Cooperativity Length Scale Research Articles

The influence of molecular shape on reorientation dynamics of sizable glass-forming isomers at ambient and elevated pressure

We used dielectric spectroscopy to access the molecular dynamics of three isomers with a structure based on a sizable, partially rigid, and non-polar core connected to a polar phenylene unit differing in the position of the polar group, and, consequently, the direction and magnitude of the dipole moment to address the question how unique molecular properties, in particular large size and elongated shape, affect the dynamics. The position of the polar group differentiates the molecular shape and isomer’s anisotropy and leads to different thermal and dynamic properties of the isomers. The shape of permittivity loss spectra was governed by magnitudes of the longitudinal and transverse components of dipole moment to a large extent. For para isomer with negligible traverse component of dipole moment, the narrowest loss peak was found while for meta isomer, the bimodal loss peak was observed at high temperatures. Its shape evolved on cooling limiting the possibility of individual mode separation near glass transition where the dynamics were more cooperative. High-pressure dielectric studies showed that sizable isomers were characterized by the pronounced sensitivity of glass transition temperature, Tg, to compression. Observed high activation volumes, such as 735 cm3/mol at Tg for para isomer, were found to correlate with the length scale of dynamic cooperativity. The number of dynamically correlated molecules depended on molecular shape and varied among isomers while the determined values were much smaller than that reported for other glass-forming liquids. We discussed here the obtained results in the context of the specific properties of the systems studied showing the overriding role of anisotropy.

Ion transport, mechanical properties and relaxation dynamics in structural battery electrolytes consisting of an imidazolium protic ionic liquid confined into a methacrylate polymer

The effect of confining a liquid electrolyte into a polymer matrix was studied by means of Raman spectroscopy, differential scanning calorimetry, temperature-modulated differential scanning calorimetry, dielectric spectroscopy, and rheology. The polymer matrix was obtained from thermal curing ethoxylated bisphenol A dimethacrylate while the liquid electrolyte consisted of a protic ionic liquid based on the ethyl-imidazolium cation [C2HIm] and the bis(trifluoromethanesulfonyl)imide [TFSI] anion, doped with LiTFSI salt. We report that the confined liquid phase exhibits the following characteristics: (i) a distinctly reduced degree of crystallinity; (ii) a broader distribution of relaxation times; (iii) reduced dielectric strength; (iv) a reduced cooperativity length scale at the liquid-to-glass transition temperature (T g); and (v) up-speeded local T g-related ion dynamics. The latter is indicative of weak interfacial interactions between the two nanophases and a strong geometrical confinement effect, which dictates both the ion dynamics and the coupled structural relaxation, hence lowering Tg by about 4 K. We also find that at room temperature, the ionic conductivity of the structural electrolyte achieves a value of 0.13 mS/cm, one decade lower than the corresponding bulk electrolyte. Three mobile ions (Im+, TFSI-, and Li+) contribute to the measured ionic conductivity, implicitly reducing the Li+ transference number. In addition, we report that the investigated solid polymer electrolytes exhibit the shear modulus needed for transferring the mechanical load to the carbon fibers in a structural battery. Based on these findings, we conclude that optimized microphase-separated polymer electrolytes, including a protic ionic liquid, are promising for the development of novel multifunctional electrolytes for use in future structural batteries.

Impact of the graft’ structure on the behavior of PMMS-based brushes. High pressure studies

In this paper, we have investigated dielectric response at ambient and elevated pressure of poly(mercaptopropyl)methylsiloxane (PMMS) based oligomeric brushes, where the thiol moiety was substituted by various butyl acrylate isomers (n-butyl acrylate (nBA), iso-butyl acrylate (isoBA), tert-butyl acrylate (tertBA)). It was found that the glass transition temperature, Tg, of PMMS is much lower with respect to the other systems despite its ability to form weak hydrogen (H) bonds. What is more, the length scale of cooperativity was the highest in homopolymer and scaled with the steric hindrance of the graft. We also demonstrated that in the examined grafted copolymers, there is one broad relaxation process in dielectric spectra which is wider than that recorded in mechanical response. That probably means that similarly to PMMS, there are two relaxation processes above Tg in grafted copolymers. However, due to similar timescale, they cannot be separated. Further, high-pressure experiments revealed that pressure coefficient of the glass transition temperature, dTg/dp, as well as the activation volume, ΔV, calculated for the segmental process surprisingly does not scale with either the size of monomer nor steric hindrance. This unexpected result must be related to the specific structure adopted by the studied grafted oligomers. Presented herein data expand our understanding on the impact of topology on the dynamics of polymers at ambient and high pressure.

