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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.

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., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

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 ⟨ r com 2 ( 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 ⟨ r com 2 ( t )⟩, we experimentally found the subdiffusive regime with an exponent close to μ = 1 2 , which, however, crosses over to Fickian diffusion not at the Rouse time, but at a later time, when the ⟨ r com 2 ( t )⟩ has covered a distance related to the tube diameter.

The static structure factor and the undulation dynamics of a solid-supported membrane stack have previously been calculated by Romanov and Ul'yanov [Romanov & Ul'yanov (2002). Phys. Rev. E, 66, 061701]. Based on this prior work, the calculation has been extended to cover the membrane dynamics, i.e. the intermediate scattering function as a Fourier transform of the van Hove correlation function of the membrane stack. Fortran code which calculates the intermediate scattering function for a membrane stack on a solid support is presented. It allows the static and dynamic scattering functions to be calculated according to the derivation of Romanov and Ul'yanov. The physical properties of supported phospholipid bilayers can be examined in this way and the results can be directly compared with results obtained from grazing-incidence neutron spin-echo spectroscopy experiments., (open access.)

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 N e,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 R g 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 ≅ 10 N e,0 with a fractal dimension d f = 3 and exponent ν = 1/3, we do not observe such a cross over, but R g ( N ) ∼ N ν=0.39 holds over the entire size range.

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.

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 d w and the Hausdorff dimension d f have been determined on the length scales covered in the neutron scattering experiments.

Here we present an approach to measure dynamic membrane properties of phospholipid membranes close to an interface. As an example we show results of the membrane dynamics of a phospholipid membrane multilayer-stack on a solid substrate (silicon). On this sample we were able to measure local interaction and friction parameters using Grazing Incidence Neutron Spin Echo Spectroscopy (GINSES), where an evanescent neutron wave probes the fluctuations close to a rigid interface. With this method it is possible to access length scales in the nano to micrometer region as well as energies in the μeV range. Using a new neutron resonator structure we achieved the required intensity gain for this experiment. During our investigations we found an excitation mode of the phospholipid membrane that has not been reported previously and only became visible using the new methodology. We speculate that the energy transported by that undulation can also serve to distribute energy over a larger area of the membrane, stabilizing it. This new methodology has the capability to probe the viscoelastic effects of biological membranes, becoming a new tool for tribology on the nanoscale and has allowed the observation of the hitherto invisible property of phospholipid membranes using neutrons.

Intrinsically disordered proteins lack a well-defined folded structure and contain a high degree of structural freedom and conformational flexibility, which is expected to enhance binding to their physiological targets. In solution and in the lipid-free state, myelin basic protein belongs to that class of proteins. Using small-angle scattering, the protein was found to be structurally disordered similar to Gaussian chains. The combination of structural and hydrodynamic information revealed an intermediary compactness of the protein between globular proteins and random coil polymers. Modeling by a coarse-grained structural ensemble gave indications for a compact core with flexible ends. Neutron spin-echo spectroscopy measurements revealed a large contribution of internal dynamics to the overall diffusion. The experimental results showed a high flexibility of the structural ensemble. Displacement patterns along the first two normal modes demonstrated that collective stretching and bending motions dominate the internal modes. The observed dynamics represent nanosecond conformational fluctuations within the reconstructed coarse-grained structural ensemble, allowing the exploration of a large configurational space. In an alternative approach, we investigated if models from polymer theory, recently used for the interpretation of fluorescence spectroscopy experiments on disordered proteins, are suitable for the interpretation of the observed motions. Within the framework of the Zimm model with internal friction (ZIF), a large offset of 81.6 ns is needed as an addition to all relaxation times due to intrachain friction sources. The ZIF model, however, shows small but systematic deviations from the measured data. The large value of the internal friction leads to the breakdown of the Zimm model.

