Normal Mode Relaxation Research Articles

Exploring the impact of alignment media on RDC analysis of phosphorus-containing compounds: a molecular docking approach.

Residual dipolar couplings (RDCs) are employed in NMR analysis when conventional methods, such as J-couplings and nuclear Overhauser effects (NOEs) fail. Low-energy (optimized) conformers are often used as input structures in RDC analysis programs. However, these low-energy structures do not necessarily resemble conformations found in anisotropic environments due to interactions with the alignment medium, especially if the analyte molecules are flexible. Considering interactions with alignment media in RDC analysis, we developed and evaluated a molecular docking-based approach to generate more accurate conformer ensembles for compounds in the presence of the poly-γ-benzyl-L-glutamate alignment medium. We designed chiral phosphorus-containing compounds that enabled us to utilize 31P NMR parameters for the stereochemical analysis. Using P3D/PALES software to evaluate diastereomer discrimination, we found that our conformer ensembles outperform moderately the standard, low-energy conformers in RDC analysis. To further improve our results, we (i) averaged the experimental values of the molecular docking-based conformers by applying the Boltzmann distribution and (ii) optimized the structures through normal mode relaxation, thereby enhancing the Pearson correlation factor R and even diastereomer discrimination in some cases. Nevertheless, we presume that significant differences between J-couplings in isotropic and in anisotropic environments may preclude RDC measurements for flexible molecules. Therefore, generating conformer ensembles based on molecular docking enhances RDC analysis for mildly flexible systems while flexible molecules may require applying more advanced approaches, in particular approaches including dynamical effects.

Molecular mobility and thermal transitions study in renewable PLA-polyols star-like copolymers

The molecular dynamics mapping in poly(lactic acid) (PLA)-based star-like copolymers is performed herein, employing dielectric spectroscopy techniques supplemented by calorimetry and other structure characterization methods. Next to the neat linear PLA, three star-like copolymers, with 3, 4 and 5 branches were synthesized via ring opening polymerization at the presence of, respectively, glycerol, pentaerythritol and sorbitol (initiators). When increasing the branch number, consequently, the overall molar mass drops, from 55 kg/mol (neat PLA) to 17k (PLA@glycerol), 25k (PLA@pentaerythritol), and 14k (PLA@sorbitol) and, thus, the branch length decreases to ∼6k, ∼6k, and ∼3 k g/mol in the stars. The latter leads to faster segmental mobility, documented by the accelerated α relaxation and the drop in the calorimetric and dielectric glass transition temperatures. Simultaneously, the cooperativity (chains’ fragility) drops. Together these results suggest possibly the increase in free volume, a factor that can potentially favour the physical biodegradability. Next to the segmental dynamics, the local beta relaxation is recorded to have a mild dependence on the type of star (mainly decelerates), while the rare case of Normal Mode relaxation is recorded here only in the stars, providing additional support for the quite short branches. The overall data suggest the co-implementation of two antagonistic effects on mobility, i.e., the chain length changes in parallel to the constraints imposed by the star-like structure. Moreover, the in general low crystallizability of linear PLA further drops in the stars in terms of both suppressed crystalline fraction and nucleation, as well as lower quality of crystals. The materials exhibit single thermal transitions, indicating a homogeneous character, whereas a variety of semicrystalline morphologies can be achieved via both the composition and the thermal treatment. This provides a tool for tuning various properties and, consequently, the manipulation of the macroscopic performance.

Molecular Dynamics of Polymyrcene: Rheology and Broadband Dielectric Spectroscopy on a Stockmayer Type A Polymer

