Cooperative Dynamics of Highly Entangled Linear Polymers within the Entanglement Tube.

We present a quantitative comparison of the dynamic structure factors from unentangled and strongly entangled poly(butylene oxide) (PBO) melts. As expected, the low molecular weight PBO displays Rouse dynamics, however, with very significant subdiffusive center-of-mass diffusion. The spectra from high molecular weight entangled PBO can be very well described by the dynamic structure factor based on the concept of local reptation, including the Rouse dynamics within the tube and allowing for non-Gaussian corrections. Comparing quantitatively the spectra from both polymers leads to the surprising result that their spectra differ only by the contribution of classical Rouse diffusion for the low molecular weight melt. The subdiffusive component is common for both the low and high molecular weight PBO melts, indicating that in both melts the same interchain potential is active, thereby supporting the validity of the Generalized Langevin Equation approach.

Dynamic structure factors of polymer melts as observed by neutron spin echo: Direct comparison and reevaluation.

In this work, we compare the single chain dynamic structure factors for five different polymers: polyolefins (PE and PEP), poly-dienes (PB and PI), and a polyether (PEO). For this purpose, we have extended the De Gennes approximation for the dynamic structure factor. We describe the single chain dynamic structure factor in multiplying the coherent scattering functions for local reptation and Rouse motion within the Rouse blob. Important results are (i) the simple De Gennes structure factor S(Q, t)DG approximates within a few Å the outcome for the tube diameter of the more elaborate structure factor (exception PI); (ii) the extended De Gennes structure factor together with the Rouse blob describes the neutron spin echo spectra from the different polymers over the complete momentum transfer range and the full time regime from early Rouse motion to local reptation; and (iii) the representation of the scattering functions could significantly be improved by introducing non-Gaussianity corrections to the Rouse-blob dynamics. (iv) The microscopic tube step length in all cases is significantly larger than the rheological one; further tweaking the relation between tube length and entanglement blob size may indicate a possible trend toward an anisotropic lean tube with a step-length larger than the lateral extension. (v) All considered polymer data coincide after proper (Q, t) scaling to a universal behavior according to the length scale of the tube, while the relevant time scale is the entanglement time τe. (vi) In terms of the packing model, the required number of chains spanning the entanglement volume consistently is about 40% larger than that obtained from rheology.

Chain Confinement and Anomalous Diffusion in the Cross over Regime between Rouse and Reptation.

By neutron spin echo (NSE) and pulsed field gradient (PFG) NMR, we study the dynamics of a polyethylene-oxide melt (PEO) with a molecular weight in the transition regime between Rouse and reptation dynamics. We analyze the data with a Rouse mode analysis allowing for reduced long wavelength Rouse modes amplitudes. For short times, subdiffusive center-of-mass mean square displacement ⟨rcom2(t)⟩ was allowed. This approach captures the NSE data well and provides accurate information on the topological constraints in a chain length regime, where the tube model is inapplicable. As predicted by reptation for the polymer ⟨rcom2(t)⟩, we experimentally found the subdiffusive regime with an exponent close to µ=12, which, however, crosses over to Fickian diffusion not at the Rouse time, but at a later time, when the ⟨rcom2(t)⟩ has covered a distance related to the tube diameter.

Quasielastic neutron scattering reveals the temperature dependent rotational dynamics of densely grafted oleic acid.

We study the dynamics of pure oleic acid and grafted oleic acid synthesized by decomposing iron oleate into oleic acid grafted iron oxide nanoparticles. Our quasielastic neutron scattering study shows that oleic acid dominantly performs translational diffusion at room temperature. On the other hand, in nanocomposites, constraints imposed by grafting and crowding of neighboring chains restrict the grafted oleic acid to uniaxial rotation. Interestingly, it also manifests mobility in grafted oleic acid below the crystallization temperature of pure oleic acid. The data from grafted oleic acid could be effectively described using a uniaxial rotational diffusion model with an additional elastic scattering contribution. This kind of elastic scattering arises due to the restricted bond mobility and increases with decreasing temperature. The radius of rotation obtained from the fitted data agrees very well with the geometry of the molecule and grafting density. These results open possibilities of research on the confined surfactant systems, which could be analyzed using the approach described here.

Nanosecond structural dynamics of intrinsically disordered ß-casein micelles by neutron spectroscopy.

