De Gennes Narrowing Research Articles

On De Gennes narrowing of fluids confined at the molecular scale in nanoporous materials.

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling in many aspects. With striking examples such as memory, i.e., non-viscous effects, intermittent dynamics, and surface barriers, the dynamics of fluids in nanoconfinement challenge classical formalisms (e.g., random walk, viscous/advective transport)-especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent Brownian motion, free volume theory, and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for collective diffusion (i.e., permeability), which characterizes the flow induced by a thermodynamic gradient, is lacking. Here, to fill this knowledge gap, we invoke the concept of "De Gennes narrowing," which relates the wavevector-dependent collective diffusivity D0(q) to the fluid structure factor S(q). First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, the departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport.

De Gennes Narrowing and Relationship between Structure and Dynamics in Self-Organized Ion-Beam Nanopatterning.

Investigating the relationship between structure and dynamical processes is a central goal in condensed matter physics. Perhaps the most noted relationship between the two is the phenomenon of de Gennes narrowing, in which relaxation times in liquids are proportional to the scattering structure factor. Here, asimilar relationship is discovered during the self-organized ion-beam nanopatterning of silicon using coherent x-ray scattering. However, in contrast to the exponential relaxation of fluctuations in classic deGennes narrowing, the dynamic surface exhibits a wide range of behaviors as a function of the length scale, with a compressed exponential relaxation at lengths corresponding to the dominant structural motif-self-organized nanoscale ripples. These behaviors are reproduced in simulations of a nonlinear model describing the surface evolution. We suggest that the compressed exponential behavior observed here is due to the morphological persistence of the self-organized surface ripple patterns which form and evolve during ion-beam nanopatterning.

De Gennes Narrowing and Hard-Sphere Approach

The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.

Br diffusion in molten NaBr explored by coherent quasielastic neutron scattering.

Molten sodium bromide has been investigated by quasielastic neutron scattering focusing on the wave vector range around the first structure factor peak. The linewidth of the scattering function shows a narrowing around the wave number of the structure factor peak, known as deGennes narrowing. In a monatomic system, this narrowing or in the time domain slowing down, has been related to a self-diffusion process of the caged particle. Here we show that this methodology can be applied to the molten alkali halide NaBr. The incoherent scattering from the sodium ions at small wave vectors provides the self-diffusion coefficient of sodium and the dynamics of bromine ions can be studied at wave numbers around the structure factor peak. With input from moleculardynamicssimulations on the partial structure factors, diffusion coefficients of the bromine ions can be obtained. These experimentally derived diffusion coefficients are in good agreement with molecular dynamics simulation results. This methodology to extract self-diffusion coefficients from coherent quasielastic neutron scattering is applicable to binary fluids in general when one particle dominates the scattering response at the structure factor maximum.

Quasi-elastic neutron scattering measurements of liquid germanium

From the quasi-elastic neutron scattering experiment, dynamic structure factors, S(Q, E) were obtained at both 1000°C and 1500°C. To understand the distribution of the dynamic structure factor as a scattering low, the half-width at half-maximum (HWHM) of dynamic structure factor was determined. It is clear that the Q dependence for HWHM of S(Q, E) does not fulfil the rigorous definition on the condition of the phenomenon called the de Gennes narrowing. From the Fourier transform, the intermediate scattering function, F(Q, t), is obtained. From the result of F(Q, t), it is clear that the relaxation process of liquid germanium is different from that of simple liquid.

Quasielastic Neutron Scattering and Molecular Dynamics Simulation Study on the Structure Factor of Poly(ethylene-alt-propylene)

By combining neutron scattering and fully atomistic molecular dynamics simulations, we have investigated the static [S(Q)] and dynamic [S(Q,t)] structure factor of poly(ethylene-alt-propylene) in a wide momentum-transfer Q range (0.2 < Q < 3 Å−1) spanning over inter- and intramolecular length scales and including also the region of intermediate length scales. The experiments consist of diffraction with polarization analysis and neutron spin-echo measurements on a fully deuterated sample. These results have been used to thoroughly validate the simulations, which have been subsequently exploited to unravel the different contributions to S(Q) and S(Q,t) and provide insights into real space. We have first disentangled the short-range order in this polymer. At the first peak of S(Q) which is clearly dominated by the interchain contribution of the main-chain/main-chain correlations, the dynamics above the glass transition reveal the genuine α-relaxation. The direct observation of the α-relaxation in this way has allowed establishing the viscosity scaling, the stretching, and the deGennes narrowing. An in-phase modulation with S(Q) is observed for the amplitude and shape parameter of the slow decay of S(Q,t) around the first peak. The corresponding time scale also displays a maximum that shifts with temperature in a much stronger way than that of S(Q). Coherency effects in the slow decay are lost above ≈1.5 Å−1, where intramolecular correlations dominate. Interestingly, the apparent activation energy of the characteristic time mirrors the structure factor in the whole Q range investigated.

