Chain dynamics in mesoscopically confined polymer melts. A field-cycling NMR relaxometry study

Polymer chain dynamics were studied with the aid of field-cycling NMR relaxometry (time scale: 10^-9s... 10^-4s) supplemented by field gradient NMR diffusometry (time scale: 10^-4s...10⁰s). Three sorts of samples of mesoscopically confined polymer melts were examined. In the first sample series, linear poly(ethylene oxide) was incorporated in strands embedded in a quasi-solid and impenetrable methacrylate matrix. The strand diameters ranged from 10 to 60 nm. It was shown that chain dynamics becomes dramatically different from bulk behavior. This so-called “corset effect” occurs both above and below the critical molecular mass and reveals dynamic features predicted for reptation. On the time scale of spin-lattice relaxation, the frequency and molecular weight, signature of reptation, T₁ ∼M⁰ ν^3/4, that is limit II of the Doi/Edwards formalism corresponding to the mean squared segment displacement law 〈r² 〉∼M⁰ t^1/4, showed up. A “tube” diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. The corset effect is traced back to the lack of the local fluctuation capacity of the free volume under nanoscopic confinements. The confinement dimension at which the cross-over from confined to bulk chain dynamics is expected was estimated to be micrometers. Using the so-called roll-coating technique, micrometer thick polymer melt layers between Kapton foils were prepared. Perceptible differences from the bulk materials were found. The polymer species studied in this case was perfluoropolyether with Flory radii in the order of 7 nm. Remarkably, the confinement effect was shown to reach polymer-wall distances of the order 100 Flory radii. As a third confinement system, melts of perfluoropolyether were filled into a porous silica glass (Vycor; 4 nm nominal pore size). In this case, a crossover from Rouse dynamics in the bulk to reptation in the Doi/Edwards limit III (T₁∼M^-1/2 ν^1/2 corresponding to 〈r² 〉∼M^-1/2 t^1/2) was observed.     

The “corset effect” of spin-lattice relaxation in polymer melts confined in nanoporous media

Linear polyethylene oxides with molecular weightsM _w of 1665 and 10170 confined in pores with variable diameters in a solid methacrylate matrix were studied by proton field-cycling nuclear magnetic resonance relaxometry. The pore diameter was varied in the range of 9–57 nm. In all cases, the spin-lattice relaxation time shows a frequency dependence close toT ₁∞ v^3/4 in the range ofv=3·10^?1-2·10¹ MHz as predicted by the tube-reptation model. This protonT ₁ dispersion essentially reproduces that found in a previous deuteron study (R. Kimmich, R.-O. Seitter, U. Beginn, M. Möller, N. Fatkullin: Chem. Phys. Lett. 307, 147, 1999). As a feature particularly characteristic for reptation, this finding suggests that reptation is the dominating chain dynamics mechanism under pore confinement in the corresponding time range. The absolute values of the spin-lattice relaxation times indicate that the diameter of the effective tubes in which reptation occurs is much smaller than the pore diameters on the time scale of spin-lattice relaxation experimens. An estimation leads to a valued ^*～0.5 nm. The impenetrability of the solid pore walls, the uncrossability of polymer chains (“excluded volume”) and the low value of the compressibility in polymer melts create the “corset effect” which reduces the lateral motions of polymer chains to a microscopic scale of only a few tenths of a nanometer.     

Field-gradient NMR diffusometry in poly(ethylene oxide) melts confined to nanoscopic pores of solid methacrylate matrices

Depending on the choice of matrix constituents, the diameters of strands of linear, monodisperse poly(ethylene oxide) confined to nanoscopic pores of cross-linked methacrylate matrices can be varied considerably. The samples were characterized by DSC, TEM, SEM and fringe field-gradient NMR diffusometry with respect to the strand diameter. A formalism evaluating diffusive spin echo attenuation curves based on the tube/reptation model allows the determination of the strand diameter. Values in the range 8-58 nm were found in accordance with TEM and SEM micrographs of shadow-cast freeze-fractured surfaces of the samples.     