Supercooled water confined in a metal-organic framework

Within the so-called “no-man’s land” between about 150 and 235 K, crystallization of bulk water is inevitable. The glass-like freezing and a liquid-to-liquid transition of water, predicted to occur in this region, can be investigated by confining water in nanometer-sized pores. Here, we report the molecular dynamics of water within the pores of a metal-organic framework using dielectric spectroscopy. The detected temperature-dependent dynamics of supercooled water matches that of bulk water as reported outside the borders of the no-man’s land. In confinement, a different type of water is formed, nevertheless still undergoing a glass transition with considerable molecular cooperativity. Two different length scales seem to exist in water: a smaller one, of the order of 2 nm, being the cooperativity length scale governing glassy freezing, and a larger one (> 2 nm), characterizing the minimum size of the hydrogen-bonded network needed to create “real” water with its unique dynamic properties.

Correlation between the temperature evolution of the interfacial region and the growing dynamic cooperativity length scale.

We study experimentally the temperature evolution of the thickness of the interfacial layer, Lint(T), between bulk matrices and the surface of nanoparticles in nanocomposites through broadband dielectric spectroscopy. Analyses revealed a power-law dependence between the logarithm of structural relaxation time in the interfacial layer, τint(T), and the Lint(T): lnτint(T)/τ0∝Lint β(T)/T, with τ0 ∼ 10-12 s, and β index ∼0.67 at high temperatures and ∼1.7 at temperatures close to the glass transition temperature. In addition, our analysis revealed that the Lint(T) is comparable to the length scale of dynamic heterogeneity estimated from previous nonlinear dielectric measurements and the four-point NMR [ξNMR(T)], with Lint(T) ∼ ξNMR(T). These observations may suggest a direct correlation between the Lint(T) and the size of the cooperatively rearranging regions and have strong implications for understanding the dynamic heterogeneity and cooperativity in supercool liquids and their role in interfacial dynamics.

Polymer tethered graphene oxide influences miscibility and cooperative relaxation in LCST blends

The miscibility of a classical lower critical solution temperature (LCST) system; PMMA/SAN was probed by different rheological fingerprints such as isochronal temperature ramps, and isothermal frequency sweeps, in presence of graphene oxide (GO) and PMMA tethered GO. The chain length of the grafted polymer was varied to study its effect on miscibility, volume cooperativity, entanglement density and localization in the blends. The PMMA tethered GO alters the chain dynamics both at local and cooperative length scale through entropic and enthalpic interactions. It was perceived that the thermodynamic miscibility, cooperative relaxations and concentration fluctuation in PMMA/SAN blends are controlled by the spatial distribution of GO in the blend. By varying the chain length, we were able to understand that shorter tethered chains lead to early phase separation whereas the tethered chain length similar to that of the host matrix delays phase separation. Interestingly, irrespective of the length of the tethered polymer chain, the grafted GO sheets were not localized in the thermodynamically preferred phase (here PMMA). These findings are of great importance to further help us understand the theories and simulations which pertain to chain dynamics of PMMA/SAN blends containing polymer-tethered nanoparticles with large specific surface area like GO.

The emergence of cooperativity accompanying vitrification: insights from density fluctuation dynamics

We discuss the emergence and growth of the cooperativity accompanying vitrification based on the density fluctuation dynamics for fragile glass-forming liquids. (i) The relaxation of density fluctuations proceeds by the particle (density) exchange process, and is diffusive; that is, the allowable kinetic paths are strongly restricted by the local conservation law. (ii) In normal liquid states, this exchange process is less cooperative, and the diffusion coefficient of density fluctuations Dc is given as , where is the particle size and is the structural relaxation time. On the other hand, in supercooled states the restriction on the kinetic path is more severe with increasing the degree of supercooling, which makes the exchange process more cooperative, resulting in with being the cooperative length scale. (iii) The molecular dynamics simulation results show that the self-diffusion coefficient of the tagged particle, Ds, almost coincides with Dc, suggesting that the collective density diffusion and the particle diffusion closely share the same mechanism: in normal states Ds determines Dc, but vice versa in supercooled states. This immediately leads to the idea that the breakdown of the Stokes–Einstein relation is not the anomaly in the single-particle dynamics but reflects the increase in the cooperativity in the density diffusion at the length scale of .