Molecular dynamics of polymyrcene (PM) covering a wide range of molecular weights from 6.7 × 103 ≤ Mw ≤ 3.47 × 105 g/mol (weight-average molecular weight Mw) with a molar mass dispersity Đ ≤ 1.16 were investigated by oscillatory shear rheology and broadband dielectric spectroscopy. The analysis of the zero-shear viscosity (η0) versus molecular weight in a double-logarithmic plot reveals a scaling exponent of ∼1.2 below the critical molecular weight and ∼3.7 above a critical molecular weight of Mc ≅ 4.4 × 104 g/mol. However, at molecular weights greater than the reptation molecular weight Mr, a molecular weight substantially larger than the entanglement molecular weight Me, the zero shear viscosity scaling decreases. A scaling of η0 ∝ M3.0, which might be attributed to a pure tube-reptation behavior, was found. The exponent of 1.2 is attributed to a Rouse-like dynamic and is interpreted in terms of PM’s bottlebrush-like nature arising from tightly packed C6/C8 pendant groups. Dielectric spectroscopy measurements revealed two relaxation processes typical for fully amorphous glassy polymers: The first is a segmental mode process, with a dynamic glass transition process (α), due to the segmental motions and the second one is a local relaxation process in the glassy state (β). Additionally, above the glass transition temperature at low frequency, another relaxation process was observed, which appears to be the normal mode process (n) due to the fluctuation of the end-to-end vector. This polymer is assigned to be a new Stockmayer type A polymer, whose normal mode relaxation is strongly dependent on its molecular weight. These findings allow for the rare possibility to explore the global dynamics of PM by using both oscillatory shear rheology and broadband dielectric spectroscopy methods over a wide range of temperatures to investigate molecular dynamics using the time–temperature superposition principle.

Disentangling proton-transfer and segmental motion relaxations in poly-vinyl-alcohol aqueous solutions by means of ultrasonic relaxation spectroscopy

A detailed temperature- and concentration-dependent ultrasonic relaxation study has been conducted in aqueous polyvinyl alcohol (PVA) solutions as a function of frequency under isobaric conditions. Concentration and temperature have similar effect on acoustic spectra. Two well-resolved relaxation processes were observed in the experimental acoustic spectra that seem to follow a Cole-Cole distribution function. The systematic analysis of the variation of the acoustic parameters with frequency, temperature and concentration revealed that both processes have collective and not local nature. The low-frequency relaxation mechanism is assigned to segmental motions of the polymer chains and the high-frequency relaxation to proton-transfer reaction, respectively. The characteristic relaxation frequencies were found independent of molecular weight, as expected for relative flexible vinyl-polymer chains with molecular weight above ~104. Based on Eyring's theory, the activation enthalpy of the low- and high-frequency relaxation were estimated equal to ΔΗ1* = 4.5 ± 0.2 kcal/mol and ΔΗ2* = 19.7 ± 0.8 kcal/mol, respectively. The contribution of the low-frequency lying normal mode relaxation has been quantitatively estimated in the context of relevant theories of the field and found almost four order of magnitude lower in amplitude compared to segmental motion process indicating that the experimentally detected relaxation is dominated by the latter. The experimental results were complemented with molecular mechanics calculations performed in parallel. The comparison between the experimental data and the outcome of the theoretical calculations evidenced that the length of the relaxing element in a PVA polymer chain is between 5 and 8 monomers in agreement with what is expected for vinyl-polymers and established the local segmental motions of the PVA polymer chains in the solution.

Supramolecular interactions involving fluoroaryl groups in hybrid blends of polylactide and ladder polysilsesquioxanes

Linear ladder polysilsesquioxanes (LPSQ-R) bearing fluoroaryl groups [R: p-fluorophenyl (F), p-trifluoromethylphenyl (F3) or pentafluorophenyl (F5)] were used to modify polylactide (PLA). Vibrational spectroscopy analysis suggested specific, non-covalent interactions between CO of PLA and fluoroaryl groups of LPSQ-R while quantum-chemical modelling performed for representative models indicated that the pattern of possible preferred contacts differs for LPSQ-F3 in respect to LPSQ-F and LPSQ-F5 (H····F hydrogen bonding against n→π* attractive interactions). It may affect interface phenomena in PLA/LPSQ-R systems. Thermal characteristics of PLA/LPSQ-R depended on the type of R and LPSQ-R content. Dielectric relaxation spectroscopy (DRS) studies revealed one relaxation process present in PLA and related to the glass transition. However, for PLA/LPSQ-R blends two processes were identified: glass transition and normal–mode relaxation. The modification with fluorinated macromolecules increased hydrophobicity of amorphous PLA and improved its mechanical and gas barrier properties, which can be of importance for packaging applications.

