Recent progress on polymer dynamics by neutron scattering: From simple polymers to complex materials

Authors

  • Juan Colmenero,

    Corresponding author
    1. Centro de Física de Materiales (CSIC-UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
    2. Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
    • Centro de Física de Materiales (CSIC-UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
    Search for more papers by this author
  • Arantxa Arbe

    1. Centro de Física de Materiales (CSIC-UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
    Search for more papers by this author

Abstract

The recent (from 2010 onward) contributions of quasielastic neutron scattering techniques (time of flight, backscattering, and neutron spin echo) to the characterization and understanding of dynamical processes in soft materials based on polymers are analyzed. The selectivity provided by the combination of neutron scattering and isotopic—in particular, proton/deuterium—labeling allows the isolated study of chosen molecular groups and/or components in a system. This opportunity, together with the capability of neutrons to provide space/time resolution at the relevant length scales in soft matter, allows unraveling the nature of the large variety of molecular motions taking place in materials of increasing complexity. As a result, recent relevant works can be found dealing with dynamical process which associated characteristic lengths and nature are as diverse as, for example, phenyl motions in a glassy linear homopolymer like polystyrene and the chain dynamics of a polymer adsorbed on dispersed clay platelets. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013

POLYMER DYNAMICS AT DIFFERENT LENGTH AND TIME SCALES: FROM SIMPLE POLYMERS TO COMPLEX MATERIALS

Polymers are composed of macromolecules which are built up by a large number N of monomer units linked together by covalent bonds. Because of this macromolecular nature, the structural and dynamic properties of polymeric systems strongly depend on a hierarchy of length and time scales. From a structural point of view, the random coil shape of linear polymer chains in the melt and glassy state—proposed by Flory in the 50s1—is nowadays well established by small angle neutron diffraction (SANS). At smaller length scales than those characteristic for the chain dimensions, the local arrangements of the atoms give rise to broad maxima in the static structure factor S(Q) also accessible by neutron diffraction. Usually, a first main peak centered at Q-values ≈ 1… 1.5 Å−1 is present. The T-dependence of this maximum, following the expansion coefficient, indicates an interchain origin, that is, it mainly relates to correlations between atoms belonging to different chains (or to the same chain but well separated segments).2 A second peak located at ∼3Å−1 can also be usually found in S(Q). The small value of the associated characteristic length and its weak T-dependence indicate the intrachain nature of the correlations giving rise to this maximum. We also note that the broadening of the Bragg peaks found in polymers reveals a clear amorphous character. In fact, the features shown in S(Q) in polymeric systems are universal for amorphous materials, not only for polymers, and in particular for glass forming systems. Thus, a universal behavior common for all glass forming materials can also be expected in the dynamics, including the observation of the glass transition phenomenon.3

As anticipated, the complexity of amorphous polymers shows up not only in the structural properties but also in the dynamics. It is easy to imagine that structure and dynamical behavior should be linked in some way and that the dynamical processes observed will depend on the length scale considered. Three main length scale regions can be distinguished where the dominant dynamical processes are different:

  • The large scale dynamics (length scales matching the chain dimensions, typically ≈ 100Å). The atomic structure at this level is not relevant and universal (entropy) effects drive the dynamical behavior. The observable processes at this scale are (from slowest to fastest): the chain diffusion, the reptation and the Rouse dynamics.4 The way these processes manifest depends on the characteristics of the macromolecular chains. These dynamics are relevant well above the glass transition temperature Tg or above the melting point in the case of semicrystalline polymers. These processes control the rheological properties of the system.

  • The intermolecular scale dynamics (typical length scales ≈ 5Å), that controls the time evolution of the interchain correlations. As we noted above, this range is dominated by the universal features of glass forming systems. The α-relaxation—which freezing at Tg leads to the glassy state—is the main dynamical process.3

  • The local scale dynamics (length scales ≈ 1Å). At such short length scales, the molecular motions are those characteristic for the glassy state. These processes are usually localized and activated, and, due to the structural disorder in the system, broad barrier distributions are found. To this kind of dynamics belong, among others, vibrations including the Boson peak,5 dynamics associated to side-groups like, for example, methyl group rotations or tunneling processes6 and secondary relaxations like the Johari–Goldstein or β-relaxation.7

A “relaxation map” showing the temperature dependence of the characteristic timescales of the different processes in the case of 1,4-polyisoprene (PI) is included in Figure 1.

Figure 1.

Relaxation map of polyisoprene. Full symbols correspond to neutron scattering results for the methyl group rotations (triangles), α-relaxation (circles: incoherent scattering at 1 Å−1; squares: coherent scattering at the first structure factor peak) and Rouse time (diamonds). The shadowed area covers the typical dynamic region of fast dynamics and vibrations including the Boson peak, also accessible by neutron scattering. Empty symbols correspond to results from BDS for the β-relaxation (triangles), α-relaxation (circles) and Rouse time (diamonds). The data corresponding to the Rouse times are taken from163 (NS) and164 (BDS). The molecular weight of the sample was 2700 g/mol. The source of the rest of the data is given in Ref. 14.

During the last decades, all these dynamical processes have been extensively investigated by different experimental techniques and most of them are reasonably understood in the case of chemically simple linear homopolymers. However, current technological demands require more versatile polymer-based materials that can be obtained by several means. Applying advanced chemistry at the monomeric level, the complexity of homopolymer systems can be tremendously increased. For example, chains can be functionalized at desired points. Another way to profoundly change properties like, for example, the rheological behavior in homopolymers, is to synthesize polymers with architectures different from linear (branched, combs, “H”, stars, rings,…). Conversely, an infinite number of systems can be obtained by combining polymeric chains of a given kind with other structural units or particles. For instance, the use of polymer blends is widely spread, and the inclusion of nanoparticles (NPs) in polymeric matrices is nowadays a promising way to obtain materials with novel properties. A first arising question is: how are all the processes present in chemically simple linear homopolymers modified by the induced complexity? In addition, in these complex systems new intriguing features appear associated to nanosegregation, confinement effects, interactions at the surfaces/interfaces, and so forth, that are still very poorly understood. To characterize them is also subject of great interest from both, a basic and an applied point of view.

POLYMER DYNAMICS BY QUASIELASTIC NEUTRON SCATTERING

What is Measured by QENS?

Neutron scattering results from the interactions of neutrons with the atomic nuclei.8, 9 These interactions are characterized by the scattering length bα, that can be positive, negative, or complex and depends on the isotope α considered (α = H, D, C, O, …). Table 1 shows the mean values of this parameter for the isotopes commonly present in polymers.

Table 1. Values of the average scattering lengths equation image, their squares equation image and their deviations equation image for different isotopes α
inline image

The double differential scattering cross section ∂2σ/∂Ω∂equation imageω measured in a neutron scattering experiment is the number of neutrons scattered into a solid angle comprised between Ω and Ω + dΩ and which have experienced a change in energy equation imageω, with respect to the total number of incident neutrons.8 Scattering events can be classified as elastic (if equation imageω = 0 or, in practice, smaller than the energy resolution of the instrument), inelastic (if equation imageω ≠ 0 and the neutron has led to an excitation in the sample), and quasielastic (if equation imageω ≠ 0 and but no excitation has been produced). Quasielastic neutron scattering (QENS) reflects dynamical processes in the sample (e. g. rotations, segmental relaxation, diffusion, …) and manifests as a broadening around the elastic line. The difference between the wavevectors of the scattered (equation image) and incident (equation image) neutron determines the momentum transfer equation image, which modulus is given by Q = 4πsin(θ/2)/λ (θ: scattering angle; λ = 2π/ko: incident wavelength).

The double differential scattering cross section has a coherent and an incoherent contribution:

equation image(1)

Here the indexes α and β run over all the different kinds of isotopes in the sample (α,β ∈ {H,D,C,O,…}). The equation image and ω-dependencies of the coherent and incoherent contributions are determined by the scattering functions. Smath image(equation image,ω) is the coherent scattering function involving pairs of atoms of kind α and β and Smath image(equation image,ω) is the incoherent scattering function of α-nuclei. These are related, via Fourier transformation, with the intermediate scattering functions [Smath image(equation image,t) and Smath image(equation image,t)] and the van Hove correlation functions [Gαβ(equation image,t) and Gmath image (equation image,t) respectively]. In the classical limit, Gαβ(equation image,t) can be written as:

equation image(2)

Here equation image(t)[equation image(0)] is the position vector of the ith atom of kind α [jth atom of kind β] at time = t [time = 0] and the sum runs over all the different atoms of kinds α and β [Nα (Nβ): total number of atoms of kind α(β); N = ∑αNα]. Thus, Gαβ(equation image,t)dequation image is the probability that, given a particle of kind β at the origin at time t = 0, any particle of kind α is in the volume dequation image at position equation image at time t. Conversely, the self-part of the van Hove correlation function Gmath image(equation image,t) is obtained by restricting the correlations considered in Eq. 2 to those relating the positions of a single particle of kind α at different times:

equation image(3)

Gmath image(equation image,t) is the Fourier transform of Smath image(equation image,t) in space: Incoherent scattering relates to single particle motions.

The weights of the coherent and incoherent contributions to the scattered intensity are determined by the scattering lengths of the isotopes involved. For systems like regular polymers that are mainly composed by the elements considered in Table 1 it is clear that:

  • Because of the large value of equation image, in H-containing systems the signal is dominated by the incoherent scattering from hydrogens, revealing their self-motions.

  • Substituting H by D this incoherent contribution is drastically reduced. Thus, selective deuteration masks the contribution of the deuterated atoms and the signal is still dominated by the incoherent scattering of the remaining hydrogens in the system (In partially deuterated samples, the incoherent scattering of Hs dominates in the high Q-range, while coherent scattering from the contrast between the labelled objects and the matrix is the major contribution at low Q-values. Usually, QENS experiments by ToF, BS-ToF, or BS on this kind of samples focus on the incoherent scattering in the high-Q range, while NSE experiments address the low-Q coherent scattering, see below.)

  • The intensity scattered by fully deuterated samples is mainly coherent and, since bDbC, all pair correlations are almost equally weighted. The function then revealed is the collective dynamic structure factor:

    equation image(4)

    where equation image(t) is the vector joining two atoms i and j and the sums extend to all atoms in the sample.

Conversely, thanks the large difference between bH and bD we can also access another important correlation function for polymer investigations: the dynamic structure factor of isotopically labeled macromolecules Schain(equation image,t). For a labeled chain containing z scattering points

equation image(5)

where now the sums extend to all the scattering points in the chain. Its static counterpart is the chain form factor. These functions are revealed by the coherent cross section measured on a mixture of protonated and deuterated chains at low scattering angles. The scattered intensity is then weighted by the scattering contrast factor Δρ2 ∝ (bHbD)2 (see, e.g., ref. 10). Diffraction experiments on this kind of samples provided experimental evidence11, 12 for the random coil conformation of macromolecules in the bulk proposed by Flory1 two decades before, as it has already been mentioned in the first section of this article. Later, dynamic measurements delivered the microscopic proof of the Rouse-like13 dynamics in unentangled chains14 and the reptation mechanism for entangled chain dynamics15 as proposed by Doi, Edward4 and deGennes16 in the 80s.