ß-casein undergoes a reversible endothermic self-association, forming protein micelles of limited size. In its functional state, a single ß-casein monomer is unfolded, which creates a high structural flexibility, which is supposed to play a major role in preventing the precipitation of calcium phosphate particles. We characterize the structural flexibility in terms of nanosecond molecular motions, depending on the temperature by quasielastic neutron scattering. Our major questions are: Does the self-association reduce the chain flexibility? How does the dynamic spectrum of disordered caseins differ from a compactly globular protein? How does the dynamic spectrum of ß-casein in solution differ from that of a protein in hydrated powder states? We report on two relaxation processes on a nanosecond and a sub-nanosecond timescale for ß-casein in solution. Both processes are analyzed by Brownian oscillator model, by which the spring constant can be defined in the isotropic parabolic potential. The slower process, which is analyzed by neutron spin echo, seems a characteristic feature of the unfolded structure. It requires bulk solvent and is not seen in hydrated protein powders. The faster process, which is analyzed by neutron backscattering, has a smaller amplitude and requires hydration water, which is also observed with folded proteins in the hydrated state. The self-association had no significant influence on internal relaxation, and thus, a ß-casein protein monomer flexibility is preserved in the micelle. We derive spring constants of the faster and slower motions of ß-caseins in solution and compared them with those of some proteins in various states (folded or hydrated powder).

Structure and Dynamics of Ribonuclease A during Thermal Unfolding: The Failure of the Zimm Model.

Disordered regions as found in intrinsically disordered proteins (IDP) or during protein folding define response time to stimuli and protein folding times. Neutron spin-echo spectroscopy is a powerful tool to directly access the collective motions of the unfolded chain to enlighten the physical origin of basic conformational relaxation. During the thermal unfolding of native ribonuclease A, we examine the structure and dynamics of the disordered state within a two-state transition model using polymer models, including internal friction, to describe the chain dynamics. The presence of four disulfide bonds alters the disordered configuration to a more compact configuration compared to a Gaussian chain that is defined by the additional links, as demonstrated by coarse-grained simulation. The dynamics of the disordered chain is described by Zimm dynamics with internal friction (ZIF) between neighboring amino acids. Relaxation times are dominated by mode-independent internal friction. Internal friction relaxation times show an Arrhenius-like behavior with an activation energy of 33 kJ/mol. The Zimm dynamics is dominated by internal friction and suggest that the characteristic motions correspond to overdamped elastic modes similar to the motions observed for folded proteins but within a pool of disordered configurations spanning the configurational space. For IDP, internal friction dominates while solvent friction and hydrodynamic interactions are smaller corrections.

Amphiphilic Comb Polymers as New Additives in Bicontinuous Microemulsions.

It has been shown that the thermodynamics of bicontinuous microemulsions can be tailored via the addition of various different amphiphilic polymers. In this manuscript, we now focus on comb-type polymers consisting of hydrophobic backbones and hydrophilic side chains. The distinct philicity of the backbone and side chains leads to a well-defined segregation into the oil and water domains respectively, as confirmed by contrast variation small-angle neutron scattering experiments. This polymer-microemulsion structure leads to well-described conformational entropies of the polymer fragments (backbone and side chains) that exert pressure on the membrane, which influences the thermodynamics of the overall microemulsion. In the context of the different polymer architectures that have been studied by our group with regards to their phase diagrams and small-angle neutron scattering, the microemulsion thermodynamics of comb polymers can be described in terms of a superposition of the backbone and side chain fragments. The denser or longer the side chain, the stronger the grafting and the more visible the brush effect of the side chains becomes. Possible applications of the comb polymers as switchable additives are discussed. Finally, a balanced philicity of polymers also motivates transmembrane migration in biological systems of the polymers themselves or of polymer-DNA complexes.

Self-Similar Polymer Ring Conformations Based on Elementary Loops: A Direct Observation by SANS.

We report small angle neutron scattering (SANS) results on very large polyethylene-oxide (PEO) rings in the melt. Major findings are (i) the observation of a cross over in the SANS pattern from a strong Q-dependence at intermediate Q to a Q-2 dependence at higher Q that is independent of the ring size. Summing up scattering amplitudes in a minimal model that contains the ring closure and a cross over from Gaussian statistics at short distances to more compact structures at larger distances, we identify the cross over to occur at a distance along the ring of Ne,0 = 45 ± 2.5. We consider this finding as a clear signature of the theoretically predicted elementary loops that build up the ring conformation. Their size is in the range of an entanglement strand for linear PEO melts and they are characterized by Gaussian statistics. (ii) The chain length dependence of the radius of gyration Rg follows rather closely the prediction of Obukhov's decorated ring model. (iii) Other than extracted from numerous simulations that are interpreted in terms of a cross over to mass fractal behavior around N ≅ 10Ne,0 with a fractal dimension df = 3 and exponent ν = 1/3, we do not observe such a cross over, but Rg(N) ∼ Nν=0.39 holds over the entire size range.

