Effects of polymer chain disentanglement on NMR properties. II. 13C magnetic relaxation in polystyrene

The transverse magnetic relaxation of ¹³C_α nuclei has been studied in concentrated solutions of polystyrene. The magnetic relaxation rate was measured as a function of molecular weight at several temperatures (313,318, and 323 K) and at several concentrations (0.53, 0.43, and 0.34 g/cm³). The spin-system response of these nuclei in natural abundance exhibits a characteristic evolution from pseudosolid properties to liquidlike one, induced by decreasing the molecular weight of polymer molecules. This evolution is analogous to that already observed in protons attached to polyisobutylene or polydimethylsiloxane chains; it is assumed to be induced by an increase of the disentanglement rate of polymer chains. The spin-system response may be considered as reflecting single-chain magnetic properties, because of the low concentration of ¹³CC_α nuclei, although all chains are in dynamic interaction with one another. The NMR disentanglement transition is interpreted in terms of a two-step motional averaging effect involving submolecules. A numerical analysis of NMR properties is given using a model of polymer chain relaxation based on a multiple-mode relaxation process, characterized by (i)a terminal relaxation time τ^v₁ depending upon M³, the molecular weight, and approximately proportional to the polymer concentration C (like the reptation time); (ii)a relaxation-time spectrum analogous to a Rouse spectrum; (iii)a terminal relaxation time τ^v₁ = 2.5 × 10^?2s for M = 2.5 × 10⁵, C = 0.53 g/cm³ in carbon tetrachloride at 313 K.     

Solid-state NMR studies of methyl celluloses. Part 1: regioselectively substituted celluloses as standards for establishing an NMR data basis

Three methyl celluloses with completely uniform substitution pattern, 2-O-methyl cellulose (1), 3-O-methyl cellulose (2) and 6-O-methyl cellulose (3), were prepared according to the cationic ring opening polymerization approaches starting from substituted 1,2,4-orthopivalate derivatives of d-glucose. These samples allowed for the first time to sort out the methyl substitution effects on solid-state NMR chemical shifts and relaxation. Dipolar dephasing experiments allowed the detection and assignment (¹H, ¹³C) of the methyl groups. In 1 and 2, these resonances overlapped with those of C-6, whereas in 3, the methyl signal experienced a low-field shift into the region of C-2,3,5. ¹³C T₁ experiments were used to verify different relaxation behavior of the carbon sites, particularly the short relaxation time of at the carbon substitution site next to the methyl groups. This effect was used to unambiguously identify the ¹³C chemical shifts of the carbons carrying the methoxyl substituent, although they overlap with all resonances in the C-2,3,5 region. The data obtained for the standard samples with uniform substitution will now be used as the basis for determining methylation patterns and substitution degree in commercial methyl celluloses.     

Polysoaps in Backbone‐Selective Solvents: Effects of Side‐Chain Length on Collapse Dynamics

Abstract

Molecular dynamics (MD) simulations of model comb‐graft heteropolymers were performed to understand general mechanistic features of coil‐to‐micelle relaxation after instantaneous quench from a nonselective solvent to solvent conditions selective for the backbone monomers and poor for the side‐chain monomers. The systems considered were single bead‐spring molecules with backbones of 30 monomers and 10 equally spaced side chains of 1, 5, 10, or 20 monomers each, immersed in dense liquids of 20,000 simple solvent particles. We find that the coil‐to‐micelle relaxation time, τ _r , averaged over 50 independent trajectories for each set of topological parameters considered, decreases with increasing side‐chain length. A two‐stage relaxation mechanism is observed: (1) a fast collapse and aggregation of neighboring side chains to form a chain of “protomicelles,” followed by (2) a slow intramolecular aggregation of protomicelles. Fast collapse dominates for molecules with relatively longer side chains due to relatively higher probabilities of initial contacts between side‐chain monomers in different side chains, while slow intramolecular aggregation dominates for molecules with relatively shorter side chains.     

Relaxation dispersion and zero-field spectroscopy of thermotropic and lyotropic liquid crystals by fast field-cycling N.M.R.