Glycerol confined in zeolitic imidazolate frameworks: The temperature-dependent cooperativity length scale of glassy freezing.

In the present work, we employ broadband dielectric spectroscopy to study the molecular dynamics of the prototypical glass former glycerol confined in two microporous zeolitic imidazolate frameworks (ZIF-8 and ZIF-11) with well-defined pore diameters of 1.16 and 1.46 nm, respectively. The spectra reveal information on the modified α relaxation of the confined supercooled liquid, whose temperature dependence exhibits clear deviations from the typical super-Arrhenius temperature dependence of the bulk material, depending on the temperature and pore size. This allows assigning well-defined cooperativity length scales of molecular motion to certain temperatures above the glass transition. We relate these and previous results on glycerol confined in other host systems to the temperature-dependent length scale deduced from nonlinear dielectric measurements. The combined experimental data can be consistently described by a critical divergence of this correlation length as expected within theoretical approaches assuming that the glass transition is due to an underlying phase transition.

Elastically Collective Nonlinear Langevin Equation Theory of Glass-Forming Liquids: Transient Localization, Thermodynamic Mapping, and Cooperativity.

We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the elastically collective nonlinear Langevin equation (ECNLE) theory. By invoking a high-temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron-scattering measurements. In contrast, in the same format, a strongly nonuniversal behavior is found for the activation barrier that controls long-time relaxation. Two measures of cooperativity in the ECNLE theory are analyzed. A particle-level total displacement associated with the alpha relaxation event is found to be only of order 1-2 particle diameters and weakly increases with cooling. In contrast, an alternative cooperativity length is defined as the spatial scale required to essentially recover the full barrier and bulk alpha time. This length scale grows strongly with cooling because of the emergence in the deeply supercooled regime of collective long-range elastic fluctuations required to allow local hopping. It becomes very large as the laboratory Tg is approached, though it is relatively modest at degrees of supercooling accessible with molecular dynamics simulation. The alpha time is found to be exponentially related to this cooperativity length over an enormous number of decades of relaxation time that span the lightly to deeply supercooled regimes. Moreover, the effective barrier height increases almost linearly with the growing cooperativity length scale. An alternative calculation of the collective elastic barrier based on a literal continuum mechanics approach is shown to result in very little change of the theoretical results for bulk properties but leads to a much smaller and less temperature-sensitive cooperativity length scale.

Structural and cooperative length scales in polymer gels.

Understanding the relationship between the material structural details, the geometrical confining constraints, the local dynamical events and the global rheological response is at the core of present investigations on complex fluid properties. In the present article, this problem is addressed on a model yield stress fluid made of highly entangled polymer gels of Carbopol which follows at the macroscopic scale the well-known Herschel-Bulkley rheological law. First, performing local rheology measurements up to high shear rates ([Formula: see text] s-1)and under confinement, we evidence unambiguously the breakdown of bulk rheology associated with cooperative processes under flow. Moreover, we show that these behaviors are fully captured with a unique cooperativity length [Formula: see text] over the whole range of experimental conditions. Second, we introduce an original optical microscopy method to access structural properties of the entangled polymer gel in the direct space. Performing image correlation spectroscopy of fluorophore-loaded gels, the characteristic size D of carbopol gels microstructure is determined as a function of preparation protocol. Combining both dynamical and structural information shows that the measured cooperative length [Formula: see text] corresponds to 2-5 times the underlying structural size D, thus providing a strong grounding to the "Shear Transformation Zones" modeling approach.

Scaling description of non-local rheology.

The plastic flow of amorphous materials displays non-local effects, characterized by a cooperativity length scale ξ. We argue that these effects enter in the more general description of surface phenomena near critical points. Using this approach, we obtain a scaling relation between exponents that describe the strain rate profiles in shear driven and pressure driven flow, which we confirm both in numerical models and experimental data. We find empirically that the cooperative length follows closely the characteristic length previously extracted in homogenous bulk flows. This analysis shows that the often used mean field exponents fail to capture quantitatively the non-local effects. Our analysis also explains the unusually large finite size effects previously observed in pressure driven flows.