QENS Instrumentation

QENS spectrometers offer a limited energy window and the measured functions are affected by the instrumental resolution function, R(Q,ω). This function is the obtained spectrum when purely elastic (equation imageω = 0) scattering events take place in the sample [i.e., it is the “image” of δ(ω)]. It can be determined from the scattering of a sample where all the dynamical processes are frozen with respect to the accessed dynamic window (for example at very low temperature of about 2 K). Most QENS spectrometers work in the (equation image,ω) space. Such instruments can be classified in three types: direct-geometry time of flight (ToF), indirect-geometry time of flight (BS-ToF), and indirect geometry without time of flight (BS). “BS” stands for “backscattering”: using perfect crystals as monochromator and/or analyzers, the instrumental resolution is optimized by working at Bragg conditions close to 90°. Table 2 offers an overview of the most important currently operating neutron facilities and with their respective QENS spectrometers. In general, QENS instruments working in ω-space cover a similar Q-range (0.2 ≲ Q ≲ 2 Å−1). BS spectrometers offer the highest energy resolution (≈ 1 μeV) but a quite limited dynamic window spanning around one to two decades (i.e., typical Fourier time window 0.3 ≲ t ≲ 3 ns). More extended dynamic windows are accessible on ToF-BS instruments, with typical energy resolutions in the order of 10–100 μeV (equivalently, they cover 5 ≲ t ≲ 100 ps). Newer instruments of this type like BASIS17 (see Table 2) now reach a couple of micro-electron-volt. Finally, ToF spectrometers are optimized for probing ps dynamical processes (they usually are run to cover the range 0.5 ≲ t ≲ 30 ps). To access the whole QENS dynamic range, it is necessary to combine results from more than one spectrometer. Covering the widest possible dynamic range is usually extremely important for polymer systems, which scattering functions commonly display stretched functional forms and distributions of characteristic times can be expected. However, due to resolution effects, direct comparison/combination of experimental results Iexp(Q,ω) ∝ ∂2σ/∂Ω∂equation imageω from different instruments is not possible. In the time-domain, this influence can easily be removed by diving the Fourier transformed spectrum at a given Q and temperature by the Fourier transformed resolution spectrum corresponding to that Q:

equation image(6)

allowing direct comparison of results obtained with different resolutions. An alternative way to analyze results in the frequency domain is to compare them with the convolution of the model function and the resolution, Iexp;(Q,ω) ↔ S(Q,ω) ⊗ R(Q,ω). Examples of both strategies will be shown below.

Table 2. Currently operating high-level neutron facilities in the world and the available QENS spectrometers on them
inline image

There is an additional class of spectrometers that allow analysis of quasielastic scattering based on a completely different concept: the neutron spin echo (NSE) technique (Mezei, 197218). This consists of coding the energy transfer in the scattering process for each neutron individually into its spin rotation. In this way, the application of precession magnetic fields before and after the scattering event results in a polarization of the neutron that depends only on the velocity difference of each neutron individually, irrespective of its initial velocity. Energy resolution and monochromatization of the incident beam are decoupled, and resolutions in energy of the order of 10−5 can be achieved with an incident neutron spectrum of 20% bandwidth. NSE instruments allow exploring dynamical processes in a wide Q-range (0.01 ≲ Q ≲ 2 Å−1) with very high energy resolution. But, their most peculiar feature is that they access the intermediate scattering functions in the time domain. This allows an easy correction for experimental resolution, just by division of the measured signal by that of the elastic spectrum. The standard time interval covered in the Q-range overlapping with the other QENS instruments is around 5 ps ≲ t ≲ 10 ns. As the accessed Fourier time by NSE is proportional to λ3, using long wavelength neutrons (i.e., for low Q-values) slower times can be reached, even close to a microsecond.

We finally mention another basic difference between “standard” QENS instruments and NSE spectrometers. The former access coherent and incoherent contributions to the scattered intensity in a simply additive way (see eq. 1), while the result of a NSE measurement is a normalized scattering function that combines the contributions from both the coherent and incoherent intermediate scattering functions in the following way:

equation image(7)

Here, Icoh(Q,t) = ∑α,βequation imageSmath image(Q,t) and Iinc(Q,t) = ∑αequation imageSmath image(Q,t). As it considerably reduces the incoherent contribution, NSE is adequate to measure coherent signals (collective dynamics). Also for this reason, NSE measurements on H/D labeled samples do not deliver clear-cut results at local length scales and in such cases QENS spectrometers in the frequency domain are the right choice to resolve component dynamics.

Advantages and Limitations of QENS. QENS vs Other Techniques

We highlight the main unique advantages of neutron scattering for the study of polymer systems:

  • 1Neutrons interact with the nuclei and ‘see’ light atoms like H.
  • 2Isotopic (in particular H/D) substitution allows selective investigation of a given component or molecular group.
  • 3Neutrons only perturb the experimental system weakly, are nondestructive and highly penetrating, allowing the study of bulk processes under realistic conditions.
  • 4Through the momentum-transfer dependence of the magnitudes measured, QENS provides spatial information—and thereby on the geometry—on the dynamical process.
  • 5The wavelengths and energies of neutrons allow investigating polymer dynamics in the proper length and time scales (ranging from vibrations to chain dynamics).
  • 6QENS is sensitive to all the motions undergone by the nuclei—it is not restricted to either rotational or translational motions.
  • 7The magnitudes measured have a clear physical meaning thanks the van Hove formalism.

Along the past years, QENS techniques have been used to investigate at microscopic level all the different dynamical processes taking place in linear homopolymer materials.10, 14, 19–22

However, QENS techniques also present limitations:

  • 1Neutron scattering accesses correlation functions in the reciprocal space (equation image), never in real space.
  • 2The signals of different atoms, if they are of the same isotopic species, are not distinguished (e.g., main-chain hydrogens vs side-group hydrogens).
  • 3Self-motions of C and O are not accessible (equation image = equation image = 0).
  • 4Spectrometers cover relatively narrow dynamic windows and usually several instruments have to be combined.
  • 5With exception of NSE, the results are affected by the instrumental resolution through convolution, which makes more difficult the combination of results from different instruments.
  • 6Though polarization analysis allows separation of coherent and incoherent contributions, in practice this is currently not possible for the dynamic window which is of interest for polymer dynamics.

Some of these limitations (4–6) might be overcome to a large extent with the development of the neutron sources and instrumentation, in particular with the spallation sources of new generation [JPARC, Spallation Neutron Source (SNS) and the future ESS]. However, points (1–3) are inherent to the scattering processes.

Though QENS provides unique insight at microscopic level, compared to other experimental techniques like broadband dielectric spectroscopy (BDS) its dynamic window is very limited (see, e.g. Fig. 1). Therefore, for some problems—in particular, those related with the glass-transition or dynamic arrest—the combination with complementary experimental techniques is mandatory. Nuclear magnetic resonance, mechanical spectroscopy, and BDS are good choices.

Conversely, the temporal and spatial ranges covered by QENS fully overlap with those currently accessible by fully atomistic molecular dynamic (MD)-simulations. Moreover, the van Hove correlation functions addressed by QENS can easily be calculated from the simulated atomic trajectories. Therefore, QENS provides a suitable validation source for simulations; conversely, MD simulation data can aid interpretation of experimental results and, once properly validated, can be exploited to investigate aspects that are not experimentally accessible by QENS (in particular, points 1–3 of the limitations list). QENS and MD simulations are “natural partners” and their combined use has proved to be a highly successful tool to unravel different aspects of polymer dynamics during the past years.23

RECENT PROGRESS ON POLYMER DYNAMICS BY NEUTRON SCATTERING

In the past, most QENS works were mainly focused on chemically simple linear homopolymers. The three main goals were (i) to study the local dynamics associated to small molecular groups (e.g., methyl groups, phenylene rings, etc; see, e.g.,22, 24–27), (ii) to characterize the dynamics at the inter-chain level, related to the structural relaxation in connection to the glass-transition phenomenon (see, e.g. ref. 14) and (iii) to investigate the single chain dynamic structure factor and check the theoretical predictions based on their macromolecular nature (Rouse dynamics and reptation) (see, e.g. refs. 14 and 19). Nowadays, we can identify a tendency to increase the complexity of the systems investigated. This does not mean that linear homopolymers made of chemically simple monomers are not subject of current interest. We can find several works dealing with this kind of simplest systems,28–31 addressing, for example, the origin of secondary relaxations28 or the transition from segmental to Rouse motions29, 30. Remarkable is the fruitful combination of QENS and MD-simulations in some of these works.29–31

A first step in complexity is given in works still considering homopolymers, but with more complex monomeric units and/or architectures. For example, for comb-like polymers (polymers with long alkyl side-groups) nano-phase separation has been identified and, under certain conditions, also confinement effects.32–34 The chain dynamics of polymer rings35 and the branch-point motions of star polymers36 have also been investigated by NSE during the recent past years, providing direct microscopic insight into their intriguing rheological properties.

Semicrystalline polymers,37, 38 solid polyelectrolytes,39–41 nano-composites39, 42–44 and polymer blends45 have been subject of QENS studies by several groups. In many of those works, confinement effects arise as a key ingredient. Confinement is in fact the focus and common denominator of a variety of recent works. Confined polymer dynamics at different levels have been characterized by QENS in systems with different confining agents, for example, polymers infiltrated in nano-pores (one-dimensional, 1D),46–50 intercalated in layered structures (2D),51 adsorbed on clays,52 surrounded by the vitrified component in a thermodynamically miscible polymer blend,45 or confined by the neighboring microphase in a diblock copolymer.53

Finally, hydrated polymers and polymer solutions—in particular, microgels—have also recently been investigated by QENS.54–63 Studies on concentrated aqueous solutions show that confinement effects also arise -in this case for the minority water component- when the polymer freezes approaching its glass-transition. The component dynamics in these solutions can be selectively monitored by QENS, a task that is not easily achievable by other usually applied experimental approaches like, for example, dielectric spectroscopy. Conversely, the microscopic insight on polymer dynamics provided by QENS can be of utmost importance to improve the performance of “smart” materials based on responsive polymers.

Chemically Simple Linear Amorphous Homopolymers

Despite its obvious technological relevance and the great effort made over more than 20 years by different techniques, the origin of secondary relaxations in polymers is not well understood yet. Recent QENS experiments on polystyrene (PS) have shed light on this problem.28 Measurements on partially deuterated samples allowed selective investigation of main-chain motions (on a sample with protonated main chain and deuterated phenyl rings) and ring motions (on the contrarily labeled sample). Combining ToF and BS instruments below Tg, it was concluded that the main-chain mobility is very similar to that observed in chemically more simple polymers in the glassy state. Contrarily, rings show enhanced mobility consisting of oscillations of increasing amplitude with temperature. These motions would be responsible for the secondary δ and γ-relaxations observed by dielectric and mechanical spectroscopies in this polymer. An important observation was also that 180°-flips occur, if any, very rarely in PS-phenyl rings. This is very different from the behavior found by previous QENS investigations on engineering thermoplastics containing the bisphenol-A unit, namely polycarbonate,24, 25 polysulfone,26 phenoxy,27 and the polymer membrane polyethersulfone,64 in which phenylene rings perform clear 180°-flips around their main-chain axis. The outcome of this kind of investigations providing such microscopic insight in the glassy dynamics could set a basis to design taylor-made plastics of daily use.