Dielectric Relaxation Spectroscopy in Synthetic Rubber Polymers: Nitrile Butadiene Rubber and Ethylene Propylene Diene Monomer

The dielectric permittivity of synthetic rubber polymers, nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM), with both frequency and temperature variations, was thoroughly investigated by dielectric relaxation spectroscopy (DRS). The spectrum versus frequency of DRS was analyzed with the semiempirical Havriliak–Negami formula and conductivity contribution by employing the newly developed “dispersion analyzer” analysis program. The main dielectric relaxations called the α‐ and β‐processes, associated with the cooperative motion of chains in polymers, were discovered in the low‐temperature region. In the high‐temperature region, we found Maxwell–Wagner–Sillars (MWS) relaxation associated with polymer interfacing and normal‐mode (α’) relaxation responsible for end‐to‐end dipole vector motion. The activation energies of schematic molecular chains responsible for the relaxation processes were obtained with the information about its motional mode. The glass transition temperature and dipole moment for the side group were also determined and compared with those from previous studies. In the EPDM specimen, the peaks of α‐ and β‐relaxation merged at high temperature and were separated with decreasing temperature. The first observations of both merging and splitting were consistent with the results on the temperature dependency of the relaxation strength. Both contour mapping and three‐dimensional plots for the two rubbers provide visual information for the distribution and mapping of relaxation.

Molecular and charge mobility of a poloxamer in the bulk and as soft component in polyurethanes

An amphiphilic PEO-b-PPO-b-PEO copolymer (poloxamer) is used as the soft phase of a biocompatible polyurethane matrix. The molecular and charge transport dynamics of the polyurethanes and the copolymer is studied in detail by broadband dielectric spectroscopy and differential scanning calorimetry. Various fitting techniques and formalisms are used for the extraction of data from the obtained dielectric spectra. As a result of incomplete phase separation, the glass transition of the polyurethanes occurs 10 K higher than that of the copolymer. The dynamic glass transition of the copolymer (α relaxation) is accompanied by a normal mode relaxation. When the poloxamer is constrained as part of the polyurethane chain, a process slower than α is observed and is likely associated with the normal mode relaxation despite a very significant spectral broadening. The dynamics of the α relaxation and this process does not depend significantly on the soft:hard segment ratio suggesting only minor differences in the consistency of the soft phases. The charge transport mechanism is similar to that of the neat copolymer for high soft segment contents, whereas for the 50 wt% material it changes, presumably as a result of a radical change in morphology.

Counterbalance between Surface and Confinement Effects As Studied for Amino-Terminated Poly(propylene glycol) Constraint in Silica Nanopores

Broadband dielectric spectroscopy (BDS) and orthopositronium annihilation lifetime spectroscopy (PALS) are combined to study the molecular dynamics and the free volume of poly(propylene glycol) terminated with amino end groups (PPG-NH2) in the bulk state and when confined in native and silanized unidirectional silica nanopores with average diameters of 4, 6, and 8 nm. In the bulk state, three dielectric relaxation processes are observed: (i) the fast β-relaxation assigned to the librational fluctuations of the −O–NH2 moiety, (ii) the α-process corresponding to the dynamic glass transition, and (iii) the (slower) chain dynamics or normal mode (NM) relaxation. Under confinement in native nanopores, the β-process becomes slower, while the α and the normal mode relaxation processes become faster and broader and demonstrate a lower dielectric strength with decreasing pore diameter. In silanized nanopores the normal and β-processes are nearly bulklike, but the α-process still remains faster than bulk closer to ...

Molecular Dynamics of Polyfarnesene

This paper represents the first comprehensive report of the molecular weight dependence of the dynamics of polyfarnesene (PF), utilizing oscillatory shear rheology and broadband dielectric spectroscopy. Extended PF chain conformations arising from tightly packed C11/C13 pendant groups reduce the probability of chain entanglements and lead to Rouse-like melt dynamics up to a critical molecular weight ∼105 g/mol. At higher molecular weights, PF behaves as an entangled polymer melt. Dielectric spectroscopy measurements establish PF as a type-A polymer, whose normal mode relaxation is strongly dependent on molecular weight, providing a compliment to melt rheology for the exploration of PF global chain dynamics.

