Neutron scattering study of the dynamics of a polymer melt under nanoscopic confinement

Relaxation dynamics of a liquid in the vicinity of an attractive surface: The process of escaping from the surface

We analyze the displacements of the particles of a glass-forming molecular liquid perpendicular to a confining solid surface using extensive molecular dynamics simulations with atomistic models. In the vicinity of an attractive surface, the liquid molecules are trapped. Transient localization of liquid molecules near the surface introduces a relaxation process related to the escape of molecules from the surface into the dynamics of the interfacial liquid layer. To describe this process, we analyze several dynamical observables of the confined liquid. The self-intermediate scattering function and the mean-squared displacement of the particles located in the interfacial layer are dominated by the process of escaping from the surface. This relaxation process is also associated with a strong heterogeneity in the mobility of the interfacial particles. The studied model liquid is hydrogenated methyl methacrylate. For the confining wall, we consider different models, namely a periodic single layer of graphene and a frozen amorphous configuration of the bulk liquid (frozen wall). Near graphene, where the liquid molecules form a layered structure and adopt parallel-to-surface orientation, a clear separation between small-scale movements of the molecules near the surface and the process of escaping from the surface is observed. This is reflected in the three-step relaxation of the interfacial layer. However, near the frozen wall, where the liquid molecules do not have a preferential alignment, a clear three-step relaxation is not seen, even though the dynamical quantities are controlled by the process of escaping from the surface.

Effect of Oligomer Addition on Tube Dilation in Polymer Nanocomposite Melts

This study investigates the effect of adding oligomers on the rheological properties of polymer nanocomposite melts with the goal of enhancing the processability of nanocomposites. The scaling analysis of plateau modulus (GN ) is used in understanding the complex mechanical behavior of entangled poly(methyl acrylate) (PMA) melts upon oligomer addition. Increasing the oligomer amount led to a decrease in GN and an apparent degree of entanglement (Z) in the neat polymer melt. The particle dispersion states at two particle loadings with oligomer addition are examined in transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS). The dilution exponent is found unchanged at 7 and 17 vol% particle loadings for the well-dispersed PMA-SiO2 nanocomposites compared to the neat PMA solution. These findings suggest that attractive particles with strong interfacial layers do not influence the tube dilution scaling of the polymer with the oligomer. To the contrary, composites with weak polymer-particle interfaces demonstrate phase separation of particles when oligomers are introduced and its exponent for tube dilution scaling reaches 4 at a particle loading of 17 vol%, potentially indicating that network-forming clusters influence chain entanglements in this scenario.

Structure and dynamics of a 1,4-polybutadiene melt in an alumina nanopore: A molecular dynamics simulation

We present results of Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene (PBD)confined in a cylindrical alumina nanopore of diameter 10 nm. The simulations are done at three different temperaturesabove the glass transition temperature T g . We investigate the density layering across the nanopore as well as theorientational ordering in the polymer melt, brought about by the confinement, on both the segmental and chain scales.For the chain scale ordering, the magnitude and orientation of the axes of the gyration tensor ellipsoid of single chainsare studied and are found to prefer to align parallel to the pore axis. Even though double bonds near the wall arepreferentially oriented along the pore walls, studying the nematic order parameter indicates that there is no nematicordering at the melt-wall interface. As for the dynamics in the melt, we focus here on the mean-square-displacement ofthe monomers for several layers across the nanopore as well as the movement of the chain center of mass which bothdisplay a slowing down of the dynamics in the layer at the wall. We also show the strong adsorption of the monomersto the pore wall at lower temperatures.