Considering now the other extreme of length scales, that is, length scales much larger than the monomer size, the chemical details can in principle be ignored in the description of the chain dynamics and polymer melts show unique dynamic processes that are controlled by the chain connectivity and the molecular weight of the macromolecules. These processes ultimately determine the rheological properties of polymer melts at high temperatures, well above Tg. The simplest model for polymer chain dynamics in the melt, the Rouse model,13 considers the conformational entropy as the only source for restoring forces which stabilize excursions from equilibrium. The chain is represented by a coarse-grained model of N beads connected by entropic springs (Gaussian chain). The contribution of the surrounding chains is introduced as a stochastic background creating also a friction characterized by the friction coefficient ξ. The resulting Langevin equation can be solved by transforming to the normal coordinates (Rouse modes: equation image with p = 0,1,2,3,…,N − 1 the mode number). The Rouse correlators 〈equation image(t)equation image(0)〉 relax independently and exponentially with p-dependent characteristic times. From a conceptual point of view this model has limitations: (i) at large distances, where long chain melt topological constraints cause entanglements leading to the reptation mechanism, and (ii) at shorter distances, where the simplifying assumptions cease to be valid and the local chain structure and dynamics comes into play. In particular, at length scales of the order of the intermolecular distances, we approach the regime of the α process. An intriguing question in polymer physics is how does the crossover from segmental to Rouse dynamics take place. One of the key ingredients to answer this question is to know when the Rouse model ceases to be valid, which has been the subject of a number of NS investigations on different polymers65–67 during the past years. However, the uncertainties involved in the experiments and the impossibility to experimentally access the Rouse correlators prevent a thorough analysis of the sources for Rouse deviations. To address this question, the best strategy is the combination of QENS with simulations, that allow calculating Rouse correlators and other interesting magnitudes like mean squared displacements. Current computing capabilities allow building big enough cells to address the chain dynamics in unentangled polymer systems with atomistic detail. Such combination of NS and MD-simulations to tackle this problem has been applied to polybutadiene,68 polyethylene (PE),69 poly(ethylene oxide) (PEO),29 and poly(ethylene propylene) (PEP).30 The latter work can be considered as a representative example and will be described in the following.

Figure 2 shows the fit of the Rouse model to the Schain(Q,t) measured on a mixture of 30% protonated and 70% deuterated PEP chains with molecular weigth of 6 kg/mol (≈ twice the entanglement mass, such that pronounced entanglement effects are not expected). Though the overall description is good, deviations—mainly at short times—can be envisaged. Moreover, the lowest-Q results show a more stretched functional form than that predicted. These experimental data were used to validate fully atomistic MD-simulations on a PEP system (Mw ≈ 5.6 kg/mol, equivalent to that of the sample measured) by direct comparison with the calculated single chain dynamic structure factor. Once validated, magnitudes that cannot be measured were computed from the simulations. Interestingly enough, inspection of the mean squared displacement of the center of mass of the chains revealed a sublinear increase with time below the longest relaxation time of the chain, presumably due to the effect of intermolecular interactions neglected in the Rouse model. This would be the reason of the stretching of Schain(Q,t) at low Q, where it is dominated by translational diffusion. In addition, a Rouse mode analysis of the simulated chains could be performed by coarse graining the atomistic MD simulations. Defining a bead as the center of mass of a monomer, the Rouse mode correlators were obtained. Regarding the static features, the amplitudes [Fig. 2(b)] show clear deviations from the Rouse prediction (Gaussian chain) for approx. N/p ≤ 5 −local length scales. They reflect the effects of the local potentials of the atomic system, in particular of the angular potential which introduces some stiffness. Concerning the dynamics, the Rouse correlators do not decay exponentially with time, but stretched exponential functions

equation image(8)

have to be used. The stretching becomes more pronounced toward local length scales (small N/p-values) and decreasing the temperature [Fig. 2(c)]. Moreover, the p-dependence of the characteristic times strongly deviates from the Rouse prediction at large p-numbers. The deviations originating from the chain stiffness could be in principle addressed in terms of the so-called all rotational state (ARS) approach.70 However, this model is not sufficient to describe the deviations from the Rouse model observed. The additional deviations can be characterized in terms of a mode-number (length scale) dependent effective friction coefficient which decreases with the length scale, reaching a constant value (pure Rouse) at N/p ≥ 8. These results underline the role of the local potentials in the chain dynamics of polymers. The experimentally accessed functions reflect these effects at high Q values and mainly short times.

Figure 2.

(a) Rouse model description (solid lines) of the NSE results on a PEP labeled sample at Tg+280 K. Dashed line: stretched exponential description of the lowest-Q data, where the β-value has been fixed to 0.8. (b) Amplitudes of Rouse correlators from the MD-simulations. Solid line corresponds to the Gaussian chain expectation. Fits of stretched exponentials to the simulated Rouse correlators deliver the stretching parameters and effective friction coefficients (after ARS corrections) displayed in (c) and (d), respectively. Rouse behavior corresponds to β = 1 and mode-independent friction (solid lines). (Reproduced with permission from R. Pérez Aparicio, F. Alvarez, A. Arbe, L.Willner, D. Richter, P. Falus, and J. Colmenero, Macromolecules 2011, 44, 3129. Copyright 2011 American Chemical Society).

The conformational rigidity was also proposed by Agapov and Sokolov71 as the reason for the observed discrepancies of the size of the dynamic bead (the smallest subchain that still exhibits Rouse-like dynamics) and the Kuhn length in polymers. That work was based on a compilation of QENS, mechanical and MD-simulation data available in the literature. In this direction, the study on polyolefins [PE, PEP, polypropylene (PP), and head-to-head PP] carried out by Boland et al.31 shed some light on the role of the potentials on the polymer dynamics. MD-simulations properly validated with QENS measurements were exploited to artificially increase the strength of the nonbonded interactions and the height of torsional barriers. The induced slowing of the dynamics followed distinct behavior: with the Vogel–Fulcher dependence

equation image(9)

of the α-relaxation when considering the nonbonded interactions and with the Arrhenius dependence

equation image(10)

of the β-relaxation in the case of the torsional barriers. We note again in this work, the potential of the combined use of QENS and MD-simulations. A study of the influence of intramolecular barriers on the α-relaxation in polymers has also been carried out recently by means of MD-simulations on coarse-grained systems based on the well-known bead-spring model.72

Polymers with Complex Monomeric Units or/and Chain Architectures

Because of their intriguing behavior, the structural and dynamical properties of homopolymers with long alkyl-side groups, like the family of poly(n-alkyl methacrylates) (PnMAs), were extensively studied during the last decades.73–92 From X-ray diffraction experiments, where mostly carbons and oxygens are highlighted without the possibility of distinguishing main-chain and side-group contributions to the patterns, it was suggested that side groups of different monomeric units tend to aggregate forming self-assembled alkyl nanodomains [called PE-like nanodomains].84, 88, 93 The rich dynamical behavior was mainly investigated by calorimetric, dielectric, and mechanical techniques, that are not selective for the different processes at a molecular level. From those experiments, the existence of two different glass-transitions was proposed: one associated to the freezing of the motions within the alkyl nanodomains and the other with that of the main-chain dynamics81, 84, 88. Using a selective technique providing space/time resolution at a molecular level like NS combined with isotopic labeling was thus essential to check the validity of such scenario. This was realized in recent works on PnMAs with different number of carbons in the alkyl side-group nC.32, 94, 95 First, regarding the structure, neutron diffraction experiments provided direct evidence for the nanosegregated structure in these polymers.94 Thanks H/D labeling the origin of the two main peaks of the structure factor measured on fully deuterated samples [see inset of Fig. 3(a)] were identified. The peak at QII ≈ 1.3 Å−1—which position is independent of the side-group length—disappears on a sample where the side-groups are protonated [Fig. 3(a)]. Moreover, this peak is very similar to the main peak of the static structure factor of molten PE, and can thus be attributed to correlations between pairs of atoms belonging to different side-groups within the alkyl nanodomains. The peak at lower Q-values—which position QI shifts toward lower Q-values with increasing side-group length—is prominent in the sample where side groups are protonated and main chains are deuterated. Therefore, it should contain correlations among main-chain atoms [see Fig. 3(a)] and its position would reveal the nanodomain sizes. Second, concerning the dynamics, applying QENS an exotic phenomenology was deduced. This technique—in particular, NSE experiments on the fully deuterated samples—allowed selectively following the collective dynamics of the main-chain system at QI and that within the alkyl nanodomains at QII. The decay of the correlations relating main chains occurred with the typical features of the structural relaxation in glass-forming polymers, that is, following a stretched exponential functional form (eq. 8) with β ≈ 0.5 and a temperature-dependent structural relaxation time obeying scaling with viscosity. This can be seen for the case of poly(hexyl methacrylate) (PHMA, nC = 6) in Figure 3(b) (full circles). On the contrary, anomalous behavior for the structural relaxation of the side-groups was observed in high-order members. This consisted of extremely stretched—even logarithmic-like—functional forms [see full squares in Fig. 3(b)]. In addition, the self-motions of hydrogens in the alkyl side-groups were investigated on a labeled PHMA sample (deuterated main chain and protonated side group) by NSE32 [empty squares in Fig. 3(b)] and also by BS-ToF34 [Fig. 4(a–c)]. The NSE investigation was restricted to a single Q-value (1.5 Å−1), where the partial structure factor displays a minimum [see Fig. 3(a)] and the coherent contribution is extremely small as compared with the incoherent signal. Such studies revealed clear signatures of confinement effects. These manifested in (i) the presence of an elastic component, even at high temperatures with respect to the glass transition of the system [see, for example, Fig. 4(c)]; (ii) again extreme stretching of the intermediate scattering function [Figs. 3(b) and 4(a–c)] and (iii) a clear decoupling from the collective relaxation, that was much slower [Fig. 3(b)]. As shown in ref. 32, the difference—of more than two orders of magnitude—between self- and collective–dynamics of the side groups is clearly beyond the standard de-Gennes-like narrowing.96 The presence of confinement effects in these samples had already been proposed in the literature,88 but QENS provided the first microscopic definite proof. Figure 3(b) also shows an important feature in this sample: the dynamic asymmetry, that is, the large difference between the mobilities of the different subsystems (main chains and side groups). About three decades in time separate the decays of collective motions of main chains and side groups. We note that decoupled self and collective dynamics for the fast component has also been observed in other mixtures with strong dynamic asymmetry, like colloidal mixtures of large and small particles,97 polymer blends,98–100 mixtures of big and small star-polymers,101 or alkali silicates.102, 103

Figure 3.

(a) Main panel: coherent scattering cross-section measured on fully deuterated (full circles) and partially deuterated (empty squares) samples of PHMA (nC = 6). The inset shows the static structure factors measured on the fully deuterated samples with nC = 6, 4 and 2 from top to bottom (relative shifts have been applied for clarity). (b) NSE signal measured on fully deuterated (full symbols) and partially deuterated (empty squares) samples of PHMA. The data for the partially deuterated sample correspond to the self-motions of the hydrogens in the alkyl side-groups at Q = 1.5 Å−1. The collective dynamics revealing the structural relaxation within the alkyl nanodomains (measured at QII) are represented by the full squares. The full circles correspond to the main-chain collective relaxation accessible at QI. They were measured at 480 K and subsequently scaled with viscosity for a direct comparison with the other data sets. Solid lines are fits to stretched exponentials (eq. 8). The obtained β-values are indicated. The dashed line is a logarithmic description (Reproduced with permission from A. Moreno, A. Arbe, and J. Colmenero, Macromolecules 2011, 44, 1695. Copyright 2011 American Chemical Society).

Figure 4.

Intermediate scattering functions of PHMA (nC = 6) at T = 175 K(a), T = 265 K (b) and T = 360 K (c) for the different Q-values indicated in (a). Circles correspond to BASIS results and diamonds to IN16. Solid lines are fits of a model function that considers simultaneous local motions of the side groups and diffusive-like dynamics. Panels (d), (e) and (f) show the equivalent plots for POO (nC = 6). In these plots, the diamonds at short times correspond to IN6 measurements. In (f), a simple stretched exponential has also been used to describe the data for comparison (dotted lines) (Reproduced with permission from C. Gerstl, G. J. Schneider, A. Fuxman, M. Zamponi, B. Frick, T. Seydel, M. Koza, A.-C. Genix, J. Allgaier, D. Richter, J. Colmenero and A. Arbe, Macromolecules 2012, 45, 4394. Copyright 2012 American Chemical Society).