Relationship between global and segmental dynamics of poly(butylene oxide) studied by broadband dielectric spectroscopy.

Relationship between segmental relaxation and normal-mode relaxation has been studied for molten poly(butylene oxide)s having various molecular weights by broadband dielectric spectroscopy over a wide temperature (T) range. We found that T dependence of the segmental relaxation time, τs, was weaker than the normal mode time, τn, at high T(>250 K ∼ Tg + 50 K), and the τn/τs ratio systematically decreased with increasing temperature. This high temperature complexity, whose mechanism has not been discussed in detail so far, was quantitatively explained by assuming the two step processes: local conformation change of polymers (elementary process) occurs first, and then the motion of a segment unit (second process) occurs. It was also found that the elementary process was strongly correlated with the experimentally observed β-relaxation.

Dynamics of model polycyclic aromatic hydrocarbon compound-epoxy composites: A dielectric study

A model polycyclic aromatic hydrocarbon (PAH) compound, anthracene, was incorporated into a thermosetting epoxy matrix as a reinforcing moiety via physical dispersion and/or chemical modification. In order to understand the “additive effect” of glass transition temperature (Tg) observed with the variation of free anthracene (AN) and bonded 2-aminoanthracene (2-AM) loading, the relaxation dynamics were investigated by broadband dielectric spectroscopy. Within the measurement range of 0.01 Hz–1 MHz and −60 to 130 °C, three relaxation processes, namely normal mode (n-mode) relaxation, α relaxation, and β relaxation, were observed for all epoxy composites with bonded and/or unbound anthracene. After eliminating the strong effect of ionic conduction by using the logarithmic derivative approximation ε''∝∂ε'∂lnω, derived from the Kramers-Kronig relations, the n-mode relaxation occurring at low frequencies above Tg for the rigid epoxy system is revealed. The Arrhenius diagram showing the temperature dependence of each relaxation process for the PAH-epoxy composites was obtained after parametric fitting using the Havriliak-Negami (HN) function in the frequency domain. The segmental α relaxation was more strongly impacted than the long-range n-mode relaxation by the different reinforcing approaches. The correlation of Tg -scaled fragility to molecular structures reveals the different mechanisms for the retardation effects on cooperative segmental and chain relaxation time. The localized β relaxation below Tg was not seemingly affected by the incorporation of bound and/or unbound anthracenes as indicated by the characteristic relaxation time and the activation energy.

Study of the Molecular Dynamics of Multiarm Star Polymers with a Poly(ethyleneimine) Core and Poly(lactide) Multiarms.

Multiarm star polymers, denoted PEIx-PLAy and containing a hyperbranched poly(ethyleneimine) (PEI) core of different molecular weights x and poly(lactide) (PLA) arms with y ratio of lactide repeat units to N links were used in this work. Samples were preconditioned to remove the moisture content and then characterized by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS). The glass transition temperature, Tg, is between 48 and 50 °C for all the PEIx-PLAy samples. The dielectric curves show four dipolar relaxations: γ, β, α, and α′ in order of increasing temperature. The temperatures at which these relaxations appear, together with their dependence on the frequency, allows relaxation maps to be drawn, from which the activation energies of the sub-Tg γ- and β-relaxations and the Vogel–Fulcher–Tammann parameters of the α-relaxation glass transition are obtained. The dependence of the characteristic features of these relaxations on the molecular weight of the PEI core and on the ratio of lactide repeat units to N links permits the assignation of molecular motions to each relaxation. The γ-relaxation is associated with local motions of the –OH groups of the poly(lactide) chains, the β-relaxation with motions of the main chain of poly(lactide), the α-relaxation with global motions of the complete assembly of PEI core and PLA arms, and the α′-relaxation is related to the normal mode relaxation due to fluctuations of the end-to-end vector in the PLA arms, without excluding the possibility that it could be a Maxwell–Wagner–Sillars type ionic peak because the material may have nano-regions of different conductivity.