Chain-End Effects on Supramolecular Poly(ethylene glycol) Polymers

In this work we present a fundamental analysis based on small-angle scattering, linear rheology and differential scanning calorimetry (DSC) experiments of the role of different hydrogen bonding (H-bonding) types on the structure and dynamics of chain-end modified poly(ethylene glycol) (PEG) in bulk. As such bifunctional PEG with a molar mass below the entanglement mass Me is symmetrically end-functionalized with three different hydrogen bonding (H-bonding) groups: thymine-1-acetic acid (thy), diamino-triazine (dat) and 2-ureido-4[1H]-pyrimidinone (upy). A linear block copolymer structure and a Newtonian-like dynamics is observed for PEG-thy/dat while results for PEG-upy structure and dynamics reveal a sphere and a network-like behavior, respectively. These observations are concomitant with an increase of the Flory-Huggins interaction parameter from PEG-thy/dat to PEG-upy that is used to quantify the difference between the H-bonding types. The upy association into spherical clusters is established by the Percus-Yevick approximation that models the inter-particle structure factor for PEG-upy. Moreover, the viscosity study reveals for PEG-upy a shear thickening behavior interpreted in terms of the free path model and related to the time for PEG-upy to dissociate from the upy clusters, seen as virtual crosslinks of the formed network. Moreover, a second relaxation time of different nature is also obtained from the complex shear modulus measurements of PEG-upy by the inverse of the angular frequency where G' and G'' crosses from the network-like to glass-like transition relaxation time, which is related to the segmental friction of PEG-upy polymeric network strands. In fact, not only do PEG-thy/dat and PEG-upy have different viscoelastic properties, but the relaxation times found for PEG-upy are much slower than the ones for PEG-thy/dat. However, the activation energy related to the association dynamics is very similar for both PEG-thy/dat and PEG-upy. Concerning the segmental dynamics, the glass transition temperature obtained from both rheological and calorimetric analysis is similar and increases for PEG-upy while for PEG-thy/dat is almost independent of association behavior. Our results show how supramolecular PEG properties vary by modifying the H-bonding association type and changing the molecular Flory-Huggins interaction parameter, which can be further explored for possible applications.

Dynamics studied by Quasielastic Neutron Scattering (QENS)

Quasielastic neutron scattering (QENS) allows measurement of the molecular displacements in time and space, from pico- to tens of nanoseconds and from Ångstroms to nanometers, respectively. The method probes dynamics from fast vibrational modes down to slow diffusive motion. Every scattering experiment leads to a dynamic structure factor $$S\left( {\vec Q,\omega } \right)$$ S Q → , ω or its spatial and temporal Fourier transform (van Hove correlation function $$G\left( {\vec r,t} \right)$$ G r → , t ). This shows exactly where the atoms are and how they move. In this manuscript the basics of the QENS method are presented and a few examples highlighting the potentials of QENS are given: (i) diffusion of liquids and gases in nano- and mesoporous materials; (ii) hydrogen dynamics in a high temperature polymer electrolyte fuel cell (HT-PEFC) and (iii) influence of the surface interactions on polymer dynamics in nanopores.

Conformation and dynamics of ring polymers under symmetric thin film confinement

Understanding the structure and dynamics of polymers under confinement has been of widespread interest, and one class of polymers that have received comparatively little attention under confinement is that of ring polymers. The properties of non-concatenated ring polymers can also be important in biological fields because ring polymers have been proven to be a good model to study DNA organization in the cell nucleus. From our previous study, linear polymers in a cylindrically confined polymer melt were found to segregate from each other as a result of the strong correlation hole effect that is enhanced by the confining surfaces. By comparison, our subsequent study of linear polymers in confined thin films at similar levels of confinements found only the onset of segregation. In this study, we use molecular dynamics simulation to investigate the chain conformations and dynamics of ring polymers under planar (1D) confinement as a function of film thickness. Our results show that conformations of ring polymers are similar to the linear polymers under planar confinement, except that ring polymers are less compressed in the direction normal to the walls. While we find that the correlation hole effect is enhanced under confinement, it is not as pronounced as the linear polymers under 2D confinement. Finally, we show that chain dynamics far above Tg are primarily affected by the friction from walls based on the monomeric friction coefficient we get from the Rouse mode analysis.