Nanomechanical Mapping, Hierarchical Polymer Dynamics, and Miscibility in the Presence of Chain-End Grafted Nanoparticles

To improve the spatial distribution of nanoparticles in a polymeric host and to enhance the interfacial interaction with the host, the use of chain-end grafted nanoparticle has gained popularity in the field of polymeric nanocomposites. Besides changing the material properties of the host, these grafted nanoparticles strongly alter the dynamics of the polymer chain at both local and cooperative length scales (relaxations) by manipulating the enthalpic and entropic interactions. It is difficult to map the distribution of these chain-end grafted nanoparticles in the blend by conventional techniques, and herein, we attempted to characterize it by unique technique(s) like peak force quantitative nanomechanical mapping (PFQNM) through AFM (atomic force microscopy) imaging and dielectric relaxation spectroscopy (DRS). Such techniques, besides shedding light on the spatial distribution of the nanoparticles, also give critical information on the changing elasticity at smaller length scales and hierarchical polyme...

Dynamic Heterogeneity and Cooperative Length Scale at Dynamic Glass Transition in Glass Forming Liquids

Understanding the evolution of the cooperative molecular mobility as a function of time and temperature remains an unsolved question in condensed matter research. However, recently great advances have been made within the framework of the Adam–Gibbs theory on the connection between cooperatively rearranging regions, or dynamic heterogeneities, i.e., domains of the supercooled liquid whose relaxation is highly correlated. The growth of the size of these dynamic domains is now believed to be the driving mechanism for different experimental parameters like relaxation times and viscosity of supercooled liquid approaching the glass transition. Recent studies have shown the evolution of cooperative motions in supercooled liquids using different experimental tools and models. In this work, broadband dielectric spectroscopy and modulated temperature differential scanning calorimetry were carried out on six different amorphous glass-forming systems in order to scan a wide range of relaxation times and temperatures...

Slow Water Dynamics near a Glass Transition or a Solid Interface: A Common Rationale.

Performing molecular dynamics simulations, we investigate the enormous slowdowns of water dynamics when approaching a glass transition or a solid interface. We show that both effects can be described on common grounds within a theoretical framework, which was recently proposed by Schweizer et al. and considers coupled local hopping and elastic distortion. For confined water, we correctly describe the variation of the α-relaxation time, τα, as a function of both temperature and position with respect to the interface. Exploiting our knowledge of a cooperative length scale ξ(T) from the confinement studies, we quantitatively rationalize the glassy slowdown, τα(T), and the Stokes-Einstein breakdown of bulk water. For both confined and bulk liquid, variations of the α-relaxation time are intimately related to changes of the cage-rattling amplitude.

Segmental mobility and glass transition of poly(ethylene-vinyl acetate) copolymers: Is there a continuum in the dynamic glass transitions from PVAc to PE?

The segmental dynamics of amorphous poly(ethylene-vinyl acetate) copolymers (from PVAc to EVA50) were studied. In that sample set with similar backbone stiffness and different amount of dipoles, the dynamic glass transition was investigated by Modulated Temperature Differential Scanning Calorimetry and Broadband Dielectric Spectroscopy measurements. A decrease of the cooperativity length scale was obtained with the vinyl acetate (VAc) content decreasing. On the other hand, there was no modification of the temperature dependence of the relaxation time. Thus, the fragility value is quite constant whatever the VAc content. These results show that fragility and cooperativity have two different origins. An extrapolation to nonconstrained polyethylene amorphous phase was proposed and new glass transition temperature and fragility values were determined.

Crystallization kinetics and structure evolution of a polylactic acid during melt and cold crystallization

The isothermal melt and cold crystallization and the evolutions of the mobile and rigid amorphous fractions during the crystallization are fully investigated for a polylactic acid using differential scanning calorimetry. The crystallization kinetics is analyzed through fitting the Avrami equation to two different sets of crystallinity data, one obtained from the crystallization extherms and one from the enthalpies of melting and cold crystallization. Both sets yield similar results, indicating the consistency between these two methodologies. The cold crystallization shows clearly faster crystallization rate and has a higher activation energy of 172.3 ± 8.9 versus 109.6 ± 8.8 kJ mol−1 for the melt crystallization. The Avrami exponent of the cold crystallization seems to decrease with increasing crystallization temperature, whereas the exponent of melt crystallization is relatively constant. In addition to the crystalline phase, properties of the mobile and rigid amorphous fractions are also studied and compared. With the increase in crystallinity, the glass transition temperature (Tg) of the mobile amorphous phase is found to decrease during the cold crystallization, whereas Tg decreases and then increases during the melt crystallization, indicating slightly different environment formed. However, no obvious difference is found regarding the heat capacity change at Tg nor the cooperative length scale associated with Tg. Furthermore, the rigid amorphous fraction is determined and found to be 30 % at the maximum crystallinity for the both cold- and melt-crystallized samples.

