Universality of Time-Temperature Scaling Observed by Neutron Spectroscopy on Bottlebrush Polymers

Reversed dynamics of bottlebrush polymers with stiff backbone and flexible side chains

The segmental dynamics of bottlebrush polymers with a stiff backbone and flexible side chains has been studied. The segmental relaxation time of side chains attached to a flexible backbone follows the same trend as linear polymers, an increase with the increasing molecular weight, but is slowed down compared to their linear counterparts. Theoretical work predicts a reversal of the molecular weight dependence of the relaxation time for stiff backbones. As a model for a stiff-g-flexible system, bottlebrushes with poly(norbornene) backbone and poly(propylene oxide) side chains, PNB-g-PPO, at a uniform grafting density have been synthesized and characterized with quasi-elastic neutron scattering. Indeed, the anticipated reversed dynamics was found. Increasing the side chain length decreases the segmental relaxation time. This indicates the importance of the characteristics of the grafting site beyond a simplified picture of an attached side chain. The mean square displacement shows a similar trend with longer side chains exhibiting a larger displacement.

Uniqueness of relaxation times determined by dielectric spectroscopy

Dielectric spectroscopy is extremely powerful to study molecular dynamics, because of the very broad frequency range. Often multiple processes superimpose resulting in spectra that expand over several orders of magnitude, with some of the contributions partially hidden. For illustration, we selected two examples, (i) normal mode of high molar mass polymers partially hidden by conductivity and polarization and (ii) contour length fluctuations partially hidden by reptation using the well-studied polyisoprene melts as example. The intuitive approach to describe experimental spectra and to extract relaxation times is the addition of two or more model functions. Here, we use the empirical Havriliak-Negami function to illustrate the ambiguity of the extracted relaxation time, despite an excellent agreement of the fit with experimental data. We show that there are an infinite number of solutions for which a perfect description of experimental data can be achieved. However, a simple mathematical relationship indicates uniqueness of the pairs of the relaxation strength and relaxation time. Sacrificing the absolute value of the relaxation time enables to find the temperature dependence of the parameters with a high accuracy. For the specific cases studied here, the time temperature superposition (TTS) is very useful to confirm the principle. However, the derivation is not based on a specific temperature dependence, hence, independent from the TTS. We compare new and traditional approaches and find the same trend for the temperature dependence. The important advantage of the new technology is the knowledge of the accuracy of the relaxation times. Relaxation times determined from data for which the peak is clearly visible are the same within the experimental accuracy for traditional and new technology. However, for data where a dominant process hides the peak, substantial deviations can be observed. We conclude that the new approach is particularly helpful for cases in which relaxation times need to be determined without having access to the associated peak position.

Effect of Bottlebrush Poloxamer Architecture on Binding to Liposomes

Poloxamers─triblock copolymers consisting of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO)─have demonstrated cell membrane stabilization efficacy against numerous types of stress. However, the mechanism responsible for this stabilizing effect remains elusive, hindering engineering of more effective therapeutics. Bottlebrush polymers have a wide parameter space and known relationships between architectural parameters and polymer properties, enabling their use as a tool for mechanistic investigations of polymer-lipid bilayer interactions. In this work, we utilized a versatile synthetic platform to create novel bottlebrush analogues to poloxamers and then employed pulsed-field-gradient NMR and an in vitro osmotic stress assay to explore the effect of bottlebrush architectural parameters on binding to, and protection of, model phospholipid bilayers. We found that the binding affinity of a bottlebrush poloxamer (BBP) (B-E₁₀⁴³P₅¹⁵, M_n ≈ 26 kDa) is about 3 times higher than a linear poloxamer with a similar composition and number of PPO units (L-E₉₃P₅₄E₉₃, M_n ≈ 11 kDa). Furthermore, BBP binding is sensitive to overall molecular weight, side-chain length, and architecture (statistical versus block). Finally, all tested BBPs exhibit a protective effect on cell membranes under stress at sub-μM concentrations. As the factors controlling membrane affinity and protection efficacy of bottlebrush poloxamers are not understood, these results provide important insight into how they adhere to and stabilize a lipid bilayer surface.