Reduced Internal Friction by Osmolyte Interaction in Intrinsically Disordered Myelin Basic Protein.

Urea is a strong denaturing osmolyte that disrupts noncovalent bonds in proteins. Here, we present a small-angle neutron scattering (SANS) and neutron spin-echo spectroscopy (NSE) study on the structure and dynamics of the intrinsically disordered myelin basic protein (MBP) denatured by urea. SANS results show that urea-denatured MBP is more compact than ideal polymers, while its secondary structure content is entirely lost. NSE experiments reveal concomitantly an increase of the relaxation time and of the amplitude of internal motions in urea-denatured MBP as compared to native MBP. If interpreted in terms of the Zimm model including internal friction (ZIF), the internal friction parameter decreased by a factor of 6.5. Urea seems to not only smooth local energy barriers, reducing internal friction on a local scale, but also significantly reduces the overall depth of the global energy landscape. This leads to a nearly complete loss of restoring forces beyond entropic forces and in turn allows for larger motional amplitudes. Obviously, the noncovalent H-bonds are largely eliminated, driving the unfolded protein to be more similar to a synthetic polymer.

Direct Observation of Dynamic Tube Dilation in Entangled Polymer Blends: A Combination of Neutron Scattering and Dielectric Techniques.

We report a microscopic observation of the time-dependent dynamic tube dilation process on isofrictional bidisperse melts. By applying neutron spin echo (NSE) and dielectric techniques on blends of long polyisoprene (PI) chains with short PI additives with different topology, we access the dynamics of the tube dilation process on a molecular scale. The time-dependent tube dilation is directly revealed by NSE as an additional time dependence of the dynamic structure factor in the local reptation regime. We identify the characteristic time of tube dilation as the terminal time of the additive.

Polymer dynamics under confinement.

We review recent neutron scattering work and related results from simulation and complementary techniques focusing on the microscopic dynamics of polymers under confinement. Confinement is either realized in model porous materials or in polymer nanocomposites (PNC). The dynamics of such confined polymers is affected on the local segmental level, the level of entanglements as well as on global levels: (i) at the segmental level the interaction with the surface is of key importance. At locally repulsive surfaces compared to the bulk the segmental dynamics is not altered. Attractive surfaces slow down the segmental dynamics in their neighborhood but do not give rise to dead, glassy layers. (ii) Confinement generally has little effect on the inter-chain entanglements: both for weakly as well as for marginally confined polymers the reptation tube size is not changed. Only for strongly confined polymers disentanglement takes place. Similarly, in PNC at higher NP loading disentanglement phenomena are observed; in addition, at very high loading a transition from polymer caused topological constraints to purely geometrical constraints is observed. (iii) On the more global scale NSE experiments revealed important information on the nature of the interphase between adsorbed layer and bulk polymer. (iv) Polymer grafts at NP mutually confine each other, an effect that is most pronounced for one component NP. (v) Global diffusion of entangled polymers both in weakly and strongly attractive PNC is governed by the ratio of bottle-neck to chain size that characterizes the 'entropic barrier' for global diffusion.

Localised contacts lead to nanosecond hinge motions in dimeric bovine serum albumin.

Domain motions in proteins are crucial for biological function. In the present manuscript, we present a neutron spin-echo spectroscopy (NSE) study of native bovine serum albumin (BSA) in solution. NSE allows to probe both global and internal dynamics of the BSA monomer and dimer equilibrium that is formed in solution. Using a model independent approach, we were able to identify an internal dynamic process in BSA that is visible in addition to global rigid-body diffusion of the BSA monomer and dimer mixture. The observed internal protein motion is characterised by a relaxation time of 43 ns. The overdamped Brownian oscillator was considered as an alternative analytical theory that was able to describe the internal process as first-order approximation. More detailed information on the physical nature of the internal protein motion was extracted from the q-dependent internal diffusion coefficients ΔDeff(q) that were detected by NSE in addition to global rigid-body translational and rotational diffusion. The ΔDeff(q) were interpreted using normal mode analysis based on the available crystal structures of the BSA monomer and dimer as structural test models. Normal mode analysis demonstrates that the observed internal dynamic process can be attributed to bending motion of the BSA dimer. The native BSA monomer does not show any internal dynamics on the time- and length-scales probed by NSE. An intermolecular disulphide bridge or a direct structural contact between the BSA monomers forms a localised link acting as a molecular hinge in the BSA dimer. The effect of that hinge on the observed motion of BSA in the used dimeric structural model is discussed in terms of normal modes in a molecular picture.