Probing interfacial dynamics of water in confined nanoporous systems by NMRD

The confined dynamics of water molecules inside a pore involves an intermittence between adsorption steps near the interface and surface diffusion and excursions in the pore network. Depending on the strength of the interaction in the layer(s) close to the surface and the dynamical confinement of the distal bulk liquid, exchange dynamics can vary significantly. The average time spent in the surface proximal region (also called the adsorption layer) between a first entry and a consecutive exit allows estimating the level of ‘nanowettablity’ of water. As shown in several seminal works, NMRD is an efficient experimental method to follow such intermittent dynamics close to an interface. In this paper, the intermittent dynamics of a confined fluid inside nanoporous materials is discussed. Special attention is devoted to the interplay between bulk diffusion, adsorption and surface diffusion on curved pore interfaces. Considering the nano or meso length scale confinement of the pore network, an analytical model for calculating the inter-dipolar spin–lattice relaxation dispersion curves is proposed. In the low-frequency regime (50?KHz–100?MHz), this model is successfully compared with numerical simulations performed using a 3D-off lattice reconstruction of Vycor glass. Comparison with experimental data available in the literature is finally discussed.     

Drift and diffusion of a confined semiflexible chain

We study the transverse and longitudinal linear response function of rigid chains subjected to an external force. Our main concern are stiff polymers confined in narrow pores with diameter less than their persistence length. We explicitly consider confinement in a transverse harmonic potential and generalize results by scaling arguments. Our results describe the drift of the filament under an external force, time evolution of the filament shape, and filament diffusion. Diffusion of a confined filament resembles the celebrated reptation process for flexible chains, albeit with distinct kinetic exponents. The limiting case of stiff free filaments is also mentioned.     

Static and dynamic properties of supercooled thin polymer films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. An analysis of the temperature dependence of the α-relaxation time suggests that the critical temperature, T _c, of MCT decreases with D. If the confinement is not too strong ( D≥10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T _c(D), to the critical temperature. This suggests that T - T _c(D) is an important temperature scale of our model both in the bulk and in the films. Received 12 September 2001     

Dynamic NMR investigation of plastic crystals in bulk and confined in porous materials

In this work, the molecular dynamics of four organic compounds confined in silica pores of nominal diameter 6 and 20 nm are studied by high-field (9.4 T) nuclear magnetic resonance (NMR), and the results are discussed with reference to the bulk substances. By using organic compounds forming soft plastic crystals on freezing as adsorbates, damage to the pore structures can be avoided. NMR lineshapes, spin-lattice relaxation times (T ₁), spin-spin relaxation timesT ₂ and diffusivities are reported as a function of temperature. Since the porous grains are much greater than the distance travelled by the molecules during the experiment, intracrystalline NMR parameters were obtained. However, the shortT ₂ (∼1 ms) encountered in both the bulk and confined samples prohibited measurements ofT ₂ and the diffusivity in the low-temperature ordered phases. The confinement in the pores gives rise to substantial changes in the phase behavior and molecular dynamics. Thus, the¹H lineshape observations of the confined samples clearly reveal a narrow-line component superimposed on a broad resonance at temperatures well below the transition point of the bulk material. In the freezing region, the narrow-line component is attributed to the surface layer and the undercooled liquid in the smaller pores that remains unfrozen. In the two-component, low-temperature region, the narrow component corresponds to the surface layer, while the broad component originates from the crystalline phase at the center of the pores.     

Dielectric relaxation studies of poly(propylene glycol) confined in vermiculite clay

The molecular dynamics of oligomeric poly(propylene glycol) (PPG) liquids (M(w)=1200, 2000 and 4000 g/mol) confined in a two-dimensional layer-structured Na-vermiculite clay has been studied by broadband dielectric spectroscopy. In addition to the alpha-relaxation, the normal mode relaxation process was studied for all samples both in bulk and confinement. For the normal mode process the relaxation rate in the clay is drastically shifted to lower frequencies compared to that of the bulk material in contrast to the alpha-process whose relaxation time is only slightly affected by the confinement. Also the temperature dependence of the relaxation time for the normal mode process is strongly affected by the confinement. Moreover, in the clay the intensity of the normal mode is stronger than that of the alpha-process, in contrast to the bulk samples where the opposite is observed.     