Self-assembly of amphiphilic molecules into micelles occurs on very short times scales of typically some milliseconds, and the structural evolution is therefore very challenging to observe experimentally. While rate constants of surfactant micelle kinetics have been accessed by spectroscopic techniques for decades, so far no experiments providing detailed information on the structural evolution of surfactant micelles during their formation process have been reported. In this work we show that by applying synchrotron small-angle X-ray scattering (SAXS) in combination with the stopped-flow mixing technique, the entire micelle formation process from single surfactants to equilibrium micelles can be followed in situ. Using a sugar-based surfactant system of dodecyl maltoside (DDM) in dimethylformamide (DMF), micelle formation can be induced simply by adding water, and this can be followed in situ by SAXS. Mixing of water and DMF is an exothermic process where the micelle formation process occurs under nonisothermal conditions with a temperature gradient relaxing from about 40 to 20 °C. A kinetic nucleation and growth mechanism model describing micelle formation by insertion/expulsion of single molecules under nonisothermal conditions was developed and shown to describe the data very well.

The bending rigidity of surfactant membranes in novel bicontinuous CO(2)-microemulsions of the type H(2)O/NaCl-scCO(2)-Zonyl FSH/Zonyl FSN 100 was determined using both high pressure small angle neutron scattering and neutron-spin echo spectroscopy. As an important result it was found, that the stiffness of the membrane increases solely by an increase of the pressure.

High-resolution inelastic neutron scattering, which is available with neutron spin-echo spectroscopy (NSE) is introduced as a tool for the analysis of biomolecule flexibility. Coherent scattering in a range where it is sensitive to length scales of nanometers and covering a time range from picoseconds to several 100 ns makes the motion of larger subdomains within proteins visible. We show that and how the internal domain motion within a protein in solution can be measured. Comparison with displacement patterns from normal mode analysis provides further insight into the nature of the geometry of the motions that lead to the observed dynamic signature. The NSE experiment on alcohol dehydrogenase (ADH) is used as example to illustrate the general principles of the method.

The route by which amphiphilic molecules self-assemble into micelles is still not fully understood. In this Letter, we present direct structural information on the birth and growth of block copolymer micelles by means of synchrotron x-ray scattering with millisecond time resolution. Using a quantitative model, we show that the self-assembly process can be viewed as a nucleation and growth type process where the elemental growth mechanism is an exchange of single molecules.

Interdomain motions in proteins are essential to enable or promote biochemical function. Neutron spin-echo spectroscopy is used to directly observe the domain dynamics of the protein alcohol dehydrogenase. The collective motion of domains as revealed by their coherent form factor relates to the cleft opening dynamics between the binding and the catalytic domains enabling binding and release of the functional important cofactor. The cleft opening mode hardens as a result of an overall stiffening of the domain complex due to the binding of the cofactor.

We measured the shape and the internal dynamics of starlike dendrimers under good solvent conditions with small-angle neutron scattering and neutron spin-echo (NSE) spectroscopy, respectively. Architectural parameters such as the spacer length and generation were varied in a systematic manner. Structural changes occurring in the dendrimers as a function of these parameters are discussed, i.e., in terms of the fractal dimension and deviations of the radius of gyration from the Gaussian value. A first cumulant evaluation of the NSE spectra for each scattering vector q separately yields the length scale dependent relaxation rates. We observe a local minimum in the normalized relaxation rates Omega(q)q(3) on length scales corresponding to the overall dendrimer dimension. The dynamics is discussed within a Rouse-Zimm approach generalized to the case of starlike dendrimers of arbitrary geometry. The model allows an identification of the modes contributing to the relaxation of the dendrimer in the q and time range of the NSE experiment. The local minimum is due to collective breathing motions of (parts of) the dendrons relative to each other. Shape fluctuations are not observed.

We have studied the influence of plasticization on the microscopic dynamics of a glass-forming polymer. For this purpose we studied polyvinylchloride (PVC) with and without the commercially used plasticizer dioctylphthalate (DOP). We used dielectric spectroscopy and inelastic neutron scattering employing the neutron spin echo (NSE) technique. For both kinds of spectra the alpha relaxation could be consistently described by a model involving a distribution of individual relaxations of the Kohlrausch type. In contrast to earlier studies it turned out that an asymmetric distribution is necessary to fit the data at the lower temperatures investigated here. The shape parameters of the distribution (width, skewness) for PVC and PVC/DOP turned out to coincide when the characteristic relaxation times were the same. This means that the plasticizer only induces a remapping of the temperature dependence of the alpha relaxation. Comparison of NSE spectra S(Q,t)S(Q) at different scattering vectors Q gave the result that the slowing down at the structure factor peak Q(max) is surprisingly small for PVC while it is in the normal range for PVC/DOP.