Proton diffusion in the catalytic layer for high temperature polymer electrolyte fuel cells.

The present study focuses on quasielastic neutron scattering (QENS) of the proton dynamics in phosphoric acid (PA) inside the catalytic layer of high-temperature polymer electrolyte fuel cells (HT-PEFCs). The nanosecond proton dynamics is investigated on the local length scale around operating temperatures (300 K-430 K) using neutron backscattering spectroscopy. We have investigated the catalyst doped with different amounts of PA in order to understand the distribution of PA inside the layer. Three approaches are considered for the description of proton dynamics: the random jump diffusion model, distribution of diffusion constants and, finally, the trap model. Due to adsorption of the PA on the Pt particles the diffusion of protons in the catalytic layer is different in comparison to the bulk acid. The proton dynamics in the catalytic layer can be described by the random jump diffusion with traps. This diffusion is significantly slower than the diffusion of free PA; this also results in a lower conductivity, which is estimated from the obtained diffusion constant.

Reverse relationships of water uptake and alkaline durability with hydrophilicity of imidazolium-based grafted anion-exchange membranes.

We found unprecedented reverse relationships in anion-exchange membranes (AEMs) for Pt-free alkaline fuel cell systems, i.e., the increase in hydrophobicity increased water uptake and susceptibility to hydrolysis. AEMs with graft copolymers that composed of anion-conducting 2-methyl-N-vinylimidazolium (Im) and hydrophobic styrene (St) units were employed. We characterized two new structures in these AEMs using a small-angle neutron scattering with a contrast variation method. (1) The distribution of graft polymers in conducting (ion channel) or non-conducting (hydrophobic amorphous poly(ethylene-co-tetrafluoroethylene) (ETFE)) phase was evaluated in a quantitative manner. High fraction in conducting layer for AEMs having high grafting degrees was found using the proposed structural model of "conducting/non-conducting two-phase system". (2) Assuming a hard-sphere fluid model, we found AEMs having high St contents and low alkaline durability possessed nanophase-separated water puddles with diameters of 3-4 nm. The AEM having a low St content and the best alkaline durability did not show evident nanophase separation. The above hierarchical structures elucidate the unexpected reverse relationships that the AEM having highly hydrophobic graft polymers was subjected to the morphological transition to give water puddles at nanoscale. The imidazolium groups that were located at the boundary between graft polymers and water puddles should be susceptible to hydrolysis.

Fractal diffusion in high temperature polymer electrolyte fuel cell membranes.

The performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity, two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension dw and the Hausdorff dimension df have been determined on the length scales covered in the neutron scattering experiments.

Influence of PEGylation on Domain Dynamics of Phosphoglycerate Kinase: PEG Acts Like Entropic Spring for the Protein.

Protein-polymer conjugation is a widely used technique to develop protein therapeutics with improved pharmacokinetic properties as prolonged half-life, higher stability, water solubility, lower immunogenicity, and antigenicity. Combining biochemical methods, small angle scattering (SAXS/SANS), and neutron spin-echo spectroscopy, here we examine the impact of PEGylation (i.e., the covalent conjugation with poly(ethylene glycol) or PEG) on structure and internal domain dynamics of phosphoglycerate kinase (PGK) to elucidate the reason for reduced activity that is connected to PEGylation. PGK is a protein with a hinge motion between the two main domains that is directly related to function. We find that secondary structure and ligand access to the binding sites are not affected. The ligand induced cleft closing is unchanged. We observe an additional internal motion between covalent bonded PEG and the protein compatible with Brownian motion of PGK in a harmonic potential. Entropic interaction with the full PEG chain leads to a force constant of about 8 pN/nm independent of PEG chain length. This additional force preserves protein structure and has negligible effects on the functional domain dynamics of the protein. PEGylation seems to reduce activity just by acting as a local crowder for the ligands. The newly identified interaction mechanism might open possibilities to improve rational design of protein-polymer conjugates.