Characterization of the “simple-liquid” state in a polymeric system: Coherent and incoherent scattering functions

By means of time-of-flight neutron scattering, we have characterized the dynamic structure factor and the hydrogen motions of polyethylene above its melting point. As signatures of simple-liquid dynamics, we observe that (i) in the explored dynamic window, the intermediate scattering functions display a single-step decay, without reminiscence of cage effects, and (ii) the structural relaxation as observed at the intermolecular structure factor peak shows a weak temperature dependence, indicating a low degree of interchain cooperativity. However, stretched functional forms are observed for all length scales and temperatures investigated. An apparent direct crossover from the microscopic regime to Rouse-like dynamics suggests an essential role of connectivity in the observed stretching. Finally, while at momentum-transfer values above the structure factor peak the relation between coherent and incoherent characteristic times is reasonably described by the de Gennes narrowing, at larger length scales it is not reproduced by any existing approach.

De Gennes slowing in a liquid metal revisited: A neutron spin-echo study

In liquids the decay of density fluctuations shows a slowing down at the structure factor maximum, which is well known as de Gennes narrowing. Molecular dynamics simulations of the liquid metal rubidium and mode coupling theory suggested that this process can be described by a two-step relaxation function. We have probed these predictions with inelastic neutron scattering using the spin-echo technique to measure the dynamics directly in the time domain. The dynamics of liquid rubidium was investigated near the melting point at times beyond the fast contribution. The resulting intermediate-scattering function is in remarkable agreement with predicted values from the mode coupling calculations.

Dynamics of propylene glycol and its 7-mer by neutron scattering

The dynamics of propylene glycol (PG) and its 7-mer have been investigated by quasielastic neutron scattering (QENS). In the case of PG we used two techniques; ordinary QENS and neutron spin-echo (NSE). The QENS and NSE experiments were carried out at the temperature ranges 300–420 K and 260–340 K, respectively. The QENS results on both the monomer and the 7-mer showed three clear dynamical processes; a weakly temperature dependent fast local motion of hydrogens in the polymeric backbone, an almost temperature independent rotational motion of the methyl groups, and a strongly temperature dependent translational process. This latter motion exhibits a clear quasi-elastic broadening proportional to Q2 at high temperatures (T⩾380 K). At lower temperatures the diffusion becomes more difficult to characterize due to the contribution from the methyl group rotation. However, despite this difficulty it is no doubt about that the diffusion is faster for the 7-mers than for the monomers at low temperatures (T⩽340 K). The reason for this anomalous behavior may be that the OH end groups of the monomers are linked together to a network at lower temperatures, which would slow down the translational diffusion. Another possible explanation can be that the dynamics of the 7-mers is dominated by segmental motions, which might be faster than the translational diffusion of single monomers at low temperatures. The NSE data on deuterated PG were described by the Kohlrausch–Williams–Watts (KWW) stretched exponential function, with a temperature independent stetching parameter βKWW. The reason for the stretched behavior of the coherent intermediate scattering function I(Q,t) is most likely that several dynamical processes, such as the primary α-relaxation and secondary β-relaxations, are observed in the experimental time window (3–1500 ps), in accordance with the QENS results given above. An interesting observation is that the dynamics is slowest and the stetching parameter βKWW is largest for Q=1.4 Å−1, corresponding to the position of the first diffraction peak in the static structure factor S(Q), a phenomenon known as de Gennes narrowing.

Dynamics in viscous orthoterphenyl: Results from coherent neutron scattering.