Motivated by the NS results on PnMAs, coarse-grained MD-simulations on a simple bead-spring model for copolymers with comblike structure were performed.104 It was found that the features observed by QENS on PnMAs are generic in comb copolymers with strong dynamic asymmetry. Interestingly, the simulations also predicted that the nanosegregation of side groups and main chains can arise as a purely entropic effect, provided that the density of branch points is large enough. In agreement with the simulations, the presence of alkyl nanodomains was also reported by neutron diffraction on another family of homopolymers with alkyl side groups of different lengths, the poly(alkylene oxide)s (PAOs).33 These polymers were subject of a thorough QENS investigation combining three different spectrometers to cover the widest possible dynamic range.34 Figure 4(d–f) show the resulting Fourier transformed results to the time domain for POO (nC = 6) after deconvolution. The intermediate scattering functions of PAOs were described taking into account localized motions for the side groups and simultaneous anomalous diffusion associated to the segmental motions involved in the α-relaxation. The spatial extent of the local motions was found to increase with temperature due to the softening of the structure and no special signature of confinement was identified in the side group dynamics of PAOs. Interestingly, the segmental motions of the main chain were found to be slightly slowed down with respect to those on PEO (PEO, the “nC = 0” counterpart of PAOs). This antiplasticization effect is antagonistic to that usually found in other families of alkyl-side group polymers. For instance, PHMA shows a decrease in the Tg-value of about 130 K with respect to that of poly(methyl methacrylate) (PMMA, the “nC = 1” counterpart of PnMAs). Thus, the phenomenology found on PAOs dynamics was very different from that observed for PnMAs. It is worth noting that the QENS investigation on PAOs also revealed the absence of strong dynamic heterogeneities between main chain and side group dynamics. This observation supports the dynamic asymmetry as the main responsible of the plasticization and confinement effects in the family of PnMAs. Thus, the ultimate microscopic origin of them would be the intrinsic rigidity of the main chain in acrylates with respect to the high flexibility of the alkyl groups. The dynamic asymmetry was also invoked for explaining the deviations with respect to the behavior of simple polymers found by a combined QENS and MD-simulation study on poly(vinyl pyrrolidone) (PVP),105 which possesses a relatively bulky side group with a much larger mobility than the main chain.

Rheological properties of polymer melts well above the glass transition are determined not only by the chain length but also—and even more so—by the polymer architecture.106 Combination of NSE and H/D labeling offers unique microscopic insight in polymer rheology,14 providing demanding tests for the existing theoretical frameworks for polymer dynamics. In this direction, a recent study by Bras et al.35 deals with polymer ring dynamics in the Rouse regime, approaching the relaxation mechanisms in melts of low molecular weight PEO chains. Ring polymers were investigated in two different environments: a melt of equivalent rings and matrix of linear polymers. Labeling the system with 20% protonated ring polymer chains in a deuterated matrix (either consisting of ring or linear chains) the dynamic structure factor of the rings was followed by NSE. Results were compared with those from the linear chain reference system (same molecular weight). For the full ring system an almost twice faster diffusion and a less subdiffusive behavior than in the linear reference system were found. Moreover, no contribution of internal modes in the accessible time and Q-window was detected. In the linear chains environment, the diffusion coefficient and the sublinear behavior of the rings were found to be closer to those in the linear reference melt. The much faster diffusion of the rings demonstrates an obvious breakdown of the Rouse model, since the center of mass diffusion appears to be not only determined by friction and number of chain segments, as predicted, but also shows an unexpected dependence on the polymer architecture. The “heat bath” assumption of the Rouse model thus seems to fail for ring polymers.

Another interesting study dealing with the influence of chain architecture on polymer dynamics was reported by Zamponi et al. in ref. 36. From macroscopic measurements, it is well known that by introducing a branching point the chain dynamics is considerably slowed down. To describe this effect, a hierarchical relaxation was postulated,107 where each branch is confined in a tube. The branched polymer, contrarily to the linear counterpart, cannot reptate; the branch point localizes the polymer in space until the different arms have fully relaxed with respect to the branch point. This effect was modeled for symmetric108 as well as for asymmetric stars.109 For the latter, it was considered that the short arm relaxes much faster than the longer arms and eventually allows the star to reptate. To provide a microscopic test for such theoretical frameworks, in Ref. 36 a NSE direct observation of the branch point motion was performed on PE-star polymer melts. Two different three-arm stars were investigated: one symmetric star with long well-entangled star arms and one asymmetric star where the third arm was shortened to a length of only one entanglement length. In both cases, only the nearest segments around the branch point were labeled (protonated in an otherwise deuterated melt). With this specific labeling the branch-point motion could be followed on a molecular level. As reference, the similarly labeled center of a “two-arm” linear polymer chain was also investigated. Figure 5(a) shows the results obtained for the symmetric star in comparison to the linear polymer. For about the first 35 ns, both systems display the same relaxation, but then the data corresponding to the branch point of the star level off into a plateau region while those of the linear chain continue to decay. Plateaus in the dynamic structure factor are signatures of spatial confinement. From the Q-dependence of the plateau-values an estimate of 42 Å for the localization space of the branch point could be made. It is confined to a length scale smaller than the tube diameter dtube for linear chains (dtube = 47 Å)110: although the center of the linear chain is also still well confined inside a tube built by the surrounding chains, the segments may move freely along the tube, causing the additional relaxation of the dynamic structure factor seen in Figure 5(a). Conversely, a short arm of only one entanglement length was observed to lead to the same topological confinement of the branch point as in the symmetric star up to intermediate times [see Fig. 5(b)]. Only at longer times as accessed by macroscopic rheological measurements the asymmetric star displayed a flow behavior similar to the linear chain —the drag of the short arm was stronger than expected, according to a larger than expected friction of the branch point. Such observation should thus be considered to refine the theoretical approach to arm retraction in asymmetric stars.

Figure 5.

Dynamic structure factor of a branch-point labeled symmetric three-arm star (open symbols) in comparison to a center labeled linear chain (closed symbols) (a) and a branch-point labeled asymmetric three-arm star (closed symbols) (b). Q-values (Å−1): 0.05 (circles), 0.077 (triangles up), 0.096 (diamonds) and 0.115 (triangles down). Dashed lines in (a) are guides for the eye; dashed lines in (b) and solid lines are different fits (Reproduced with permission from M. Zamponi, W. Pyckhout-Hintzen, A. Wischnewski, M. Monkenbusch, L. Willner, G. Kali, and D. Richter, Macromolecules 2010, 43, 518. Copyright 2010 American Chemical Society).

Semicrystalline Polymers

About two-thirds of the annual production of synthetic polymers mainly consists of semicrystalline polymers. In this kind of materials, the amorphous phase can be considered as self-confined within the restricted environment imposed by the crystalline phase. A strong interaction between the amorphous phase and the crystalline one is expected as polymer chains in the former are physically connected with the crystals. This type of materials have been investigated by QENS over the last decades (see, e.g. refs. 111–114). During the period considered in this review, the impact of confinement on the structural relaxation was investigated by Sanz et al.37 by applying NSE techniques to deuterated semicrystalline poly(ethylene terephthalate). In that work, the selectivity of neutron scattering to particular correlations was exploited. Measuring the decay of the dynamic structure factor at the Q-value corresponding to the maximum reflecting intermolecular correlations in the amorphous phase of the semicrystalline material, the dynamics of the α-relaxation in this phase was isolated. The functional form associated to this process turned out to be describable by a stretched exponential (eq. 8) with an exponent βNSE = 0.5. This is the same value as that found in the amorphous polymer, where the stretching can be considered as an intrinsic feature of the α-process (homogeneous scenario115). It was thus concluded that the dynamics of semicrystalline polymers also occurs in a homogeneous scenario. Accordingly, the intermolecular cooperativity would be expected to be rather similar in both amorphous and semicrystalline polymers. The slowing down of the characteristic segmental relaxation found in a semicrystalline polymer in comparison with that of an amorphous one would be caused by a retardation of the intramolecular mobility provoked by the anchoring of the polymer chains of the amorphous phase bounded to the crystalline one. The reduced segmental mobility of the semicrystalline polymer would be restricted to well-differentiate spatial regions, probably in the crystal/amorphous interface. Moreover, from BDS a much smaller value was deduced for the β-exponent in the semicrystalline material (βBDS ≈ 0.2). This was attributed to the averaging effect of measuring a homogeneous relaxation with similar values of the stretching parameter over an inhomogeneous environment providing different characteristic relaxation times.

Another interesting recently published QENS work focused on a semicrystalline natural polymer: wormsilk. Humid silk fibers are mechanically significantly different from dry silk fibers. Motivated by this fact, Seydel et al.38 investigated the dynamical response on a molecular level to an externally applied tensile force on humid fibers. The experimental setup used allowed combined in situ hydration and in situ tensile testing with ToF spectroscopy on aligned fiber bundles. By BS, complementary information on unstretched samples that were humidified ex situ was recorded. The results showed that the presence of water fluidifies the amorphous polymer fraction such that both, water and polymer chains display a diffusive mobility that is absent in the dry silk fibers. For fibers at 100% relative humidity, a strong effect of tensile strain was observed on the mobility of the amorphous fraction of the fibers, also absent in the dry sample. In the direction perpendicular to the fiber axis, an increased mobility was observed that was attributed to a better alignment of the amorphous chains. This was also supported by the change in geometry found for the involved confined motions.

Confinement in Polymer Systems

Most of the advanced materials based on polymers are multicomponent or(and) nanostructured. In these systems “confinement effects” at molecular level (topological constraints at the interface, interactions, etc.) emerge in a natural way, and they can affect both the structure and the dynamics of the system and the macroscopic properties as well. This is a rather general problem of utmost importance in the field of nanomaterials technology that also poses new challenges in fundamental science. During past years, QENS has been exploited in a variety of systems to contribute to this question (see, e.g. refs. 116–124 and, as a general recent ref. 125).

The most obvious way to confine macromolecules is placing them in a rigid structure with nanometer size cavities (hard confinement). This has been subject of a series of recent works on model systems, where the very flexible PEO has been confined in well-defined pores of nanometric diameters. Different aspects of polymer chain dynamics were investigated by NSE experiments under diverse conditions. Mixtures of deuterated and protonated chains matching the scattering length density of the porous matrix were infiltrated. We first describe the experiments on PEO confined in porous silicon by Kusmin et al.46 Unentangled and weakly entangled melts were investigated, consisting of chains of molecular weights of 3 and 10 Kg/mol, respectively, infiltrated in pores of 13 nm diameter. In porous silicon, the pores run strictly perpendicular to the wafer surface, allowing selectively probing molecular motions along the pore and in the radial direction, testing for a dynamic anisotropy. Spectra recorded in both orientations were analyzed in the frame of a two-state model where free chains undergo Rouse dynamics and diffuse within an infinite cylinder in the center of the pore and adsorbed chains have immobile center-of-mass and substantially slower (relative to free chains) internal dynamics. For both molecular weights, the internal dynamics of free chains was apparently unaffected by the confinement, as evidenced by the friction coefficient similar to the values reported for the bulk PEO melts. For the smaller chains, the radius of the infinite cylinder was found to be 1.4 nm (thickness of an adsorbed layer approximately equal to the Flory radius) and the diffusion rate along the pore appeared to be slower than in the radial direction. Such an anisotropy was attributed to the fact that for a molecule to move along the pore (or in the radial direction) neighboring molecules must make space by moving in the radial direction (or along the pore); because of the walls, there is a resistance to their movement in the radial, but not in the axial, direction. For the larger chains, the details on the CM diffusion could not be discerned. Furthermore, the same two-state model was also applied by the same authors to a melt of n-hexatriacontane confined in similar pores.47 “Sticky boundary layers” were also reported, which corresponded to a bilayer at 364 K and a monolayer at 435 K, while at 512 K no evidences for an adsorbed layer were found.