Wave-Vector Dependence of the Dynamics in Supercooled Metallic Liquids

We present a detailed investigation of the wave-vector dependence of collective atomic motion in Au_{49}Cu_{26.9}Si_{16.3}Ag_{5.5}Pd_{2.3} and Pd_{42.5}Cu_{27}Ni_{9.5}P_{21} supercooled liquids close to the glass transition temperature. Using x-ray photon correlation spectroscopy in a previously uncovered spatial range of only a few interatomic distances, we show that the microscopic structural relaxation process mimics the structure and presents a marked slowing down at the main average interparticle distance. This behavior is accompanied by dramatic changes in the shape of the intermediate scattering functions, which suggest the presence of large dynamical heterogeneities at length scales corresponding to a few particle diameters. A ballisticlike mechanism of particle motion seems to govern the structural relaxation of the two systems in the highly viscous phase, likely associated with hopping of caged particles in agreement with theoretical studies.

Elucidating the impact of extreme nanoscale confinement on segmental and chain dynamics of unentangled poly(cis-1,4-isoprene)

Broadband dielectric spectroscopy is employed to probe dynamics in low molecular weight poly(cis-1,4-isoprene) (PI) confined in unidirectional silica nanopores with mean pore diameter, D, of 6.5 nm. Three molecular weights of PI (3, 7 and 10 kg/mol) were chosen such that the ratio of D to the polymer radius of gyration, R_g, is varied from 3.4, 2.3 to 1.9, respectively. It is found that the mean segmental relaxation rate remains bulk-like but an additional process arises at lower frequencies with increasing molecular weight (decreasing D/R_g. In contrast, the mean relaxation rates of the end-to-end dipole vector corresponding to chain dynamics are found to be slightly slower than that in the bulk for the systems approaching D/R_g ∼ 2, but faster than the bulk for the polymer with the largest molecular weight. The analysis of the spectral shapes of the chain relaxation suggests that the resulting dynamics of the 10kg/mol PI confined at length-scales close to that of the R_g are due to non-ideal chain conformations under confinement decreasing the chain relaxation times. The understanding of these faster chain dynamics of polymers under extreme geometrical confinement is necessary in designing nanodevices that contain polymeric materials within substrates approaching the molecular scale.

Proton Spin-Lattice Relaxation in Organic Molecular Solids: Polymorphism and the Dependence on Sample Preparation

We report solid-state nuclear magnetic resonance ¹ H spin-lattice relaxation, single-crystal X-ray diffraction, powder X-ray diffraction, field emission scanning electron microscopy, and differential scanning calorimetry in solid samples of 2-ethylanthracene (EA) and 2-ethylanthraquinone (EAQ) that have been physically purified in different ways from the same commercial starting compounds. The solid-state ¹ H spin-lattice relaxation is always non-exponential at high temperatures as expected when CH₃ rotation is responsible for the relaxation. The ¹ H spin-lattice relaxation experiments are very sensitive to the "several-molecule" (clusters) structure of these van der Waals molecular solids. In the three differently prepared samples of EAQ, the relaxation also becomes very non-exponential at low temperatures. This is very unusual and the decay of the nuclear magnetization can be fitted with both a stretched exponential and a double exponential. This unusual result correlates with the powder X-ray diffractometry results and suggests that the anomalous relaxation is due to crystallites of two (or more) different polymorphs (concomitant polymorphism).