Relevance of Internal Friction and Structural Constraints for the Dynamics of Denatured Bovine Serum Albumin.

A general property of disordered proteins is their structural expansion that results in a high molecular flexibility. The structure and dynamics of bovine serum albumin (BSA) denatured by guanidinium hydrochloride (GndCl) were investigated using small-angle neutron scattering (SANS) and neutron spin-echo spectroscopy (NSE). SANS experiments demonstrated the relevance of intrachain interactions for structural expansion. Using NSE experiments, we observed a high internal flexibility of denatured BSA in addition to center-of-mass diffusion detected by dynamic light scattering. Internal motions measured by NSE were described using concepts based on polymer theory. The contribution of residue-solvent friction was accounted for using the Zimm model including internal friction (ZIF). Disulfide bonds forming loops of amino acids of the peptide backbone have a major impact on internal dynamics that can be interpreted with a reduced set of Zimm modes.

Chemically defined, ultrasoft PDMS elastomers with selectable elasticity for mechanobiology.

Living animal cells are strongly influenced by the mechanical properties of their environment. To model physiological conditions ultrasoft cell culture substrates, in some instances with elasticity (Young's modulus) of only 1 kPa, are mandatory. Due to their long shelf life PDMS-based elastomers are a popular choice. However, uncertainty about additives in commercial formulations and difficulties to reach very soft materials limit their use. Here, we produced silicone elastomers from few, chemically defined and commercially available substances. Elastomers exhibited elasticities in the range from 1 kPa to 55 kPa. In detail, a high molecular weight (155 kg/mol), vinyl-terminated linear silicone was crosslinked with a multifunctional (f = 51) crosslinker (a copolymer of dimethyl siloxane and hydrosilane) by a platinum catalyst. The following different strategies towards ultrasoft materials were explored: sparse crosslinking, swelling with inert silicone polymers, and, finally, deliberate introduction of dangling ends into the network (inhibition). Rheological experiments with very low frequencies led to precise viscoelastic characterizations. All strategies enabled tuning of stiffness with the lowest stiffness of ~1 kPa reached by inhibition. This system was also most practical to use. Biocompatibility of materials was tested using primary cortical neurons from rats. Even after several days of cultivation no adverse effects were found.

Imidazolium-based anion exchange membranes for alkaline anion fuel cells: (2) elucidation of the ionic structure and its impact on conducting properties.

In our previous study (Soft Matter, 2016, 12, 1567), the relationship between the morphology and properties of graft-type imidazolium-based anion exchange membranes (AEMs) was revealed, in that the semi-crystalline features of the polymer matrix maintain its mechanical properties and the formation of interconnected hydrophilic domains promotes the membrane conductivity. Here, we report a novel ionic structure of the same graft-type AEMs with different grafting degrees, analyzed using a small-angle X-ray scattering method under different relative humidity (RH) conditions. The characteristic "ionomer peak" with a corresponding correlation distance of approximately 1.0 nm was observed at RH < 80%. This distance is much smaller than the literature-reported mean distance between two ionic clusters, but close to the Bjerrum length of water. Since the representative number of water molecules per cation, nw, was small, we proposed that dissociated ion-pairs are distributed in the hydrophilic domains (ion-channels). At RH < 80%, ion-channels are disconnected, however in liquid water, they are well-connected as evidenced by the sharp increase in nw. The disconnected ion-channels even under relatively high RH conditions should be a substantial factor for the low power generation efficiency of AEM-type fuel cells.

Description of poly(ethylenepropylene) confined in nanopores by a modified Rouse model.

A recent model for unentangled polymer chains in confinement [M. Dolgushev and M. Krutyeva, Macromol. Theory Simul. 21, 565 (2012)] is scrutinized by small-angle neutron scattering (SANS) with respect to its static prediction, the single-chain structure factor. We find a remarkable agreement although the model simplifies the effect of the confinement to a harmonic potential. The effective confinement size from fits of SANS data with the model agrees well with the actual pore size. Starting from this result we discuss the possibility of an experiment on the dynamic structure factor predicted by the model. It turns out that such an experiment would need a large ratio polymer dimension/pore size which is difficult but not impossible to achieve.