First evidences of confinement effects on the reptation mechanism were reported in ref. 48 for PEO severely confined in cylindrical nanopores of anodic alumina oxide (AAO). In that work, samples where the chain dimensions (average bulk end-to-end distance Re) were either much larger or smaller than the lateral pore sizes were investigated by NSE: (i) a sample with Re = 59.7 nm in pores with diameter Dpores = 25 nm and (ii) a sample with Re = 13.5 nm in pores with Dpores = 35 nm. By means of SANS, the optimal experimental conditions to perform the dynamic measurements by NSE were first determined. Figure 6 shows the NSE results obtained for both samples. At intermediate timescales (Rouse regime) the data show a clear slowing down compared to the bulk behavior. This effect could not be related to a general increase of the friction between monomers, since in a previous work by other QENS techniques,126 the local dynamics at short times was found to be largely unchanged. At long times, the curves tend to finite plateaus that reflect confinement effects on the dynamics of the polymer chains—the single chain fluctuations are laterally restricted giving rise to a Debye–Waller type form factor. As can be seen in Figure 6(a), the tube diameter deduced for the shorter (less-confined) chains is not appreciably influenced with respect to that found in the bulk (dtube = 52 Å). The situation is clearly different for the more confined long chains [Fig. 6(b)]. In such case, a 15% expanded entanglement network is observed. Thus, the NSE results reported in ref. 48 provided direct evidence that under strong confinement conditions, the topological constraints imposed by the neighboring chains become diluted. These results obviously ruled out the presence of the invoked “Corset effect”127 from NMR relaxometry studies, that would imply an order of magnitude reduction in effective tube diameter. The same conclusion about the absence of Corset effect was drawn by another research team (Lagrene et al.49, 50) applying NSE on a PEO melt weakly confined in AAOs (Re = 16.4 nm in Dpores = 18 nm), who accordingly did neither find a change in the tube dimensions.

Figure 6.

Single chain dynamic structure factor of PEO chains under weak (a) and strong (b) confinement at the Q-values indicated. Dashed lines represent De Gennes curves fitting the bulk PEO behavior. Solid lines in (b) are fits with the value of the Rouse rate fixed to that in the bulk, delivering a confinement diameter value of 60.3 Å. (Reproduced with permission from J. Martín, M. Krutyeva, M. Monkenbusch, A. Arbe, J. Allgaier, A. Radulescu, P. Falus, J. Maiz, C. Mijangos, J. Colmenero, and D. Richter, Phys. Rev. Lett. 2010, 104, 197801). Copyright (2010) by the American Physical Society.

Polymers intercalated in layered systems is another topic that has attracted increasing scientific interest over last years. One of the reasons is that this type of confining media can be a convenient platform for much-needed studies of macromolecules under extreme 2D confinement—a situation for which theoretical predictions have also been reported.128 Studies of polymers intercalated between the layers of natural silicates with interlayer distances of 1–2 nm129 show that there is not any trace of the glass-transition process by differential scanning calorimetry (DSC). Additionally, dielectric spectroscopy measurements show that the segmental motions become very fast and display an Arrhenius temperature dependence going through the bulk polymer Tg. Similar results have recently been reported130, 131 for PEO intercalated into subnanometer graphite oxide (GO) layers. The segmental dynamics of poly(hexa(ethylene glycol) methacrylate) intercalated in a layered silicate (hydrophilic sodium montmorillonite)(Na+-MMT) has also been investigated by BS by Fotiadou et al.51 Figure 7 taken from the original publication51 shows as an example the incoherent structure factor measured in the bulk polymer and in the intercalated polymer at a Q-value of 1.3 Å−1 and at different temperatures. From this figure, it is obvious that the temperature dependence of S(Q,ω) is much weaker for the intercalated polymer than for the bulk polymer. The S(Q,ω) data were analyzed by assuming an elastic and a quasielastic contribution, the latter being represented by a stretched exponential (see eq. 8) with β = 0.5. The relaxation time for the intercalated polymer shows a very weak, if any, Q-dependence. Conversely, its temperature dependence is Arrhenius-like and its values are significantly faster than those of the bulk polymer. This confirms by a microscopic technique the trend observed by dielectric spectroscopy in other intercalated polymers. Although it is not mentioned by the authors, the results obtained by QENS suggest that the segmental dynamics in the intercalated polymers is dominated by localized motions.

Figure 7.

Incoherent structure factor S(Q,ω) for different temperatures at wavevector Q = 1.3 Å−1 of (a) PHEGMA and (b) PHEGMA/Na+-MMT: 30/70 nanohybrid. The scale of the y-axis corresponds to 20% of the maximum intensity at 220 K. The solid lines correspond to the total fit whereas the dotted and dashed lines denote the elastic and quasielastic contributions, respectively. The insets highlight the quasielastic part of the spectra (Reproduced from S. Fotiadou, K. Chrissopoulou, B. Frick, and S. H. Anastasiadis, Journal of Polymer Science: Part B: Polymer Physics 2010, 48, 1658, with permission from Wiley).

Conversely, high-resolution inelastic neutron scattering measurements have been carried out in PEO under subnanometer confinement in hydrophilic GO layers.130, 131 By means of this technique, the vibrational density of states of intercalated PEO was determined, which strongly differs from that corresponding to bulk PEO (see Fig. 8). The obtained results unambiguously show that under these extreme confinement conditions PEO adopts a planar zig-zag conformation, in no way resembling the characteristic 72 helical structure of the bulk crystal or the random coil conformation of the melt state. It is expected that ongoing QENS experiments combined with MD-simulations will shed a new light on the local and chain dynamics of intercalated PEO.

Figure 8.

Mass-normalized inelastic neutron scattering spectra of GO, PEO, and PEO/GO measured on TOSCA (ISIS) at 30 K. Inset: spectra at low energy transfers (Reproduced with permission from F. Barroso-Bujans, F. Fernandez-Alonso, S. Cerveny, S. F. Parker, A. Alegría, and J. Colmenero, Soft Matter 2011, 7, 7173. Copyright (2011) by the Royal Society of Chemistry).

Much less restrictive is the confinement imposed by platelets on polymer chains adsorbed to them in solution (“single-sided confinement”). This situation was recently investigated by Frielinghaus et al.52 with NSE experiments on solutions of 6% (exfoliated) laponite clay and either 4% or 8% PEO in deuterated water. The intermediate scattering functions showed plateaus at long times that are absent in free-polymer solutions. The NSE results were interpreted in terms of an immobile and a mobile contribution. The former would correspond to the chain segments being rather tightly bound to the platelet and the latter to the polymer loops that would be rather free. The immobile fraction turned out to be Q-dependent. From such dependence, a localization length of 9 Å independent of the polymer concentration was deduced, that would be directly connected to the polymer layer thickness. The behavior shown by the mobile contribution was compatible with Zimm-like4 dynamics (the counterpart of the Rouse model for polymer solutions). Enhanced mobility was found for the higher polymer concentration, which was interpreted by the authors as a signature of confined dynamics.

The ability of block-copolymers to self-assemble in well-ordered nanostructures provides another elegant route to induce confinement effects. By means of this procedure, the chain dynamics of PI under confinement has been recently investigated by the NSE technique.53 The copolymer considered was polyisoprene-b-poly(dimethyl siloxane) (PI6-PDMS30), where the numbers indicate the molecular weights in kg/mol. As shown by SANS, this system forms hexagonally ordered cylindrical structures composed of a PI-phase (with a cylinder radius of about 6.4 nm) in a continuous PDMS matrix, which acts as a confining melt for PI-chains. As PDMS is more flexible than PI, the domain walls are not expected to be static but will be subject of fluctuations and the interface dynamics will also play an important role. Confinement of this type can be referred to as “soft” in contraposition to the “hard” walls encountered, for example, in nanoporous materials.

By playing with selective deuteration techniques and to separate the different contributions to the dynamics of confined PI, two samples with different scattering contrast were prepared. One which was mostly sensitive to the dynamics driven by the surface of the interface between PI and PDMS phases, and the second one highlighting the single-chain motions inside the cylindrical domains. A detailed characterization of these samples was first performed by SANS. By combining the NSE results from the two different contrasts, it was possible to quantitatively describe the PI-chain dynamics by a model (see upper part of Fig. 9) which takes into account the interface dynamics and restricted Rouse-like chain motions in addition to slow diffusive processes. The overall chain diffusion is found to be greatly reduced in the system; however, a significant mobility is found, which is likely to be caused by a 2D diffusion of the junction point along the cylindrical surface. The lower part of Figure 9 shows that this model describes rather well the chain dynamic structure factor measured by NSE. It also shows the relevance of the interfacial dynamics.

Figure 9.

Upper part: A conceptual hierarchical figure showing possible dynamical processes present in the cylindrical block copolymer system. Part (a) shows hexagonally-ordered cylinders, where the center of mass motion of the individual cylinders is essentially frozen within the crystal structure (cage) on the presently considered time scale. Part (b) demonstrates the center of mass chain diffusion processes, where the connection point between the two blocks essentially undergoes a 2D movement on the surface of the cylinder. Part (c) indicates local undulations of the interface (capillary waves) that cause oscillation of the anchorage point in the z-direction while the thin intermixing zone renders segmental 2D diffusion in the plane. The latter feature will be mostly visible in the bulk contrast, which is very sensitive because of the mixing of purely protonated and deuterated segments. Lower part: NSE results showing the intermediate dynamic structure factor from the single chain contrast (24% h-PI-dPDMS/d-PI-d- PDMS mixture) at different Q-values. The solid lines display fits from the model taking restricted Rouse motion modulated by chain-end fluctuations as well as interfacial undulations and Rouse segmental diffusion in addition to the overall slower chain-diffusion of the entire PI-PDMS block copolymer. The dotted lines show the prediction of the model without the contributions from the surface undulations and segmental diffusion (Reproduced with permission from L. Willner, R. Lund, M. Monkenbusch, O. Holderer, J. Colmenero, and D. Richter, Soft Matter 2010, 6, 1559. Copyright (2010) by the Royal Society of Chemistry).

Block copolymers have also been used to investigate the effect of confinement on proton transport mechanisms in block copolymer/ionic liquid membranes. Mixing a block copolymer with an ionic liquid has proved to be one route to obtain nanostructured, ion-conducting membranes having ionic conductivity coupled to favorable mechanical durability. In a recent work by Hoarfrost et al.,132 QENS—combined with other techniques—has been used to study the effect of confinement on the mechanisms of conduction in mixtures of the diblock copolymer poly(styrene-b-2-vinyl pyridine) (PS-b-P2VP) with the proton conducting ionic liquid imidazolium:bis-(trifluoromethylsulfonyl)imide ([Im][TFSI]) having an excess of imidazole. The block copolymer used selfassembles in a lamellar structure in which the ionic liquid is selective for the P2VP phase. Backscattering measurements were carried out on the block-copolymer containing the ionic liquid in the P2VP phase and also on the mixture of the ionic liquid and the bulk P2VP. The Q-dependence of the quasielastic signal proved that the proton dynamics can be described in terms of the well-known jump-diffusion model.133, 134 Moreover, it was found an increasing of the proton hopping in the copolymer with respect to the homopolymer. The authors proposed that block chain stretching or confinement affect the hydrogen-bond structure of the ionic liquid, leading to this increase. In the context of confining mesophases, we finally mention another interesting ToF and BS work by Lyonnard et al.135 focused on the dynamics of water confined in mesomorphous phases of perfluorinated sulfonic surfactants. Such systems mimic the physico-chemical properties of the perfluorinated Nafion membranes which are used as electrolyte in fuel cells. As surfactants self-assemble in well-defined organized phases, they were used as model charged systems to understand the structure–transport relationship in complex real materials. Analysis of the results with localized translational diffusion models showed the existence of a strong confinement effect that depends on the geometry (hexagonal and lamellar phases were investigated).

