ ) and the coupling strength (α and β) under the reference temperatures are derived from the exact definition of isochoric fragility. So the theory of dynamic fragility for glass substances at isochoric state is developed. The theory can predict the following main features of structural relaxations and behavior of isochoric fragility: the temperature dependence of peak relaxation frequency exhibits a bifurcation with a pair of single α and single β relaxations; the temperature dependence of Stickel equation on 1/T exhibits two crossovers with VFTH(1) and VFTH(2) at the temperatures of T f and T g regime; there are two linear correlations between isochoric fragility index (m να and m νβ ) and the coupling strength. Fine agreements between the theoretical calculation and experimental results are obtained.

Is there a connection between fragility of glass forming systems and dynamic heterogeneity/cooperativity?

Although fragility of glass forming liquids is traditionally related to cooperativity in molecular motion, the connection between those parameters remains unclear. In this paper we present the estimates of cooperativity (heterogeneity) length scale ξ obtained from the boson peak spectra. We demonstrate that ξ agrees well with the dynamic heterogeneity length scale for the structural relaxation estimated by 4-dimensional NMR, justifying the use of ξ. Presented analysis of large number of materials reveals no clear correlation between ξ and fragility. However, there is a strong correlation between the cooperativity volume ξ 3 and the activation volume measured at T g. This observation suggests that only the volume (pressure) dependence of structural relaxation time correlates directly with the cooperativity size. However, the pure thermal (energetic) contribution to the structural relaxation, the so-called isochoric fragility, exhibits no correlation to the heterogeneity length scale ξ, or the amount of structural units in ξ 3. The presented results call for a revision of traditional view on the role of cooperativity/heterogeneity in structural relaxation of glass forming systems.

Erratum: “Isobaric and isochoric fragilities and the influence of volume on the temperature dependence of local segmental relaxation in polyvinylethylene networks” [J. Chem. Phys. 123, 204905 (2005)

Erratum: “Isobaric and isochoric fragilities and the influence of volume on the temperature dependence of local segmental relaxation in polyvinylethylene networks” [J. Chem. Phys. 123, 204905 (2005)

An equation for the description of volume and temperature dependences of the dynamics of supercooled liquids and polymer melts

A recently proposed expression to describe the temperature and volume dependences of the structural (or α-) relaxation time is discussed. This equation satisfies the scaling law for the relaxation times, τ ( T , V ) = I ( TV γ ) , where T is temperature, V the specific volume, and γ a material-dependent constant. The expression for the function I ( TV γ ) is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover, providing a description of the dynamics with a minimal number of parameters. The results herein can be reconciled with previously found correlations of the isochoric fragility with both the isobaric fragility at atmospheric pressure and the scaling exponent γ.

Comment on “Correlations between isobaric and isochoric fragilities and thermodynamical scaling exponent for glass-forming liquids”

For nonassociated, glass-forming liquids and polymers, thermodynamic scaling of structural relaxation times and viscosities is an empirical fact, demonstrated by various groups for dozens of materials. The P and T invariance of the isochoric fragility follows directly from this scaling. Apparent inconsistencies with these statements were reported recently by Grzybowski [A. Grzybowski, K. Grzybowska, J. Zioło, and M. Paluch, Phys. Rev. E 74, 041503 (2006)]; however, the putative inconsistencies arise from use at higher pressures of parameters to correlate the isobaric and isochoric fragilities that are valid only for ambient pressure.

Reply to “Comment on ‘Correlations between isobaric and isochoric fragilities and thermodynamical scaling exponent for glass-forming liquids’”

Our recent paper [A. Grzybowski, K. Grzybowska, J. Zioło, and M. Paluch, Phys. Rev. E 74, 041503 (2006)] tested the correlations between isobaric and isochoric fragilities, m_{P} and m_{V} , as well as the scaling exponent gamma under elevated pressure conditions. The preceding paper [R. Casalini and C. M. Roland, Phys. Rev. E 76, 013501 (2007)] is a Comment by the authors of the correlations originally determined for atmospheric pressure. In this Reply we present our point of view on criticisms contained in the Comment. We clarify and maintain our previously drawn conclusions.