Studies on the Temperature and Time Induced Variation in the Segmental and Chain Dynamics in Poly(propylene glycol) Confined at the Nanoscale

The effect of 2D confinement on the dynamics of the normal mode (chain mobility) and segmental relaxation in poly(propylene glycol) (PPG) has been studied with the use of broadband dielectric spectroscopy (BDS) and differential scanning calorimetry (DSC). It is shown that both processes become faster with increasing degree of confinement. Interestingly, the crossover from VFT to the Arrhenius-like behavior of chain and segmental dynamics, observed in the examined system, is strictly related to the vitrification of the adsorbed polymers. We also report that the mean relaxation times of the normal, τNM, and segmental modes, τα, depend on the thermal history of confined PPG and can be significantly modified using different thermal treatments. It is demonstrated that annealing of the samples below the crossover temperature, Tc, leads to a systematic shift of the segmental relaxation and normal mode toward lower frequencies, resulting in an increase in the glass transition temperature of the spatially restrict...

Influence of block sequence and molecular weight on morphological, rheological and dielectric properties of weakly and strongly segregated styrene-isoprene triblock copolymers

Abstract In this work, morphological, thermal, viscoelastic and dielectric properties of triblock copolymers consisting of styrene (S) and isoprene (I) blocks are discussed. SIS and ISI triblock copolymers were synthesized by sequential anionic polymerization, three of them exhibiting molecular weights below the entanglement molecular weight Me, three of them exhibiting molecular weights in the order of Me and two of them exhibiting molecular weights above Me. The objective of this work is the investigation of the influence of molecular weight and block sequence on relaxation of the block copolymer chains. Morphological investigations using small angle X-ray scattering and transmission electron microscopy studies reveal that a larger molecular weight is associated with a more pronounced microphase separation. The presence of two glass transition temperatures reveals microphase separation of the PI and PS blocks. The Fox-Flory equation was applied in order to describe the molecular weight dependence of the glass transition temperature of the polyisoprene and the polystyrene blocks. The analysis of rheological data reveals a Maxwell fluid behavior for the weakly segregated block copolymers, whereas for the strongly segregated block copolymers a pronounced elastic behavior at low frequencies of small amplitude shear oscillations was observed. In the intermediate regime of molecular weight, a complex viscoelastic behavior appears. The plateau modulus G N o is influenced by the sequence of the PS and the PI blocks (SIS or ISI). Our analysis of segmental and normal mode relaxation in dielectric spectroscopy experiments show that the relaxation processes are strongly influenced by the block sequence (PI blocks tethered at one or both ends) and the molecular weight. As a result, the block sequence in triblock copolymers influences dynamical properties in the glassy state and in the melt.

Charge transfer mobility of naphthodithiophenediimide derivative: Normal-mode and bond length relaxation analysis

In this letter, the charge transfer mobility of naphthalenediimide (NDTI) derivative is investigated. By employing the normal-mode analysis and bond length relaxation analysis, the influences of chemical elements on reorganization energies and intermolecular electronic couplings are investigated in NDTI derivative. The results show that the introduction of atom O would decrease reorganization energy in hole-hopping process and increase electronic coupling. This analysis encourages the molecular and material design in organic semiconductors.

The features of the normal mode relaxation as studied by thermally stimulated currents

The slow molecular mobility in high-cis poly (1,4-isoprene) has been studied by the dielectric technique of thermally stimulated currents. Three different kinds of motional processes have been identified: the Johari–Goldstein relaxation, the main or α-process and a mobility appearing above Tg that has been ascribed to the normal mode process. The temperature location of these relaxations was respectively at −85 to −80°C, at −73°C and at −65°C. The fragility or steepness index was found to be mα=60 and mn=37, respectively for the α and the normal mode processes, in excellent agreement with the results obtained by dielectric relaxation spectroscopy (DRS).