Dynamics of water confined on a nanometer length scale in reverse micelles: ultrafast infrared vibrational echo spectroscopy

The dynamics of water, confined on a nanometer length scale (1.7 to 4.0 nm) in sodium bis-(2-ethylhexyl) sulfosuccinate reverse micelles, is directly investigated using frequency resolved infrared vibrational echo experiments. The data are compared to bulk water and salt solution data. The experimentally determined frequency-frequency correlation functions show that the confined water dynamics is substantially slower than bulk water dynamics and is size dependent. The fastest dynamics (approximately 50 fs) is more similar to bulk water, while the slowest time scale dynamics is much slower than water, and, in analogy to bulk water, reflects the making and breaking of hydrogen bonds.     

On the freezing and structure of hard spheres under spherical confinement

The equation of state and the structure of hard spheres confined in spherical pores have been investigated via molecular dynamics for different pore radii ranging from 5.0 to 10.0?σ, where σ is the particle diameter. The hard boundary is chosen to capture the pure geometric effect of spherical confinement. A discontinuity in the equation of state was observed, indicating the onset of a freezing-like phase transition, which was similar to that of the bulk hard-sphere fluids. The behaviour of confined particles resembles that of the bulk with increase in the pore size, while its deviation from the bulk is found to be larger at the solid-like phase. For the pore radius below 5.0, FCC-like crystal clusters are not formed in spherically confined hard spheres.     

Raman spectroscopy: Probing dynamics of water molecules confined in nanoporous silica glasses

In order to explore the influence of nanoscopic confinement on the vibrational properties of H-bonded liquids, we performed a detailed Raman scattering study, as a function of temperature, on water confined in 75 ? and 200 ? pores of a Gelsil glass. A detailed evaluation of the observed changes in the O-H stretching profile has been achieved by decomposing the O-H band into individual components, corresponding to those found for bulk water and associated to different levels of water connectivity. As main result, a similar effect produced by enlarging pore diameter and lowering T has been put into evidence. Again, the “structure-breaker” role of the GelSil glass on physisorbed water is confirmed and shown to be enhanced by the diminishing of the pore size.     

How we can interpret the T1 dispersion of MC, HPMC and HPC polymers above glass temperature?

The chain dynamics in methyl cellulose (MC), hydroxypropylmethyl cellulose (HPMC) and hydroxypropyl cellulose (HPC) were studied with the aid of field-cycling NMR relaxometry technique in the temperature range from 300 to 480 K that is above the glass transition, but below thermal degradation. The frequency dependence of proton spin-lattice relaxation time was determined between 24 kHz and 40 MHz for selected temperatures. The experimental spin-lattice relaxation dispersion data were fitted with the power law relations of T(1) proportional variant omega(gamma) predicted by the tube/reptation model. The exponent's values found from the fitting procedure for MC, HPMC and HPC almost exactly match the ones predicted in tube/reptation model for limit II (gamma=0.75) and in MC also for limit III (gamma=0.50). Remarkably, this finding concerns the polymers in networks formed of the same polymer species.     

Compression and stretching of a self-avoiding chain in cylindrical nanopores

Force-induced deformations of a self-avoiding chain confined inside a cylindrical cavity, with diameter D, are probed using molecular dynamics simulations, scaling analysis, and analytical calculations. We obtain and confirm a simple scaling relation -fD approximately R(-9/4) in the strong-compression regime, while for weak deformations, we find fD = -A(R/R0) + B(R/R0)(-2), where A and B are constants, f the external force, and R the chain extension (with R0 its unperturbed value). For a strong stretch, we present a universal, analytical force-extension relation. Our results can be used to analyze the behavior of biomolecules in confinement.     