On the correlation between fragility and stretching in glass-forming liquids

We study the pressure and temperature dependences of the dielectricrelaxation of two molecular glass-forming liquids, dibutyl phthalate andm-toluidine. We focus on two characteristics of the slowing down of relaxation, the fragilityassociated with the temperature dependence and the stretching characterizing therelaxation function. We combine our data with data from the literature to revisit theproposed correlation between these two quantities. We do this in light of constraintsthat we suggest to put on the search for empirical correlations among propertiesof glass-formers. In particular, we argue that a meaningful correlation is to belooked for between stretching and isochoric fragility, as both seem to be constantunder isochronic conditions and thereby reflect the intrinsic effect of temperature.

Correlations between isobaric and isochoric fragilities and thermodynamical scaling exponent for glass-forming liquids

Two correlations concerning the isobaric and isochoric fragilities, m(P) and m(V), as well as the scaling exponent gamma reported by Casalini and Roland [Phys. Rev. E 72, 031503 (2005)] have been examined for several van der Waals and hydrogen-bonded glass formers. It has been pointed out that the correlations lead to some serious inconsistency with the exponent gamma, which is expected to be a constant dependent only on material, but varies also on pressure if experimentally found pressure dependences of m(P) are taken into account. This problem could be solved in the case of van der Waals liquids, but then at least one of the correlations becomes dependent on thermodynamic conditions, and consequently, loses its universality. However, some H-bonded systems, due to properties of hydrogen bonding, have been well argued not to be included to determine the correlations independently of thermodynamic conditions. Furthermore, it has been noticed that another correlation concerning the fragility, between m(P) and the structural relaxation peak breadth, yields discrepancies in comparison with results of experiments under elevated pressure.

Isobaric and isochoric properties of decahydroisoquinoline, an extremely fragile glass-former

Pressure–volume–temperature (PVT) measurements were obtained on decahydroisoquinoline (DHIQ). From the resulting equation of state in combination with previously reported dielectric relaxation data, an analysis of the volume contribution to the dynamics was carried out for this very fragile glass-former (isobaric fragility, mP=163). We find that the ratio of the isochoric and isobaric fragilities equals 0.71±0.02, reflecting a strong temperature effect, consistent with the large fragility. The relaxation times superpose when plotted versus temperature times the specific volume raised to the 3.55 power. This is a larger value of the exponent than expected based on the fragility of DHIQ. The implication is that for molecular glass-formers, the classical Lennard-Jones 6–12 repulsive potential may represent the limit for fragile liquids.

What Can We Learn by Squeezing a Liquid?

Relaxation times tau(T,upsilon) for different temperatures, T, and specific volumes, upsilon, collapse to a master curve vs Tupsilon(gamma), with gamma a material constant. The isochoric fragility, mV, is also a material constant, inversely correlated with gamma. From these experimental facts, we obtain a three-parameter function that accurately fits tau(T,upsilon) data for several glass-formers over the supercooled regime, without any divergence of tau below Tg. Although the values of the three parameters depend on the material, only gamma significantly varies; thus, by normalizing material-specific quantities related to gamma, a universal power law for the dynamics is obtained.

Isobaric and isochoric fragilities and the influence of volume on the temperature dependence of local segmental relaxation in polyvinylethylene networks

The ratio of the isochoric and isobaric activation enthalpies at T(g) is used to quantify the relative contributions of the specific volume and temperature to the local segmental dynamics of polyvinylethylene networks. The dynamics of the networks become more dominated by temperature with increasing cross-link density, consistent with an increasing isobaric fragility. We also find a correlation between the isochoric and isobaric fragilities for the polyvinylethylene networks, in accord with a previously reported relationship between these two quantities for polymers and molecular glass-forming liquids [R. Casalini and C. M. Roland, Phys. Rev. E 72, 031503 (2005)].