Nanocomposites, Solid Polyelectrolytes and Blends

Nowadays there is not any doubt that polymer nanocomposites—polymer matrices filled with NPs of different nature—are the core of many advanced applications of polymers due to their high potential for taylor-made materials and functionality.136 They are also frequently used as commodities. Consequently, there exist uncountable studies of the dynamic properties of different nanocomposites by means of “macroscopic techniques” as for instance dielectric and mechanical spectroscopies, calorimetric techniques, and rheological measurements. However, in spite of this effort, many fundamental questions concerning the molecular origin of the nanocomposite properties remain unsolved yet. It is obvious that QENS offers unprecedented possibilities in this field. Not only because the dynamic processes of the polymer matrix take place at the time and length scale covered by QENS but also mainly because by appropriate isotopic substitution and contrast matching methods, these processes can be selectively isolated from the total response of the nanocomposite. In spite of these capabilities, investigations by QENS of polymer dynamics—in particular, chain dynamics—in well-defined nanocomposites are still scarce. It seems that the potentiality of QENS in this field has not been totally exploited yet.

The dynamics of entangled chains in polymer nanocomposites with nonattractive interactions has been recently investigated by NSE by Schneider et al.42 The nanocomposites consisted of a matrix of PEP filled with hydrophobically modified silica particles (average diameter Dav = 17.0 ± 0.2 nm) at different concentrations (volume fractions of NPs Φ ranging from 0 to 0.6). The samples were previously characterized by SANS,137 showing good dispersion of the NPs. The isotopic contrast matching conditions to actually measure the chain dynamic structure factor by NSE were also determined by SANS. Figure 10(a) shows the normalized chain dynamic structure factor at Q = 0.96 nm−1 as a function of the filler concentration. Without any modeling, it is obvious that the value of the long-time plateau increases with the filler concentration. This increasing directly signifies an increase of the apparent confinement for chain motion. As the molecular weight of the pure PEP (Mw = 50 kg/mol) is well above the entanglement mass of PEP (Me ≈ 3.4 kg/mol), the chain dynamics data of the pure PEP need to be interpreted in terms of the reptation model. In this framework, the analysis of the long-time plateau gives a value for the “tube” diameter of 5 nm. For the different concentrations, a similar analysis provided an apparent tube size dapp that decreases with increasing Φ [see the inset of Fig. 10(a)]. This behavior was interpreted by the authors as being due to the competition of two different chain-confining mechanisms in this type of nanocomposites: the confinement by the surrounding chains (entanglement mechanism) driven by the molecular weight and the geometrical confinement due to the presence of the NPs—impenetrable particle structure—[see Fig. 10(b)]. In this framework, the reduction of the measured apparent chain-confinement length dapp is the result of a crossover from polymer-caused entanglement constraints to chain motion in the presence of obstacles. Conversely, by analyzing the short-time behavior of the chain dynamic structure factor, information of the Rouse regime could be obtained. The experimental results obtained do not indicate a general slowing down of the Rouse modes—at least the basic segmental relaxation dynamics is not altered by the presence of fillers. Nevertheless, a particular slowing down of long-wavelength Rouse modes cannot be excluded, since the signature of such Rouse modes would be overshadowed by confinement effects. In a following article43 it is also shown that the extracted confinement length can be directly connected with rheological data from the same samples. In addition, qualitative evidences were also found from the rheological data that the contour length fluctuations and constraint release mechanisms are less effective in nanocomposites with high concentration of NPs. This result is in agreement with the idea that in that concentration range, the chain confinement is dominated by the geometrical constraints induced by the impenetrable particle structure.

Figure 10.

(a) Dynamic structure factor of PEP at various nanofiller volume fractions 0 ≤ Φ ≤ 0.6 at T = 423 K and Q = 0.96 nm−1 (□, ▵, •, ▿, and tilted ▿ represent Φ = 0, 0.18, 0.35, 0.50, and 0.6, respectively). Solid lines are fits with the tube model in the long time regime. Inset: resulting apparent confinement length dapp[nm](Φ). (b) Characteristic confinement lengths in the PEP/NP system: dapp = apparent confinement length from the NSE measurements; dgeo = calculated geometrical confinement length; dtube = topological tube confinement (Reproduced with permission from G. Schneider, K. Nusser, L. Willner, P. Falus, and D. Richter, Macromolecules 2011, 44, 5857. Copyright 2011 American Chemical Society).

The microscopic mechanisms behind the mechanical reinforcement have also been recently investigated by Akcora et al.44 combining mechanical measurements and QENS (elastic scans). The samples investigated consisted of silica NPs (diameter ≈ 14 nm) isotropically grafted with PMMA chains in matrices of PMMA. To selectively observe by neutron scattering either the grafted chains or the matrix chains selective deuteration was used. Two extreme cases were considered: samples with well-dispersed NPs and samples showing NPs' clusters. Although the former case shows liquid-like mechanical behavior, the latter displays strong mechanical reinforcement, as characterized by a low frequency plateau in the frequency-dependent mechanical storage modulus. The mean-squared displacement of protons, calculated from the measured elastic scans, showed very different temporal behavior. The behavior of those corresponding to the matrix polymers results to be independent of annealing time for both type of samples, as is that corresponding to the grafted chains in the well dispersed case. In contrast, the dynamics of the protons of the grafted chains slow as the NPs aggregate in the composite where these particles form anisotropic structures. Based on these data in combination with other results, the authors proposed that the mechanical reinforcement would be driven purely by the grafted NPs, forming a particle network with the grafted chains providing the mechanical “bridges” between the NPs.

Addition of NPs can also improve the ionic conductivity in solid polymer electrolytes (SPEs), of great interest for the production of rechargeable Lithium-ion batteries. A systematic study by Fullerton-Shirey and Maranas39 combining DSC, BDS, SANS, and QENS addressed the mechanism for such improvement in SPEs containing PEO and LiClO4 upon inclusion of Al2O3-NPs. A wide range of compositions and NP-concentrations were explored. It was found that the glass-transition and and pure PEO crystal fraction were not altered by the presence of NPs, which formed aggregates as observed by SANS. Nevertheless, the NPs improved conductivity at all the temperatures but only at the eutectic concentration. QENS experiments provided direct insight on the segmental motions of the polymer, that were found to be unaffected by NPs addition (see Fig. 11). This implies that the enhancement of conductivity is not due to an increased polymer mobility. The QENS spectra revealed a rotation in both filled and unfilled samples that would be consistent with rotation of (PEO)6:LiClO4, a channel-like structure that is more conductive than the amorphous equivalent. The authors suggested that the NP surface would stabilize the conductive (PEO)6:LiClO4 structure, allowing them to persist long enough for conduction to occur.

Figure 11.

S(Q,t) for 10:1 and all NP concentrations investigated at Q = 1.04 Å−1: (A) 75 °C and (B) 50 °C. The lines represent fits (Reproduced with permission from S. K. Fullerton Shirey and J. K. Maranas, J. Phys. Chem. C 2010, 114, 9196. Copyright 2010 American Chemical Society).

In other works,40, 41 Maranas et al.40, 41 also considered an additional route to design improved SPEs for Li-ion batteries, namely PEO-based single ion conductors (ionomers). In these systems, the anion is covalently bonded to a PEO spacer through a comonomer unit, so that only the cation contributes to the conductivity. This prevents the undesired accumulation of anions at the electrodes that results in a reverse polarization that degrades battery life. A combination of ToF and BS was applied to investigate the spacer polymer dynamics under different ion content conditions. These were varied by changing the ratio between ionized and nonionized comonomers40, 41 and the spacer length.41 Always two segmental processes were observed, that were attributed to the presence of two kinds of spacer atoms. The faster atoms would be located in the midspacer region (bridge atoms) and the slower atoms near the ionized comonomers (anchor atoms). Thus, QENS allowed identifying a large dynamic heterogeneity in the system. From the quantitative analysis of the spectra the fraction of both kinds of atoms was determined, and their ionic compositions were estimated. Spatial segregation of the two dynamically distinct regions was proposed, evidences of which were sought in a thorough X-ray study. The authors suggested that the ion aggregates found would play an as yet unknown role in ion conduction for single ion conductors. We note the similarity of this scenario with that found in PnMAs as it has been described above, where nanosegregation in distinctly dynamic domains was also reported.

Apart from nanocomposites, polymer blends composed of two thermodynamically miscible polymer systems conform another well-known class of two-component systems based on polymers. This type of systems also offer the possibility of engineering new materials with tuned specific properties. The dynamics of polymer blends in general has been investigated over last decades by means of different experimental techniques including QENS.98 In particular, the so-called “dynamically asymmetric polymer blends,” that is, systems where the two components display very different segmental mobility (or glass-transition temperatures), have been the focus of may recent works. A “canonical” polymer blend of this type is that composed by PEO and PMMA. The segmental dynamics of this system was investigated by QENS over last ten years (see refs. 138–140 as representative references). The works were also extended to other asymmetric blends based on PEO (PEO/poly(vinyl acetate)141, 142 and PEO/polyethersulfone).143 Recently, the single chain dynamic structure factor of PEO in blends with PMMA has also been measured by NSE.45, 144 It is noteworthy that in the latter paper45, the NSE measurements were combined with fully atomistic MD-simulations carried out on a system with the same molecular weight than that measured. In this way the simulations were used to understand the contributions to the total scattered signal in the context of the random phase approximation. Moreover, the validity of the Rouse-like single chain dynamic structure factor Schain(Q,t) in asymmetric polymer blends was also investigated. Although the expression giving the relative segment mean squared displacements 〈rmath image〉 seems to remain valid, the calculation of Schain(Q,t) in terms of 〈rmath image〉 and the Gaussian approximation fails likely due to the strong heterogeneities present in asymmetric blends at low temperatures.

Hydrated Polymers, Polymer Solutions, and Microgels

Concentrated aqueous polymer solutions (water/polymer mixtures) have been subject of great interest in recent years. Works on these systems were motivated by different reasons. First of all, water-polymer interactions and their mutual effects on the dynamics are issues of fundamental interest per se, both from a basic and from an applied point of view. We commented above the role of hydration on the properties of natural polymers in silk fibers, that can be extended to synthetic polymers like nylon. Conversely, the dynamical behavior of interfacial and confined water at super-cooled temperatures is a hot topic of research essentially because the properties of biopolymers (proteins and DNA) depend on the dynamics of water in the first hydration shell.145–147 Typical biological water environments (for instance in proteins) include hydrophilic and hydrophobic sites/regions/interactions that are also present in aqueous synthetic polymer solutions. Therefore, the latter could be considered as (extremely) simplified models to address these questions. Another important driving force for these studies is the understanding of supercooled water dynamics.148–150 The reason is that water crystallization can be inhibited in solutions at sufficiently high solute concentration, allowing the study of water dynamics in the so-called “no-man's land” where bulk water unavoidably crystallizes. QENS techniques have been repeteadly applied to investigate water dynamics for a long time (see, e.g. refs. 151, 152). Because of the big dipole moment of water molecule, dielectric spectroscopy (BDS) is a very suitable technique to address its reorientational dynamical behavior in a wide frequency range and has been applied to a large variety of concentrated solutions. It turns out that the characteristic times of the main water relaxation process detected by BDS exhibits peculiar features, including (at least one) crossovers in their temperature dependence. The origin(s) of the crossover(s) observed for water dynamics is still subject of strong controversy in the scientific community (see, e.g. ref. 153). The main crossover observed, from non-Arrhenius to Arrhenius behavior, appears to show universal features in solutions of hydrophilic polymers, biopolymers, and small glass-forming materials.154 It was reported that such crossover takes always place at the global glass-transition of the system.154 However, in a later work on hydrated semicrystalline and amorphous polyamides,56 the crossover was found at temperatures well below the calorimetric glass-transition of the systems, although in this case, we note that the water concentration was lower than in the other cases (see below).