Abstract

Systematic field-cycling measurements of the T ₁ relaxation dispersion in numerous nematic liquid crystals (azoxybenzenes, Schiff's bases, biphenyls, phenyl-cyclohexanes, cyclo-cyclo-hexanes) confirm our previous observations obtained for PAA and MBBA that order fluctuations of the nematic director are a significant relaxation contribution only at low Lamor frequencies v, i.e. far below the usual megahertz range. Their significance is demonstrated most convincingly by the characteristic square-root dispersion law, T ₁ ～ v ^1/2, which occurs in the kilohertz range and which completely disappears above the nematic–isotropic phase transition. The strength of the collective relaxation mechanism varies by more than two orders of magnitude in the sequence (selection) PAA-d ₈ PAA, PAA-d ₆ PAB, OCB7, MBBA, CB7, PCH7, MBBA-d ₆ MBBA-d ₁₃ and CCH7. This finding can be understood almost quantitatively by the widely differing separations and orientations of proton pairs on the molecules, together with the different viscoelastic parameters of the nematogens. In addition, the underlying slow molecular reorientations have been observed in MBBA and PAA by intensity changes of the zero-field spectra, which are absent for high-field measurements. Similarly, smectic type order fluctuations in layered liquid crystal structures prove to be an effective relaxation mechanism only at low Lamor frequencies. This has been verified by the related linear relaxation dispersion profile, T ₁ ～ v ¹, for both thermotropic systems (TBBA, C₁₂-AA) and lamellar lyotropic mixtures (e.g. potassium laurate in water and phospholipids in water). Our results concerning the time scale of the T ₁ ～ v ^1/2 and T ₁ ~ v ¹ regime do not agree with conclusions drawn from conventional high-field techniques.     

Tube dilation process in star‐branched cis‐polyisoprenes

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type‐A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]² if the tube actually dilates in the time scale of the star relaxation. For 6‐arm star cis‐polyisoprene (PI) chains (having those type‐A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight M_a. However, in the range of M_a examined, M_a ≤ 8M_e (M_e = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of M_a, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000     

一维和二维镝(Ⅲ)配合物的慢磁弛豫

分别用稀土醋酸盐和稀土高氯酸盐与希弗碱配体和巯基烟酸配体反应得到了两例镝配合物[Dy₂(OAc)₆H₂O]_n(1)和{[DyL(H₂O)₄]ClO₄·H₂O}_n(2)(L=2,2'-二硫代-二(3-吡啶甲酸)),并通过单晶X-射线衍射、元素分析、红外光谱和磁性测试对其进行了表征。结构研究和磁性测试表明:化合物1是羧基桥连的一维链结构,该化合物表现出慢磁弛豫性质,有效能垒为2 K;化合物2是通过原位生成的二硫键桥连的二维网状结构,表现出明显的铁磁相互作用和慢磁弛豫行为。     

Segmental relaxation and partial crystallization of chain‐extended Poly(l‐lactic acid) reinforced with carboxylated carbon nanotube

Temperature‐modulated differential scanning calorimetry (TMDSC) and broadband dielectric spectroscopy (BDS) were employed to study the glass transition, size of the cooperative rearranging regions (CRRs), crystallization kinetics, and dielectric relaxation response of nanocomposites constituted by chain‐extended poly(L‐lactide) (PLLA) and carboxylated carbon nanotubes (f‐CNTs). The CRR size and the number of relaxing structural units decreased in the presence of crystals during isothermal crystallization. All samples displayed both a primary (α) and secondary (β) relaxation in BDS spectra. The relaxation dynamics of PLLA chains was barely affected by the presence of the f‐CNT. Constrained polymer chains and thickness of interphase (t _i) were measured using dielectric spectra in tan δ representation. t _i values were found to be 46 and 24 nm for sample containing 0.2 and 0.5% weight fraction of f‐CNT, respectively. All samples underwent partial crystallization (with roughly 30% of final crystalline fraction) some 15 or 20° above their glass‐transition temperature (T _g). Crystallization leads to a fragile‐to‐strong transition in the temperature dependence of the cooperative α relaxation and to the increased visibility of a Maxwell–Wagner–Sillars (MWS) interfacial relaxation, which appears to be present in all samples. The heterogeneity of the polymeric samples was quantified in terms of a new parameter, the heterogeneity index (H). © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 222–233     