Molecular observation of contour-length fluctuations limiting topological confinement in polymer melts

In order to study the mechanisms limiting the topological chain confinement in polymer melts, we have performed neutron-spin-echo investigations of the single-chain dynamic-structure factor from polyethylene melts over a large range of chain lengths. While at high molecular weight the reptation model is corroborated, a systematic loosening of the confinement with decreasing chain length is found. The dynamic-structure factors are quantitatively described by the effect of contour-length fluctuations on the confining tube, establishing this mechanism on a molecular level in space and time.     

How confinement affects the dynamics of c60 in carbon nanopeapods

The dynamics of confined systems is of major concern for both fundamental physics and applications. In this Letter, the dynamics of C60 fullerene molecules inside single walled carbon nanotubes is studied using inelastic neutron scattering. We identify the C60 vibrations and highlight their sensitivity to temperature. Moreover, a clear signature of rotational diffusion of the C60 is evidenced, which persists at lower temperature than in 3D bulk C60. It is discussed in terms of confinement and of reduced dimensionality of the C60 chain.     

Diffusion studies in confined nematic liquid crystals by MAS PFG NMR

Pulsed field gradient (PFG) NMR and magic-angle spinning (MAS) NMR have been combined in order to measure the diffusion coefficients of liquid crystals in confined geometry. Combination of MAS NMR with PFG NMR has a higher spectroscopic resolution in comparison with conventional PFG NMR and improves the application of NMR diffusometry to liquid crystals. It is found that the confinement of the liquid crystal 5CB in porous glasses with mean pore diameters of 30 and 200 nm does not notably change its diffusion behavior in comparison with the bulk state.     

Study of the effects of confinement in the collective excitations of liquid deuterium

The spectrum of collective excitations of liquid deuterium in the bulk and confined within a MCM-41 matrix having pores of an average diameter of 2.4 nm has been studied by means of neutron scattering and molecular dynamics simulations. The main effects of confining liquid D₂ consist in a shift of the characteristic frequencies associated with damped density oscillations to higher energies. A strong decrease in diffusivity is also observed upon confinement.     

On the dynamics of polymers in dense systems – Results of neutron spin echo spectroscopy

One of the basic problems in the dynamics of polymers concerns the importance of geometrical or topological interactions which are directly related to the large scale molecular structures. In the famous reptation model these constraints are pictured in terms of a tube of localization following the average chain profile and confining the chain motion to the curve‐linear tube. Recently studying the dynamic structure factor of a single labeled chain in a polymer melt by means of neutron spin echo spectroscopy (NSE) led to a direct observation of these tube constraints. Here I shall summarize these neutron spin echo experiments. I shall address the NSE technique, present results on the entropy driven segmental chain dynamics, discuss the dynamics of single chains in the melt where the chain length is increased through the transition to “reptation” dynamics and display NSE measurements on long chain systems which revealed the molecular existence of the entanglement distance. Their magnitudes agree very well with tube diameters derived from dynamical mechanical measurements on the basis of the reptation model proving thereby the basic assumption of this Nobel Price winning concept. This revised version was published online in August 2006 with corrections to the Cover Date.     

Segmental dynamics of poly(methyl phenyl siloxane) confined to nanoporous glasses

The effect of a nanometer confinement on the molecular dynamics of poly(methyl phenyl siloxane) (PMPS) was studied by dielectric spectroscopy (DS), temperature modulated DSC (TMDSC) and neutron scattering (NS). Nanoporous glasses with pore sizes of 2.5–20 nm have been used. DS and TMDSC experiments show that for PMPS in 7.5 nm pores the molecular dynamics is faster than in the bulk which originates from an inherent length scale of the underlying molecular motions. For high temperatures the temperature dependence of the relaxation rates for confined PMPS crosses that of the bulk state. Besides finite states effects also the thermodynamic state of nano-confined PMPS is different from that of the bulk. At a pore size of 5 nm the temperature dependence of the relaxation times changes from a Vogel/Fulcher/Tammann like to an Arrhenius behavior where the activation energy depends on pore size. This is in agreement with the results obtained by NS. The increment of the specific heat capacity at the glass transition depends strongly on pore size and vanishes at a finite length scale between 3 and 5 nm which can be regarded as minimal length scale for glass transition to appear in PMPS.