In this context and trying to provide microscopic insight with space/time resolution on the dynamics of both components, neutron scattering was applied in a series of polymer/water mixtures: a poly(vinyl methyl ether) (PVME) solution with 30 wt% water content54, a PVP solution with 40 wt % water content55 and the two aforementioned polyamides/water mixtures (≈16 wt % water concentration).56 In the three cases, the intermediate scattering function of water hydrogens displayed a strong stretching with respect to the simple diffusive behavior (single exponential). The spectra could be described by assuming stretched exponentials (eq. 8) with βmath image = 0.5, and the resulting characteristic times followed Q-dependences close to Q−2-laws (typical for simple diffusion). These two simultaneous observations could be explained invoking the presence of heterogeneous environments for water diffusion.115 As can be seen in Figure 12, for all the systems the average diffusion coefficients found were rather similar (in PVME slightly larger at high temperatures) and clearly smaller than that of bulk water. Thus, no significant differences were observed for water dynamics in all the cases. The possibility of labeling the components by selective deuteration allowed following also the dynamics of the matrix, that is invisible by BDS due to the overwhelming strength of the water component. Also common for all systems was the finding of a large dynamic asymmetry, as shown in Figure 13 for the PVME/water system. In PVME and PVP solutions, the polymer component also reflected the heterogeneous environments in a resulting anomalous stretching (βpolymer ≈ 0.3). It is worth noting that in both cases, the calorimetric glass-transition is compatible with the extrapolation of the Vogel–Fulcher behavior (eq. 9) of the polymer component as resolved by QENS (see Fig. 13, ref. 55) and the crossover found from BDS takes place when the polymer component freezes. This scenario was proposed in ref. 154, but no experimental proof could be provided from BDS to identify the calorimetric glass-transition with the freezing of the α-process of the solute component. In the case of the polyamides, the segmental α-relaxation could not be resolved by QENS (very slow for the QENS dynamic window) in the temperature range of interest. The weak Q- and temperature dependences of the dynamic process measured on the polymer component suggested that the motions observed could be related to a secondary relaxation of the polyamides (the so-called γ-process). In fact, the relaxation times found by QENS are in the same range of values of those reported for the γ-process. Conversely, in the case of polyamides, it was also observed that the crossover in the water dynamics takes place when its characteristic relaxation times reach the values of the γ-relaxation. This could suggest that the local mobility of the polymer could play an important role in the origin of this crossover.

Figure 12.

Average diffusion coefficients of water in mixtures with PVME,54 PVP,55 and amorphous and semicrystalline polyamides copolymers56 as functions of temperature, compared with that of bulk water.152

Figure 13.

(a) Derivative of the specific heat of PVME/H2O as function of the inverse temperature. (b) Relaxation map of the PVME/H2O system. Filled symbols: NS characteristic times at Q = 1 Å−1 for the PVME (♦) and water (▪) components. Empty symbols: BDS relaxation times for the slow (□) and fast (⊞) processes. Results obtained on dry PVME are shown for comparison: α- (▵) and β-process (▿) observed by BDS, and NS characteristic times at Q = 1 Å−1 (▾).165 Solid, dashed-dotted and dotted lines are VF laws and the dashed line is an Arrhenius fit to the “slow” process below 200 K. Shadowed area indicates the region of the calorimetric glass-transition in the wet PVME system (Reproduced with permission from S. Capponi, A. Arbe, S. Cerveny, R. Busselez, B. Frick, J. Embs, and J. Colmenero, J. Chem. Phys. 2011, 134, 204906. Copyright 2011, American Institute of Physics).

In the previous section, we commented on works focused on the development of solid polyelectrolytes. Considering now polyelectrolyte solutions, they also remain incompletely understood due to several reasons: their multicomponent nature, their structural complexity—that can be even increased with the polymer architecture—, and the presence of short- and long-range interactions. The investigation carried out by Horkay et al.57 was conducted on semidiluted solutions of a semirigid biological polyelectrolyte: the sodium salt of hyaluronic acid, one of the most abundant biopolymers in the human body. In this polymer, the local configuration is simpler than that of more flexible polyelectrolytes. Varying the conditions of added salt, the effects in the collective diffusion due to long-range interactions were distinguished from those emerging from the short-range excluded volume. Dynamic light scattering (DLS) and NSE experiments were carried out to investigate the mutual diffusion between hydrogenated polyelectrolyte chains and a deuterated solvent. Both techniques are sensitive to the contrast between polymer and solvent, but they explore different length-scale ranges ∼ 1/Q. NSE is sensitive to more local length scales, where individual chain segments are resolved. Figure 14 shows the diffusion coefficients deduced from the two techniques (DNSE and DDLS) as a function of the ionic strength J. In salt-free conditions, DNSE deduced at high Q-values is more than one order of magnitude smaller than DDLS obtained for larger length scales. This behavior contrasts with neutral polymer solutions. As can be seen in the figure, DDLS is a decreasing function of J and approaches the value of DNSE at high J-values. The DLS results agree with the theoretical prediction based on the coupling between the polymer and the ion cloud155, 156 (see Fig. 14). On the contrary, DNSE was found to be independent of ionic strength. Decoupling from the ion cloud was observed by NSE in the range 0.06 ≤ Q/k ≤ 1.6 (k−1: Debye-Hückel screening length), which is smaller than the limit Q/k ≫ 1 predicted by the mode coupling model.

Figure 14.

(Left axis) Dependence of diffusion coefficient on the ionic strength J in 2% (w/w) hialuronic acid solutions. O: DDLS. •: DNSE. Continuous line: mode coupling model prediction. (Right axis) Dependence of osmotic modulus on J (♦) (Reproduced with permission from F. Horkay, P. Falus, A. Hecht, and E. Geissler, J. Phys. Chem. B. 2010, 114, 15445. Copyright 2010 American Chemical Society).

Focusing on the internal dynamics of the polyelectrolyte, Li et al.58 investigated D2O-solutions of poly(amidoamine) dendrimers (generation 5) with varying molecular protonation. Using complementary NMR spectroscopy, the center of mass translational diffusion was first measured. This information was used to isolate the internal dynamics contribution to the spectra measured by QENS. This could be phenomenologically characterized by a localized diffusive motion which turned out to become more rapid as the acidity increased. Such surprising observation was attributed to interactions with the surrounding counterions and solvent molecules as the segments explore additional intra-dendrimer volume made available by slight electrostatic swelling and redistribution of mass in the dendrimer interior (additional “maneuverability”). This charge-induced dynamical change could be of importance for the design of polyelectrolyte dendrimer-based packages as delivery vehicles under operational conditions with pH-values of biological relevance.

Because of their response with a volume change to weak external stimuli (e.g., small variations in temperature or ionic strength, exposure to light, electric or magnetic fields) the so-called “smart” hydrogels are also promising materials for medical and drug delivery (among other) applications. In particular, poly(N-isopropylacrylamide) (PNIPAM) is a very well-known LCST thermoresponsive polymer showing a coil-to-globule collapse at the volume phase transition temperature VPTT = 32 °C, where water is released from the polymer backbone. Crosslinking PNIPAM or polymerizing it with other polymer blocks, new responsive materials can be obtained. Some of them have been extensively investigated by several techniques including SANS (of utmost interest to characterize the structural changes across the transition) and QENS. First QENS reports on a slowing down of the dynamics at the VPTT were based on the local dynamics investigations by Rubio-Retama et al.157, 158 Aqueous (D2O) solutions of triblock copolymers P(S-b-NIPAM-b-S) were recently studied by Adelsberger et al.59 The polymer forms micelles with a rigid PS core and a PNIPAM shell, that aggregate in clusters right after the collapse temperature is crossed. Using samples with deuterated PS blocks, the scattering from the solvent was matched and NSE revealed the PNIPAM dynamics. This consisted of segmental motions and the overall diffusive contribution. The Q-dependence of the segmental component allowed to discern between the two possible scenarios for shell chain motions, namely Zimm-like in loosely packed shells of “hairy” micelles or breathing modes in densely packed shells of “crew-cut” micelles. The latter was observed. Below the VPTT, the values of the average diffusion coefficient associated to the segmental motions Dinternal were found to decrease with increasing polymer concentration. This was attributed to an increase in local PNIPAM concentration due to the overlap of micellar shells. Above the VPTT, Dinternal is higher than below and does not depend on concentration. To explain this observation, the existence of a gradient of mobilities across the shell was invoked: below the VPTT, the mobility of most segments would be in the time window of NSE, and an average value of the segmental dynamics in the micellar shell would be obtained. In contrast, above the collapse temperature, most of the segments collapse and form a relatively immobile PNIPAM melt. Only few PNIPAM blocks would stick out into the solution, and some of them may bridge two micelles. NSE would be sensitive only to the very mobile segments, resulting in an average diffusion coefficient higher than in the swollen state. An analogous study of the same group on solutions of diblock copolymers PS-b-PNIPAM60 revealed a more complex collapse transition that was associated to the absence of bridging. Again breathing modes were found for the PNIPAM shell, that become slower with increasing polymer concentration and (apparently) faster when heating above the collapse transition. Incomplete averaging was also invoked to explain this observation. Compared to the triblock copolymer, the segmental dynamics of the PNIPAM shell in the diblock micelles was faster (see Fig. 15). This was attributed to the tethering of only one end of the PNIPAM block to the core, to the absence of bridging, and to the lower grafting density.

Figure 15.

Intermediate scattering functions for different concentrations at Q = 0.15 Å−1. Open symbols are results for the triblock copolymer at 24.4 °C. Open squares, 200 mg/mL; open circles, 300 mg/mL. Filled symbols are results for the diblock copolymer at 23.5 °C. Filled squares, 200 mg/mL; filled circles, 300 mg/mL. The lines are fits (Reproduced with permission from J. Adelsberger, A. Meier-Koll, A. M. Bivigou-Koumba, P. Busch, O. Holderer, T. Hellweg, A. Laschewsky, P. Müller-Buschbaum, and C. M. Papadakis, Colloid Polym. Sci. 2011, 289, 711. Copyright 2011 Springer).

In addition to thermoresponsive behavior, PNIPAM shows cononsolvency. Methanol and water are good solvents of PNIPAM around RT, but in certain mixtures of them a PNIPAM particle becomes insoluble and collapses at the same temperature. This effect was used to collapse the solvent-sensitive polymer part of the microgels investigated by means of NSE by Scherzinger et al.61 without changing the temperature. The systems studied were PNIPAM, poly(N,N-diethylacrylamide)—another thermoresponsive with a lower VPTT at 26 °C—and two microgels based on them, namely a P(NIPAM-co-DEAAM) copolymer and a core-shell microgel with a PDEAAM core and a PNIPAM shell. The solvent was a mixture of deuterated water/methanol with xMeOD = 0.2, for which PNIPAM shows a maximum collapse at the temperature investigated (10 °C)159. Under these conditions, the P(NIPAM-co-DEAAM) microgel and the shell of the PDEAAM-core/PNIPAM-shell particles are also in the collapsed state, while PDEAAM and the core of the core-shell particles are swollen. The dynamics of collapsed PNIPAM and P(NIPAM-co-DEAAM) microgels characterized by NSE experiments was that corresponding to solid diffusing objects with only very small additional contributions from internal motions. PDEAAM exhibited Zimm segmental dynamics at Q > 0.11 Å−1 and a crossover to a collective diffusive motion for smaller Q-values (see Fig. 16). The collapse of the shell in the core/shell particles induced a reduced fraction of the Zimm segmental dynamics in the particles scattering function as compared to the pure PDEAAM particle. Conversely, a strongly increased viscosity was observed in the PDEAAM microgel as compared to that of the bulk solvent (see Fig. 16), that was attributed to an increased amount of inhomogeneities induced by the swelling of the particle. The apparent viscosity deduced for the PDEAAM-core of the core-shell particle was also higher than in the bulk solvent but different from that in the PDEAAM microgel. This could be a result of the confinement of the swollen PDEAAM-core by the collapsed PNIPAM-shell, leading to modifications of the hydrodynamic interactions of the Zimm model in the restricted environment inside the particle.