Supercritical carbon dioxide-assisted silanization of multi-walled carbon nanotubes and their effect on the thermo-mechanical properties of epoxy nanocomposites

Supercritical carbon dioxide was employed as the solvent for the functionalization of multi-walled carbon nanotubes (MWCNTs) with an epoxy-capped silane. The silanization protocol was found to be a suitable green alternative to traditional routes that rely on organic solvents for grafting nearly monolayers of silane molecules onto the nanotube surfaces. The addition of silanized MWCNTs to a model epoxy markedly increased its Tg, and measurements of the network cooperativity length scale linked this change to a reduction in polymer segment mobility. Composites filled with low loading levels of both pristine and silanized MWCNTs exhibited significantly higher strain at break and toughness than the neat epoxy, and the greatest improvements were observed at low loading levels. SEM analysis of the composite fracture surfaces revealed that nanotube pullout was the primary failure mechanism in epoxy loaded with pristine MWCNTs while crack bridging predominated in composites containing silanized MWCNTs as the result of strong interfacial bonding with the matrix. The elevated Tg and toughness achieved with small additions of silanized MWCNTs promise to extend the engineering applications of the epoxy resin.

Evidence of cooperativity length anisotropy in drawn polymers

The goal is to quantify the respective influence on relaxation dynamics of the molecular orientation and of the crystallinity in uniaxially drawn polyethylene terephthalate and poly(ethylene glycol-co-cyclohexane-1,4-dimethanol terephthalate) films, the last one presenting a lower ability to crystallize under drawing. Combining Temperature Modulated Differential Scanning Calorimetry and Dynamical Mechanical Analysis investigations we evidenced that cooperativity length scale becomes anisotropic with the molecular orientation induced by drawing.

Cooperativity length scale in nanocomposites: Interfacial and confinement effects

Interfacial and confinement effects on the evolution of cooperativity on approaching the glass transition have been studied in poly(propylenecoethylene) functionalized with diethylmaleate, polyethylene 1,4-cyclohexylenedimethylene terephthalate glycol and their nanocomposites with montmorillonite. A small increase of the structural dynamic cooperativity, a weak alteration of the temperature dependence of the characteristic relaxation frequency, and no changes in the glass transition temperature observed in poly(propylenecoethylene)-based samples can be rationalized in terms of interfacial interactions between polymer and exfoliated clay. On the other hand, confinement of polymer chains in the galleries of clay (intercalated nanocomposite) produces a strong reduction of cooperativity, of the temperature dependence of the characteristic relaxation frequency, and of the glass transition temperature in polyethylene 1,4-cyclohexylenedimethylene terephthalate glycol samples. Finally, by investigating the temperature dependence of a generalized fragility and of cooperativity, we evidenced that fragility of glass formers is determined not only by cooperativity.

Confined flows of a polymer microgel

In this paper, we probe the influence of confinement on the flows of a polymer microgel, namely Carbopol. We compare its bulk rheological behavior, measured with a rheometer and well described by a Hershel-Bulkley law, to velocity profiles measured in rough microchannels, obtained with a particle tracking velocimetry technique. We show a strong disagreement between the bulk prediction for the velocity profiles and the measured ones in the microchannels. Velocity profiles in confined conditions are successfully analyzed within the framework of a non-local fluidity model introduced recently (J. Goyon et al. Nature, 454, 84 (2008)). This allows to determine a cooperativity length ξ, whose order of magnitude compares with the structure size of the microgel. Moreover, we measure flow curves using a rheometer for different gap conditions and also show that this set of data exhibit a strong effect of the confinement on the measured rheological properties. This is again characterized by a typical length of the same order as the cooperativity length scale ξ. We thus evidence confinement effects with two complementary experiments which both give the same typical length for the rearrangements in the flows.