Inelastic and quasi-elastic neutron scattering. Application to soft-matter

Microscopic dynamical events control many of the physical processes at play in condensed matter: transport, magnetism, catalysis and even function of biological assemblies. Inelastic (INS) and Quasi-Elastic Neutron Scattering (QENS) are irreplaceable probes of these phenomena. These experimental techniques reveal the displacements of atoms and molecules over distances spanning from angstroms to a few tens of nanometers, on time scales ranging from a fraction of picoseconds to microseconds. In this context, the different INS and QENS machines (Time-of-Flight (ToF), Backscattering (BS) and Neutron spin-echo (NSE)) stand at a central position. After introducing an underlying basic theoretical toolbox for neutron scattering, the principles and key elements of a ToF measurement are described. While, here, we mainly focus on disk choppers spectrometers, all the INS/QENS instruments share a common ground: they directly and simultaneously probe correlation functions in both time and space, so that the scattering vector (Q) dependence of the systems characteristic time(s) can be measured. To illustrate, the potentialities of the technique in the field of soft-matter, we show a multiscale approach of the dynamics of a polymer melt. The system is probed from the molecular to the mesoscopic scale (1 ps to 0.6 μs and 0.1 to 40 nm), in bulk and under nanometric confinement. We address the different dynamical modes of a high mass entangled polymer chain: local monomer dynamics, Rouse modes up to the reptation process. This study exemplifies that, used in conjunction with hydrogen/deuterium isotopic effects, high resolution QENS can be bridged to the Zero Average Contrast (ZAC) method to probe, in a non destructive way, the dynamics of a single polymer chain in bulk but also under severe nanometric confinement. Connection and complementarity of the neutron derived analysis with Pulsed-Field Gradient and Relaxation NMR techniques are discussed.

Relaxation processes and glass transition of confined polymer melts: A molecular dynamics simulation of 1,4-polybutadiene between graphite walls

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, F_s(q_z, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2T_g down to about 1.15T_g, where T_g is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to T_g the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Reduced-mobility layers with high internal mobility in poly(ethylene oxide)-silica nanocomposites

A series of poly(ethylene oxide) nanocomposites with spherical silica was studied by proton NMR spectroscopy, identifying and characterizing reduced-mobility components arising from either room-temperature lateral adsorption or possibly end-group mediated high-temperature bonding to the silica surface. The study complements earlier neutron-scattering results for some of the samples. The estimated thickness of a layer characterized by significant internal mobility resembling backbone rotation ranges from 2 nm for longer (20 k) chains adsorbed on 42 nm diameter particles to 0.5 nm and below for shorter (2 k) chains on 13 nm particles. In the latter case, even lower adsorbed amounts are found when hydroxy endgroups are replaced by methyl endgroups. Both heating and water addition do not lead to significant changes of the observables, in contrast to other systems such as acrylate polymers adsorbed to silica, where temperature- and solvent-induced softening associated with a glass transition temperature gradient was evidenced. We highlight the actual agreement and complementarity of NMR and neutron scattering results, with the earlier ambiguities mainly arising from different sensitivities to the component fractions and the details of their mobility.

Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments

Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions. These fluctuate due to translational displacements and to a lesser degree also by rotational reorientations in the short-range limit. The analysis of the inter-molecular proton spin-lattice relaxation rate thus permits one to evaluate self-diffusion variables such as the diffusion coefficient or the mean square displacement on a time scale from nanoseconds to several hundreds of microseconds. Numerous applications to solvents, plastic crystals and polymers will be reviewed. The technique is of particular interest for polymer dynamics since inter-molecular spin-lattice relaxation diffusometry bridges the time scales of quasi-elastic neutron scattering and field-gradient NMR diffusometry. This is just the range where model-specific intra-coil mechanisms are assumed to occur. They are expected to reveal themselves by characteristic power laws for the time-dependence of the mean-square segment displacement. These can be favorably tested on this basis. Results reported in the literature will be compared with theoretical predictions. On the other hand, there is a second way for translational diffusion phenomena to affect the spin-lattice relaxation dispersion. If rotational diffusion of molecules is restricted, translational diffusion properties can be deduced even from molecular reorientation dynamics detected by intra-molecular spin-lattice relaxation. This sort of scenario will be relevant for adsorbates on surfaces or polymer segments under entanglement and chain connectivity constraints. Under such conditions, reorientations will be correlated with translational displacements leading to the so-called RMTD relaxation process (reorientation mediated by translational displacements). Applications to porous glasses, protein solutions, lipid bilayers, and clays will be discussed. Finally, we will address the intriguing fact that the various time limits of the segment mean-square displacement of polymers in some cases perfectly reproduce predictions of the tube/reptation model whereas the reorientation dynamics suggests strongly deviating power laws.