Side Chain Dynamics of Poly(norbornene)-g-Poly(propylene oxide) Bottlebrush Polymers

The segmental dynamics of the side chains of poly(norbornene)-g-poly(propylene oxide) (PNB-g-PPO) bottlebrush polymer in comparison to PPO is studied by quasi-elastic neutron scattering. Having experimental time and length scale information simultaneously allows to extract spatial information in addition to relaxation time. Tethering one end of the PPO side chain onto a stiff PNB backbone slows down the segmental relaxation, over the length and time scales investigated. The power law dependence of the relaxation time on the momentum transfer, Q, indicates a more heterogeneous relaxation pattern for the bottlebrush polymer, whereas the linear PPO has less deviations from a homogenous relaxation. Similar conclusions can be drawn from the time dependent mean square displacement, 〈r² (t)〉, and the non-Gaussian parameter, α₂ (t). Herein, the bottlebrush polymer shows a more restricted dynamics, whereas the linear PPO reaches 〈r² (t)〉∝t^0.5 at the highest temperature. The deviations from Gaussian behavior are evident at the α₂ (t). Both samples show a decaying α₂ (t). The non-Gaussian parameter supports the results from the power law dependence of the relaxation times, with lower α₂ (t) values for PPO compared to those for PNB-g-PPO, pointing to less deviations from Gaussian behavior.

Predicting Solute Diffusivity in Polymers Using Time-Temperature Superposition

We demonstrate a novel application of the time-temperature superposition (TTS) principle to predict solute diffusivity D in glassy polymers using atomistic molecular dynamics simulations. Our TTS approach incorporates the Debye-Waller factor ⟨u²⟩, a measure of solute caging, along with concepts from thermodynamic scaling methods, allowing us to balance contributions to the dynamics from temperature and ⟨u²⟩ using adjustable parameters. Our approach rescales the solute mean-squared displacement curves at several temperatures into a master curve that approximates the diffusive dynamics at a reference temperature, effectively extending the simulation time scale from nanoseconds to seconds and beyond. With a set of "universal" parameters, this TTS approach predicts D with reasonable accuracy in a broad range of polymer/solute systems. Using TTS greatly reduces the computational cost compared to standard MD simulations. Thus, our method offers a means to rapidly and routinely provide order-of-magnitude estimates of D using simulations.

Broadband Wide-Angle VElocity Selector (BWAVES) neutron spectrometer designed for the SNS Second Target Station

A recently proposed wide-angle velocity selector (WAVES) device for choosing the velocity of detected neutrons after they have been scattered by the sample paves the way for inverted geometry neutron spectrometers with continuously adjustable final neutron wavelength. BWAVES broadband inverted geometry spectrometer proposed for the Second Target Station at the Spallation Neutron Source at Oak Ridge National Laboratory is designed using WAVES to simultaneously probe dynamic processes spanning 4.5 decades in time (energy transfer). This makes BWAVES a uniquely flexible instrument which can be viewed as either a quasielasitc neutron scattering (QENS) spectrometer with a practically unlimited (overlapping with the vibrational excitations) range of energy transfers, or a broadband inelastic vibrational neutron spectrometer with QENS capabilities, including a range of accessible momentum transfer (Q) and a sufficiently high energy resolution at the elastic line. The new capabilities offered by BWAVES will expand the application of neutron scattering in ways not possible with existing neutron spectrometers.

Dynamics of bottlebrush polymers

Bottlebrushes are an interesting class of polymers which shows intriguing material properties often associated with dynamics. While dynamical phenomena in linear polymers are well understood and existing theories can describe them in a good way, bottlebrush dynamics have only rarely been investigated. Therefore, we performed dielectric spectroscopy and quasi-elastic neutron scattering to study the dynamics of polydimethylsiloxane-based bottlebrush polymers, PDMS-g-PDMS focusing mostly on the segmental dynamics of the side chains. Comparing the relaxation times of the α – relaxation, tracked with dielectric spectroscopy, of bottlebrush polymers with those of their respective linear side chains show a slowing down once the side chains are attached to the backbone. This effect diminishes and finally vanishes with increasing side chain length. The time and length scale, offered by quasi-elastic neutron scattering, fits for the segmental dynamics together with faster processes. The Q-dependence of the segmental relaxation times allows to classify bottlebrush polymers as heterogenous including a non-Gaussian character. For such a dynamical system, the mean square displacement needs to be separated into single processes before an overall mean square displacement can be generated by applying the time temperature superposition principle.