Effect of nanoclay on relaxation of poly(vinylidene fluoride) nanocomposites

The effect of Lucentite™ STN nanoclay on the relaxation behavior of poly(vinylidene fluoride) (PVDF) nanocomposites was investigated using dielectric relaxation spectroscopy (DRS) and wide- and small-angle X-ray scattering. Lucentite™ STN is a synthetic nanoclay based on hectorite structure containing an organic modifier between the hectorite layers. The addition of this nanoclay to PVDF results in preferential formation of the beta-crystallographic phase. When the STN content increased to 5% and 10%, only the beta-phase was observed. Bragg long period and lamellar thickness both decrease with STN addition. The relaxation rates for processes termed α_a (glass transition, related to polymer chain motions in the amorphous regions) and α_c (related to polymer chain motions in the crystalline regions and fold surfaces) can be described either with the Vogel-Fulcher-Tamman equation or with Arrhenius behavior, respectively. DRS shows that the α_a relaxation rate increases with the concentration of STN because of the reduction of intermolecular correlations between the polymer chains, caused by the presence of layered silicate nanoclay particles, which serve to segregate polymer chains in the amorphous regions. Comparing samples with beta-crystal phase dominant, the relaxation rate for the α_c relaxation also increases with concentration of STN in all nanocomposite samples. Dielectric properties at low frequencies are dominated by the dc conductivity, and as more STN is added, the conductivity increases rapidly. The addition of 10% STN makes the dc conductivity increase by almost four decades when compared with neat PVDF. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2520–2532, 2009     

Minute Additions of DMSO Affect Protein Dynamics Measurements by NMR Relaxation Experiments through Significant Changes in Solvent Viscosity

Studies of protein−ligand binding often rely on dissolving the ligand in dimethyl sulfoxide (DMSO) to achieve sufficient solubility, and then titrating the ligand solution into the protein solution. As a result, the final protein−ligand solution contains small amounts of DMSO in the buffer. Here we report how the addition of DMSO impacts studies of protein conformational dynamics. We used ¹⁵N NMR relaxation to compare the rotational diffusion correlation time (τ_C) of proteins in aqueous buffer with and without DMSO. We found that τ_C scales with the viscosity of the water−DMSO mixture, which depends sensitively on the amount of DMSO and varies by a factor of 2 across the relevant concentration range. NMR relaxation studies of side chains dynamics are commonly interpreted using τ_C as a fixed parameter, obtained from backbone ¹⁵N relaxation data acquired on a separate sample. Model-free calculations show that errors in τ_C, arising from mismatched DMSO concentration between samples, lead to significant errors in order parameters. Our results highlight the importance of determining τ_C for each sample or carefully matching the DMSO concentrations between samples.     

Effects of hydroxy compounds on gel formation of gelatin

 Network formation of gelatin gel is known to consist of three-dimensionally cross-linked triple helices among polypeptide chains. The effects of added low molecular weight mono-ols, diols and polyols on the higher-order structure formation of gelatin chains were investigated using the following measurements: melting temperature, viscoelasticity and spin-lattice relaxation time (T ₁) of H¹⁷ ₂O of gels, and circular dichroism spectra of diluted gelatin solutions. Furthermore, hydration behaviors of these hydroxy compounds were evaluated from the dynamic hydration numbers (n _DHN) derived from T ₁ of H¹⁷ ₂O in the solutions. It was found that network structures of gelatin gels containing hydoxy compounds were influenced by the number and position of hydroxyl groups as well as the number of carbon atoms of these coexisting compounds. The effect of hydroxyl groups of hydroxy compounds was considered to stabilize the helices among gelatin chains. Especially, the addition of polyols with large number of hydroxyl groups increased the number of cross-linking junctions in the gel networks, which consist of the aggregation among the helices. On the contrary, the effect of carbon atoms of hydroxy compounds is to disturb the formation of the helices and the aggregation among the helices. Received: 18 April 1996/Accepted: 23 July 1996     

Orientational relaxation times of worm-like chains

A semi-empirical formula for orientational relaxation times of worm-like chains in dilute solutions is proposed where τ_rod = τ₀N³ is the relaxation time of a rigid rod composed of N segments, and x = 2a/L is the chain rigidity, i.e. the ratio of the double persistence length to the chain contour length, L. The formula, which can be used in the entire range of molecular rigidities and chain lengths, has been tested against segment relaxation times for semi-rigid chains calculated from the optimized Rouse-Zimm model.     