Fabrication and mechanical characterization of semi-free-standing (conjugated) polymer thin films

Polymers undergo severe low-dimensionality effects when they are confined to ultrathin films since most of the structural and dynamical processes involving polymer molecules are correlated to length scales of the order of nanometers. However, the real influence of the size limitation over such processes is often hard to identify as it is masked by interfacial effects. We present the fabrication of a new type of nanostructure consisting of poly[[9-(1-octylnonyl)-9H-carbazole-2,7-diyl]-2,5-thiophenediyl-2,1,3-benzothiadiazole-4,7-diyl-2,5-thiophenediyl] (PCDTBT) thin film that is held up exclusively over tips of poly(ether-ether-ketone) (PEEK) nanopillars. The fabrication method exploits the nonwetting behavior of PCDTBT onto an ordered PEEK nanopillar array when the mobility of the PCDTBT molecules is enhanced by a solvent annealing process. We use this new configuration to characterize the mechanical behavior of free-standing thin film regions, thus in the absence of underlaying substrate, by means of an atomic force microscope (AFM) setup. First, we study how the finite thickness and/or the presence of the underlying substrate influences the mechanical modulus of the material in the linear elastic regime. Moreover, we analyze deep indentations up to the rupture of the thin film, which allow for the measurement of important mechanical features of the nanoconfined polymer, such as its yield strain, the rupture strain, the bending rigidity, etc., which are impossible to investigate in thin films deposited on substrates.

Acceleration of membrane dynamics adjacent to a wall

The dynamics of an induced lamellar microemulsion adjacent to a planar hydrophilic surface (45 ns) were found to be three times faster compared to the bicontinuous bulk structure (133 ns). For these investigations the grazing incidence technique for neutron spin echo spectroscopy has been developed to resolve the depth dependent near surface dynamics. The observation is rationalized in terms of membrane hydrodynamics, where the flow fields reflected by the surface lead to a crossover from classical to confined fluctuations, and faster dynamics on large length scales (also known as "lubrication") are predicted.

Self-diffusion of poly(propylene glycol) in nanoporous glasses studied by pulsed field gradient NMR: A study of molecular dynamics and surface interactions

Pulsed field gradient NMR is applied to investigate the self-diffusion of poly(proypylene glycol) in nanoporous glasses (nominal pore sizes of 2.5-7.5 nm). In general, the diffusion is slowed down by the confinement compared to the bulk. For native pore surfaces covered by hydroxyl groups the spin echo attenuation Ψ displays a bimodal behavior versus q(2)t (q-norm of a generalized scattering vector). This was explained assuming spatial regions of different diffusivities in a two-phase model. The slow component is assigned to segments forming a surface layer close to the pore walls in which the segments have a lower mobility than those located in the center of the pores. By variation of observation time it was concluded that time constant for the dynamic exchange of segments between these two regions is around 100 ms at room temperature. For silanized pores, the bimodal behavior in the spin echo attenuation Ψ shows a stretched exponential decay versus q(2)t. The estimated diffusion coefficients decrease strongly with decreasing pore size. The temperature dependence of the diffusion coefficient can be approximated by an Arrhenius law where the activation energy increases with decreasing pore size. The observed pore size dependence for the diffusion of poly(propylene glycol) in silanized nanoporous glasses can be discussed assuming interaction and confining size effects.

Direct observation of confined single chain dynamics by neutron scattering

Neutron spin echo has revealed the single chain dynamic structure factor of entangled polymer chains confined in cylindrical nanopores with chain dimensions either much larger or smaller than the lateral pore sizes. In both situations, a slowing down of the dynamics with respect to the bulk behavior is only observed at intermediate times. The results at long times provide a direct microscopic measurement of the entanglement distance under confinement. They constitute the first experimental microscopic evidence of the dilution of the total entanglement density in a polymer melt under strong confinement, a phenomenon that so far was hypothesized on the basis of various macroscopic observations.