We have measured coherent neutron scattering from deuterated orthoterphenyl on a spin echo and a backscattering spectrometer. In agreement with mode coupling theory, pair correlations decay in two steps and follow the same scaling laws as those found previously for self-correlations. The temperature evolution of the intermediate plateau is compatible with the previously established ${\mathit{T}}_{\mathit{c}}$=290 K. The spatial resolution has not been sufficient to fully resolve oscillations of parameters as functions of Q, which are predicted by mode coupling theory. Within this limitation, we find that the double peak structure of S(Q) is not expressed in the nonergodicity parameter ${\mathit{f}}_{\mathit{Q}}^{\mathit{c}}$ and that the de Gennes narrowing is missing.

Quasi-elastic neutron scattering studies of collective and correlated tracer diffusion in the systems α′-NbDx and α′-NbHx

The technique of neutron polarization analysis has been applied to the problem of separating the coherent and incoherent quasi-elastic scattering from deuterium in α-NbD0.7. The coherent scattering has provided a first experimental test of a theory due to Sinha and Ross (S. K. Sinha and D. K. Ross, Physica B, 149 (1988) 51) with some simplifying assumptions. The coherent quasi-elastic spectra exhibit a behaviour analogous to a De Gennes narrowing, corrected for tracer and mobility correlation factors. The tracer correlations have been studied in more detail by incoherent quasi-elastic neutron scattering from α′-NbH0.79. The results indicate a significant Q and ω dependence of the tracer correlation factor for which the Q dependence in the long time limit indicates an expected periodicity in the Brillouin zone of the interstitial lattice.

Quasi-elastic neutron scattering studies of collective and correlated tracer diffusion in the systems α'-NbDx and α'-NbHx

The technique of neutron polarization analysis has been applied to the problem of separating the coherent and incoherent quasi-elastic scattering from deuterium in α-NbD 0.7 . The coherent scattering has provided a first experimental test of a theory due to Sinha and Ross (S. K. Sinha and D. K. Ross, Physica B, 149 (1988) 51) with some simplifying assumptions. The coherent quasi-elastic spectra exhibit a behaviour analogous to a De Gennes narrowing, corrected for tracer and mobility correlation factors. The tracer correlations have been studied in more detail by incoherent quasi-elastic neutron scattering from α′-NbH 0.79 . The results indicate a significant Q and ω dependence of the tracer correlation factor for which the Q dependence in the long time limit indicates an expected periodicity in the Brillouin zone of the interstitial lattice.

Inelastic neutron scattering studies of the dynamics of molten alkali halides

The authors have measured the inelastic neutron scattering spectra of samples of molten RbCl, CsCl and NaI using the time-of-flight technique. These show broadening of the quasi-elastic peak associated with diffusion together with an extended inelastic spectrum associated with collective motions. They present a set of definitions of correlation functions for binary systems in terms of which the spectra are analysed. Single-ion motion is shown to be consistent with simple diffusion up to the first peak in S+-(Q) after which it becomes more gas-like. de Gennes narrowing of the quasi-elastic peak due to collective motions is observed. The inelastic scattering is discussed in terms of these collective motions which are represented by mass ('acoustic' type mode) and charge ('optic' type mode) current correlations. Quantitative comparison is made with the results of computer simulation and of the inelastic neutron scattering spectra at various temperatures in both the solid and molten states.

Quasielastic Neutron Scattering in Normal and Deuterated P-Azoxyanisole

The neutron scattering from normal (protonated p-PAA) and deuterated (d-PAA) para-azoxyanisole has been measured in the isotropic liquid phase at momentum transfers 0.8 A-1 < Q < 5 A-1 and energy transfers ℏω up to 25 mev. For p-PAA the spectra can be interpreted on a model of continuous, uniaxial rotational diffusion around the long molecular axis with diffusion coefficient D = 0.18 meV. For d-PAA, which is a coherent scatterer, the structure of the liquid manifests itself through the structure factor S(Q), which modulates the scattered intensity and introduces an energy narrowing (de Gennes narrowing) at the maxima of S(Q). Data on unoriented samples of d-PAA in the nematic phase are indistinguishable from those measured in the isotropic phase, suggesting that no collective excitations of the nematic phase do exist.

Dynamics of the Liquid-Solid Transition

Associated with the stability limit of the liquid phase, we find a soft mode with purely imaginary frequency at a wave vector corresponding to the first peak of the structure factor. The corresponding critical fluctuations show up in neutron-scattering experiments as the de Gennes narrowing of the quasielastic peak.