We report on neutron spin echo experiments on hydrogen-bonded polymers and compare the experimentally found dynamical structure factor with theoretical predictions. Surprisingly, we find that in the melt phase the expected scaling of the Rouse dynamics is not satisfied. We propose an explanation based upon the large spatial volume occupied by the connecting groups. When the effects of these bulky groups on the local friction are taken into account, the usual scaling behavior is restored.

Long-range conformational changes in proteins are ubiquitous in biology for the transmission and amplification of signals; such conformational changes can be triggered by small-amplitude, nanosecond protein domain motion. Understanding how conformational changes are initiated requires the characterization of protein domain motion on these timescales and on length scales comparable to protein dimensions. Using neutron spin-echo spectroscopy (NSE), normal mode analysis, and a statistical-mechanical framework, we reveal overdamped, coupled domain motion within DNA polymerase I from Thermus aquaticus (Taq polymerase). This protein utilizes correlated domain dynamics over 70 angstroms to coordinate nucleotide synthesis and cleavage during DNA synthesis and repair. We show that NSE spectroscopy can determine the domain mobility tensor, which determines the degree of dynamical coupling between domains. The mobility tensor defines the domain velocity response to a force applied to it or to another domain, just as the sails of a sailboat determine its velocity given the applied wind force. The NSE results provide insights into the nature of protein domain motion that are not appreciated by conventional biophysical techniques.

The properties of bicontinuous microemulsions, consisting of water, oil, and a surfactant, can be modified by the addition of diblock copolymers (boosting effect) and homopolymers (inverse boosting effect) or a combination of both. Here, the influence of the addition of homopolymers (PEP(X) and PEO(X), X=5k or 10k molecular weight) on the dynamics of the surfactant layer is studied with neutron spin echo spectroscopy (NSE). Combining the results with the previous findings for diblock copolymers allows for a better separation of viscosity and bending modulus effects. With the addition of homopolymers, a significant increase of the relaxation rate compared to the pure microemulsion has been observed. The influence on the bending rigidity kappa is measured with NSE experiments. Homopolymer addition reduces kappa by up to Deltakappa approximately -0.5k(B)T, whereas the diblock copolymer yields an increase of kappa by approximately 0.3k(B)T. Comparison of the bending moduli that are obtained by analysis of the dynamics to those obtained from small angle neutron scattering (SANS) sheds light on the different renormalization length scales for NSE and SANS. Variation of the surfactant concentration at otherwise constant conditions of homopolymer or diblock-copolymer concentration shows that NSE results are leading to the pure bending rigidity, while the renormalized one is measured with SANS.

By using small-angle neutron scattering (SANS) and neutron spin echo (NSE), we have quantitatively investigated the static inhomogeneity in poly (N-isopropyl acrylamide) gel (PNIPA) in microscopic length scales of 0.015

Lamellar phases consisting of water and oil with intervening surfactant monolayer interfaces (eventually containing low molecular weight amphiphilic block-copolymers) are studied. Structural and dynamical investigations of oriented lamellar phases at the length scale of the intermembrane distance and beyond are performed using small-angle neutrons scattering and neutron spin-echo spectroscopy. The data analysis in terms of static and dynamic structure factors for a stack of elastic interfacial membranes yields information of the membrane curvature elasticity and membrane interactions in terms of phenomenological parameters such as the bending elastic modulus kappa and compression modulus (-)B, and on the dissipation related to the viscosity eta. The influence of the block-copolymers anchored to the surfactant monolayers is studied for a series of lamellar phase microemulsions containing equal volume fraction of surfactant and polymer, by varying only the polymer molecular weight. Based on numerical evaluations and fits to the data the conditions of applicability of the available theoretical concepts are discussed.