Dissipative particle dynamics simulation of dilute polymer solutions—Inertial effects and hydrodynamic interactions

We examine the accuracy of dissipative particle dynamics (DPD) simulations of polymers in dilute solutions with hydrodynamic interaction (HI), at the theta point, modeled by setting the DPD conservative interaction between beads to zero. We compare the first normal-mode relaxation time extracted from the DPD simulations with theoretical predictions from a normal-mode analysis for theta chains. We characterize the influence of bead inertia within the coil by a ratio Lm/Rg, where Lm is the ballistic distance over which bead inertia is lost, and Rg is the radius of gyration of the polymer coil, while the HI strength per bead h* is determined by the ratio of bead hydrodynamic radius (rH) to the equilibrium spring length. We show how to adjust h* through the spring length and monomer mass, and how to optimize the accuracy of DPD for fixed h* by increasing the friction coefficient (γ ≥ 9) and by incorporating a nonlinear distance dependence into the frictional interaction. Even with this optimization, DPD simulations exhibit deviations of over 20% from the theoretical normal-mode predictions for high HI strength with h* ≥ 0.20, for chains with as many as 100 beads, which is a larger deviation than is found for Stochastic rotation dynamics simulations for similar chains lengths and values of h*.

Molecular Order and Dynamics of Nanometric Thin Layers of Poly(styrene-b-1,4-isoprene) Diblock Copolymers

Order and dynamics of poly(styrene-b-1,4-isoprene), P(S-b-I), diblock copolymers in nanometer thin layers with different isoprene volume fractions (fPI) and identical molecular weight of the styrene blocks are studied by a combination of grazing-incidence small-angle X-ray scattering (GISAXS), atomic force microscopy (AFM), and broadband dielectric spectroscopy (BDS). GISAXS and AFM reveal randomly oriented lamellar structures in the films and a parallel orientation at the top surface, respectively. Using BDS, three well separated relaxation processes are detected: (i and ii) the dynamic glass transitions (segmental mode) in the styrene and isoprene blocks, respectively, and (iii) the normal mode relaxation representing fluctuations of the isoprene chain as a whole or parts of it. While the first two do not show any thickness dependence in their spectral positions, the latter becomes faster with decreasing sample thickness. This reflects the difference in the length-scale on which the molecular fluctuatio...

The segmental and global dynamics in lamellar microphase-separated poly(styrene-b-isoprene) diblock copolymer studied by 1H NMR and dielectric spectroscopy

The nuclear magnetic resonance (NMR) and dielectric spectroscopy (DS) methods were used to investigate the segmental and global dynamics in lamellar microphase separated poly(styrene-b-isoprene) (SI) diblock copolymer. For the first time, the susceptibility representation of the NMR relaxation data is applied to the analysis of the molecular dynamics in complex polymer systems like the diblock copolymer. This approach in combination with the frequency-temperature superposition (FTS) allows one to compare directly the NMR and DS data in an extended frequency range providing a unique comprehensive picture of various relaxation processes present in the system studied. The findings of these investigations include structural relaxations of the polyisoprene (PI) and the polystyrene (PS) blocks, a normal mode relaxation of the PI block, and an extra low frequency interfacial relaxation. Special attention has been devoted to influence of the copolymer morphology on the segmental and global dynamics in PI.

End-to-End Vector Dynamics of Nonentangled Polymers in Lamellar Block Copolymer Melts: The Role of Junction Point Motion

By using dielectric spectroscopy, we investigate the chain dynamics of nonentangled polyisoprene (PI) under soft confinement in lamellar domains of block copolymer melts with polydimethylsiloxane (PDMS). The data show a dramatic difference in the end-to-end vector dynamics of the PI blocks as compared not only with that of the corresponding homopolymer PI chains but also with respect to previous results for the same blocks under soft confinement in cylindrical domains. Two contributions to the dielectric normal mode relaxation are detected. The data are analyzed by means of a model including contributions from internal chain modes (accounting for the fastest component) and a slow component attributed to the junction point dynamics. The contribution of the internal chain modes is modeled according to the analysis of the Rouse modes obtained from simulations of a generic bead–spring model for strongly segregated symmetric diblock copolymers. In this way it is shown that the internal chain modes of the blocks have time scales close to those expected from the homopolymer chain independently of the structural details. In contrast, the contribution attributed to the junction point dynamics depends critically on minor structural differences. We interpret these findings as a result of the presence of fast moving defects and/or grain boundaries in the lamellar structures formed by these relatively short, nonentangled diblock copolymers.