Local mobility in grafted polydimethylsiloxane melts

Spin–lattice relaxation time constants, T₁, were studied for low-molecular-weight linear and grafted polydimethylsiloxane over a wide temperature and frequency range. Quantitative evaluations of proton T₁ measurements indicated two relaxation processes: anisotropic rotation of methyl groups around the Si–C bond (low temperature process) and motions of the PDMS side-chains connected with the glass transition (high temperature process). Additional analyses of the T₁ relaxation dispersion profiles revealed specific local segment fluctuation times, which are characteristic of the coherent motions in the grafted polymer chains.     

Morphology and dynamics of the poly(ϵ‐caprolactone)‐b‐poly(L‐lactide) diblock copolymer and its inclusion compound with α‐cyclodextrin: A solid‐state 13C NMR study

A biodegradable diblock copolymer of poly(ϵ‐caprolactone) (PCL) and poly(L ‐lactide) (PLLA) was synthesized and characterized. The inclusion compound (IC) of this copolymer with α‐cyclodextrin (α‐CD) was formed and characterized. Wide‐angle X‐ray diffraction showed that in the IC crystals α‐CDs were packed in the channel mode, which isolated and restricted the individual guest copolymer chains to highly extended conformation. Solid‐state ¹³C NMR techniques were used to investigate the morphology and dynamics of both the bulk and α‐CD‐IC isolated PCL‐b‐PLLA chains. The conformation of the PCL blocks isolated within the α‐CD cavities was similar to the crystalline conformation of PCL blocks in the bulk copolymer. Spin–lattice relaxation time (T₁C) measurements revealed a dramatic difference in the mobilities of the semicrystalline bulk copolymer chains and those isolated in the α‐CD‐IC channels. Carbon‐observed proton spin–lattice relaxation in the rotating frame measurements (T_1ρH) showed that the bulk copolymer was phase‐separated, while, in the IC, exchange of proton magnetization through spin‐diffusion between the isolated guest polymer chains and the host α‐CD was not complete. The two‐dimensional solid‐state heteronuclear correlation (HetCor) method was also employed to monitor proton communication in these samples. Intrablock exchange of proton magnetization was observed in both the bulk semicrystalline and IC copolymer samples at short mixing times; however, even at the longest mixing time, interblock proton communication was not observed in either sample. In spite of the physical closeness between the isolated included guest chains and the host α‐CD molecules, efficient proton spin diffusion was not observed between them in the IC. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2086–2096, 2005     

Cooperative chain relaxation in miscible polymer blends

Orientation relaxation of dissimilar chains in the molten miscible blends, poly(methyl methacrylate)/poly(vinylidene fluoride) and poly(methyl methacrylate)/poly(vinylidene fluoride-co-trifluoroethylene), were investigated by measuring (1) the change of infrared dichroic ratio with time after the uniaxial stretching of film specimens, (2) the shear stress relaxation spectrum, and (3) birefringence relaxation in shear. The dissimilar polymers showed an identical time variation of the normalized Hermans orientation function. The blend showed a relaxation spectrum with a single characteristic relaxation time τ_c, depending on the blend composition. The birefringence relaxed monotonically, remaining positive. These results suggest that the dissimilar polymers do not relax independently but cooperatively. This behavior may be induced by a constraint due to the specific interactions between the dissimilar polymers, e.g., weak hydrogen bonding. For the cooperative chain relaxation, a third power relationship was found; τ_c/τ_e vprop; (M/M_e),³ where τ_e and M_e are the relaxation time and molecular weight of entanglement strand, respectively, and M is the number average molecular weight in the blend.     

New approximate formulae for the retardation factors of nematic liquid crystals with simple uniaxial anisotropy

Abstract

Simple formulae which yield a close approximation to the exact analytic solution for the longitudinal and transverse relaxation times T _|| and T _⊥ of the components of the dipole moment of a nematic liquid crystal with simple uniaxial anisotropy are presented. The new formula for T _|| yields a substantial correction to the Meier-Saupe formula [1966, Molec. Crystals, 1, 515]. It appears that both the longitudinal and transverse relaxation processes may be accurately described by a single Debye type relaxation mechanism with relaxation times T _|| and T _⊥.     