Figure 16.

S(Q,t)/S(Q,t = 0) vs. the Fourier time of a PDEAAM microgel at Q = 0.05 (black squares), 0.08 (red circles), 0.11 (blue triangles) and 0.15 Å−1 (green diamonds). Solid lines are individual fits, with diffusive Q2-dependent dynamics for Q = 0.05, 0.08, and 0.11 Å−1, and Zimm segmental dynamics for Q = 0.15 Å−1. The green dashed line indicates the expected relaxation curve for Q = 0.15 Å−1 with the solvent viscosity of 2.5 mPa s (Reproduced with permission from C. Scherzinger, O. Holderer, D. Richter, and W. Richtering, Phys. Chem. Chem. Phys. 2012, 14, 2762. Copyright (2012) by the Royal Society of Chemistry).

Isotopic labeling was also exploited by Ghugare et al.62 to investigate the component dynamics in aqueous solutions of crosslinked poly(vinyl alcohol) (PVA) /poly(methyl methacrylate-co-N-isopropyl acrylamide) microgels. The samples investigated undergo a VPTT of 40 °C and are good candidates for carriers of anticancer drug doxorubicin. Water motions were characterized from the analysis of BS-ToF spectra from the fully protonated sample, assuming an elastic response for the polymer component. The data were interpreted in terms of two distinct water populations: slow relaxing water molecules associated to the polymer network and loosely coordinated, fast relaxation water, including interstitial water molecules. Each contribution was represented by a single Lorentzian (equivalent to a single exponential intermediate scattering function). For the slow molecules, the motion was described in terms of the random jump diffusion model, where the diffusion process consists of a set of uncorrelated jumps from one site to another in an unconfined lattice. Upon heating, an enhancement of this motion was evidenced by a broadening of the corresponding Lorentzian, and at temperatures above the VPTT both Lorenzians converged toward a single one (see Fig. 17). This was considered as a clear indication of the transition from a dual water dynamic behavior, when strongly associated and loose water molecules both exist in the microgel, to a single fast relaxing water above the transition. Conversely, the better resolution of BS (SPHERES spectrometer) allowed addressing the polymer dynamics on a sample with deuterated water. They could be described in terms of confined motions within a spherical space where spatial fluctuations occur. These fluctuations would result from different dynamical processes reflecting structural features of the network in the Ångstrom scale as cross-linking degree and hydrophobic/hydrophilic balance. Typical confinement sizes of average radius around 5 Å were observed. The associated local diffusion coefficient showed an intermediate value between that of a PNIPAM microgel (lower limit) and that of a microgel with identical structure but not containing NIPAM residues (upper limit). This finding was rationalized considering the presence of the fast relaxation modes introduced by the flexible chains of PVA and to an increase in the overall segmental dynamics of the polymer network. Assessing separately the contributions of PNIPAM and PVA chains within the same network by QENS on isotopically labeled polymers was pointed as an interesting subject of future investigations.

Figure 17.

QENS spectra at 293 K (left) and 318 K (right) at Q = 0.55 Å−1: (a) experimental data, (b) total fit, (c) elastic polymer component, (d) slow relaxing water component, and (e) fast relaxing water component. For making the fit curves visible, only 30% of the data points are shown (Reproduced with permission from S. V. Ghugare, E. Chiessi, M. T. F. Telling, A. Deriu, Y. Gerelli, J. Wuttke, and G. Paradossi, J. Phys. Chem. B 2010, 114, 10285. Copyright 2010 American Chemical Society).

Incorporating other counterparts to thermoresponsive microgels opens the possibility to produce multiresponsive materials. For instance, hybrid materials including magnetic NPs offer potential applications as targeted drug delivery systems. However, the new interactions emerging between the components of the system may lead to modifications of some of the properties of the neat microgel. QENS was used by Rubio-Retama et al.63 to characterize the effects of inclusion of γ-Fe2O3-NPs on the polymer dynamics in core-shell poly(N-isopropylacrylamide-sodium acrylate) microgels. Using samples with deuterated water, the dynamics of the protons in the polymeric component was investigated by BS as function of temperature and NPs concentration (the cross-section of the NPs is negligible in such samples). From measurements of the elastic intensity the apparent mean-squared displacements 〈u2〉 of polymer protons was obtained. With increasing temperature they nicely mirrored the melting of the solvent, giving rise to an enhanced mobility in the swollen state and a subsequent dynamic arrest in the collapsed state above the VPTT (see Fig. 18). With respect to the neat microgel, a decrease of the mobility in the swollen state was deduced from the average 〈u2〉-values, from 5.6 to 3.6 Å2. In addition, from the quasielastic spectra, the diffusion coefficient of the polymer segments with respect to center of mass of the microgel was obtained. This became smaller when the iron oxide content was increased. These effects on the polymer dynamics, as well as the observed increase of the VPTT and the polymer degradation temperature, were attributed by the authors to the formation of H-bonds between amide groups of the polymer matrix and the OH-groups of the NPs as observed by infrared spectroscopy.

Figure 18.

Apparent mean-squared displacement of the polymer network as a function of temperature for PNIPAM microgels and P(NIPAM-AAS) microgels with different amounts of γ-Fe2O3 (Reproduced with permission from J. Rubio-Retama, N. Zafeiropoulos, B. Frick, T. Seydel, and E. López-Cabarcos, Langmuir 2010, 26, 7101. Copyright 2010 American Chemical Society).

CONCLUSIONS AND OUTLOOK

This article summarizes the status of the application of QENS techniques to the study of the dynamic processes at different length and time scales in polymer systems of increasing complexity. The recent (from 2010 onward) literature in this field has been revised and discussed in a general framework.

We have learnt that concentrated solutions, blends and melts of polymers themselves constitute highly complex systems from a dynamic point of view. Molecular engineering by controlled synthesis at the nano-scale produces additional complexity as branching and inclusion of block-copolymer structures. The addition of nano-objects to polymer materials modifies drastically their properties. New nano-confinement effects emerge in multicomponent polymer systems.

The current tendency toward increasing complexity is one of the main characteristics of the development of polymer science and technology, posing challenging problems to basic science. The relationships between structure and dynamics at different length- and time-scales, the understanding of the interplay of geometry and topology, the characterization of the interfacial features and the dynamics at the interfacial level, the way local friction arises in crowded environments that are chemically heterogeneous, the kinetics of macromolecular self-assembly, are, among others, fundamental problems but of utmost importance for the future developments of novel technologies based on polymers.

Because of its unique properties, QENS—in combination with advanced chemistry (well-defined model systems, selective isotopic substitution methods, etc.)—is one of the main tools for facing the new challenges in the field of polymer dynamics. However, neutrons have also some limitations for this task. In particular, the relatively narrow dynamic range covered by QENS currently limits the capabilities of these techniques to follow in a wide temperature range the “slow” dynamic processes which take place in polymer systems. Moreover, in multicomponent systems with isotopic substitutions, sometimes the separation of coherent and incoherent contributions is not an easy task, complicating the analysis and interpretation of the experimental data. Conversely, the properties of multicomponent systems are often determined by key components that are very dilute, and thereby difficult to observe by QENS. Some of these limitations might be overcome in the near future with the developments of new neutron sources and instrumentation. The goal is to improve the sensitivity of observing small signals and/or slower processes, that is, roughly speaking, to increase the neutron flux at the sample (ultimately, the “good” neutrons at the detector) and to improve the instrumental resolution. Moreover, the implementation of polarization analysis in high-resolution QENS instruments would also open new possibilities. In any case, we have to remind that the combination of QENS with broadband relaxation spectroscopy always results to be of utmost importance (see Fig. 1).

There is another aspect which has to be always taken into account when neutron scattering and in particular QENS is applied to polymer systems: most of these systems are usually noncrystalline or they are in a “liquid-like” melt state. In such conditions, we cannot simply speak in terms of Bravais lattices and “canonical” phonons of other well-defined excitations anymore. This in some way downgrades the simple sentence formulated by C. G. Shull and B. N. Brockhouse when they were awarded with the Nobel Prize in Physics in 1994: “Neutrons tell us where atoms are and what they do”. Neutrons remain the unique probe for delivering information about molecular motions (self and collective) with space/time resolution. However, without the crystalline periodicity, we should in principle explore all relevant length scales between atomic and mesoscopic distances, something that is a more difficult task from an experimental point of view. Moreover, neutron scattering always works in the reciprocal space (equation image) and the atomic correlations in the real space are not directly accessible. All these constraints make the analysis and interpretation of QENS data in polymers (and also in noncrystalline materials in general) more challenging. Over the last years, the synergetic combination of QENS and fully atomistic MDs simulations has proved to be the right methodology to overcome some of these difficulties, in particular in linear homopolymer (unentangled) melts (see, e.g., the recent review on this topic23). Taking into account the rapid development of the field of computational methods, we are confident that this approach will also provide in the near future unprecedented capabilities to address dynamic problems arising in polymer systems of increasing complexity.

Last but not least, we would like to highlight the important role that QENS is also playing in other fields related to polymers that have not been covered in this article, In particular, soft matter systems other than polymers and some biological systems (see, e.g., the recent reviews160, 161). These systems show dynamic processes which in some aspects remind those characteristics of polymers and that, thereby, can be investigated following the same QENS methods. As an example, we can mention the recent extension of the NSE methods, often used to investigate large-scale dynamics in polymers, to the study of large-scale motions of protein domains (see, e.g. ref. 162).

The main conclusion from this insight in the recent literature is that QENS provides a unique tool to investigate dynamic processes in polymer systems of increasing complexity and that there is still plenty of room to exploit the capabilities of QENS in this and related fields.

Acknowledgements

The authors thank the members of our group and our colleagues in the neutron scattering field, with whom they have maintained a fruitful collaboration over the last years; in particular, and specially, to Prof. D. Richter (Forschungszentrum Jülich, Germany) and his research group, B. Frick and B. Farago (ILL) and V. García-Sakai (ISIS). Financial support from the projects MAT2007-63681 and IT-436-07 (GV) is acknowledged.

Biographical Information

original image

Juan Colmenero

Juan Colmenero is Professor of Condensed Matter Physics at the University of the Basque Country and the leader of the Polymers & Soft Matter Group in the Material Physics Center. His research interests cover the study of the structure and dynamics of polymer systems in general by combining relaxation, scattering and simulations methods. He has published more than 350 scientific papers and received the medal of the Spanish Royal Society of Physics (2003) among other awards and distinctions.

Biographical Information

original image

Arantxa Arbe

Arantxa Arbe is Research Professor at the Spanish Scientific Research Council (CSIC) in the Material Physics Center since 2009. She is the responsible for the application of scattering techniques in the Polymers & Soft Matter Research Group. Her research interests include the glass-transition question and the interrelation between structure and dynamics in polymer-based materials. She has published about 130 scientific papers including 5 reviews.