Rheological properties of rodlike polymers in solution. 2. Linear and nonlinear transient behavior

Rheological and rheo-optical studies are reported for isotropic solutions of the mesogenic rodlike polymer poly(1,4-phenylene-2,6-benzobisthiazole) (PBT). Several PBT samples were used with average contour lengths from 95 to 135 nm. Concentrations were varied over a range just below the concentration C_c for the formation of an ordered (nematic) state. The predictions of a single-integral constitutive equation of the BKZ type utilizing experimental estimates of the distribution of discrete relaxation times is compared with experimental data on the steady-state viscosity η_κ, the recoverable compliance function R_κ, and the steady-state flow birefringence as functions of the shear rate κ, with satisfactory results. The relaxation of the shear stress and the flow birefringence on cessation of steady-state flow at shear rate κ are also compared with the single-integral constitutive equation, and it is found that in the nonlinear response range the data can be superposed over a wide range in κ. The overall behavior is qualitatively similar to that for flexible chains, which can also be fitted by the single-integral constitutive equations over similar ranges of η₀R₀κ, with η₀ and R₀ the limiting values of η_k and R_κ for small κ. Of course, the dependence of η₀ and R₀ on concentration and molecular weight differs markedly for rodlike and flexible-chain polymers.     

N.M.R. study of collective molecular motions in smectogen liquid crystals

Abstract

The proton spin relaxation dispersion, T ₁(v), was studied by field-cycling techniques over a broad Larmor frequency range in the nematic and smectic phases of several liquid crystals (4,4′-bis-heptyloxyazoxybenzene, 4-cyano-4′-8-alkylbiphenyl, 4-cyano-4′-9-alkylbiphenyl, 4-cyano-4′-11-alkylbiphenyl and 4-cyano-4′-9-alkoxybiphenyl) with different sites of the nitrogen atom. The results can be explained quantitatively in terms of nematic and smectic order fluctuations (T ₁ ∝ v ^1/2, T ₁ ∝ v ¹), molecular self-diffusion, molecular rotations and up to six cross-relaxation resonances due to a nitrogen-proton coupling The order fluctuations contribution and the transition from the v ^1/2 to the v ¹ dispersion profile occurs always at Larmor frequencies in the kilohertz range. Some additional measurements of the frequency dependence of the dipolar relaxation time T _1D(v), are not in accord with existing theories.     

Polysiloxane dizwitterionomers. IV. Mechanical and dielectric relaxations

The relaxation behavior of a series of polysiloxane dizwitterionomers has been studied by using dynamic mechanical and dielectric spectroscopy. The temperature range was 100–375 K and the frequency was ca. 1 Hz in the mechanical measurements and 50 Hz–50 kHz in the dielectric measurements. Three relaxation regions, labeled α_s, β, α_z in order of increasing temperature, were observed. The β_s relaxation was assigned to the nonionic portion of the siloxane chain and correlated with the glass transition of polydimethylsiloxane. The β and α_z processes are ionic-related relaxations; β probably originated from the motion of a chain segment carrying a dizwitterion, and α_z, from the collapse of the organization in the ionic domains. Absorbed water exerts a profound influence on relaxation behavior–primarily on α_z ionic relaxation and the relative rigidity of the samples. The water molecules solvate the ions and thus shift the α_z relaxation to lower temperatures. Some aspects of the effect of thermal history on the microphase separation into domains have also been investigated. The results indicate that the organization of the zwitterions in the ionic domains is improved at slow cooling rates.     

Nuclear magnetic relaxation and molecular motion in poly(vinylidine fluoride)

Pulsed NMR T₁, T₂, and T_1ρ measurements are reported for poly(vinylidine fluoride) (PVF₂). The results demonstrate clearly the presence of four relaxation processes, three amorphous and one crystalline. The α relaxation is undoubtedly a crystalline one, while β and γ are both amorphous, in agreement with earlier conclusions from dielectric and dynamic mechanical measurements. The fourth relaxation (β′) observed initially in the mechanical measurements of Kakutani, but undetected in dielectric experiments, has been confirmed in our results and the process is described by an activation energy of 15.1 kcl/mole. Motion of folds on the surface of crystal lamellae is deemed to be the responsible mechanism for the β′ relaxation. Two models have been considered in the interpretation of the α process; rotation of crystalline chains in the vicinity of defects and rotational oscillation of restricted amplitude of all crystalline chains about the main chain axes. Rotation of amorphous chains is a possible mechanism for the γ process while motions of a general nature are responsible for the β relaxation. Our experimental results again indicate that spin diffusion plays an important role in the overall NMR response of the polymer.