Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Relation of the decay of free radicals in irradiated polyethylene to the molecular motion of the polymer and the configurations of the free radicals

Decay reactions of the free radicals produced in irradiated polyethylene (high-density and low-density materials) were examined in connection with the molecular motion of the matrix polymer. Three temperature regions, in which the free radicals decay very rapidly, at around 120, 200, and 250°K, were designated T_A, T_L, and T_B, respectively. The decay of the free radicals at these temperatures had activation energies in high-density polyethylene of 0.4 kcal/mole for T_A, 9.4 kcal/mole for T_L, and 18.4 kcal/mole for T_B. In low-density polyethylene these quantities were 0.7 kcal/mole for T_A, 23.1 kcal/mole for T_L, and 24.8 kcal/mole for T_B. Comparison of time constants for the decay reactions and for molecular motion of the matrix polymer indicate that the decay in T_A and T_B is closely related to molecular motion in the amorphous regions of the polymer. The decay of the free radicals at T_L in high-density polyethylene is due to molecular motion associated with local mode relaxation at lamellar surfaces, while that of low-density polyethylene is due to local mode relaxation in the completely amorphous region. Steric configurations of the free radicals which decay in the respective temperature regions were also investigated.     

Interpretation of NMR Relaxation as a Tool for Characterising the Adsorption Strength of Liquids inside Porous Materials

Nuclear magnetic resonance (NMR) relaxation times are shown to provide a unique probe of adsorbate–adsorbent interactions in liquid‐saturated porous materials. A short theoretical analysis is presented, which shows that the ratio of the longitudinal to transverse relaxation times (T₁/T₂) is related to an adsorbate–adsorbent interaction energy, and we introduce a quantitative metric e_surf (based on the relaxation time ratio) characterising the strength of this surface interaction. We then consider the interaction of water with a range of oxide surfaces (TiO₂ anatase, TiO₂ rutile, γ‐Al₂O₃, SiO₂, θ‐Al₂O₃ and ZrO₂) and show that e_surf correlates with the strongest adsorption sites present, as determined by temperature programmed desorption (TPD). Thus we demonstrate that NMR relaxation measurements have a direct physical interpretation in terms of the characterisation of activation energy of desorption from the surface. Further, for a series of chemically similar solid materials, in this case a range of oxide materials, for which at least two calibration values are obtainable by TPD, the e_surf parameter yields a direct estimate of the maximum activation energy of desorption from the surface. The results suggest that T₁/T₂ measurements may become a useful addition to the methods available to characterise liquid‐phase adsorption in porous materials. The particular motivation for this work is to characterise adsorbate–surface interactions in liquid‐phase catalysis.     

NMR spin–spin relaxation in solid and molten polyethylene structures

The NMR spin-spin relaxation (T₂) spectra of high-density polyethylene (PE) has been investigated over a wide range of temperatures, both in the solid and molten states. Previous work in these laboratories has shown that the T₂ relaxation spectrum of molten polyethylene differs from that of other polymers studied in that (a) it cannot be decomposed into two relaxation spectra (T_2S and T_2L) and (b) there is some evidence of a memory effect. This paper attempts to elucidate these observations, and compare them with the spin-spin relaxation of polyethylene at lower temperatures. In the solid state, the T₂ decay comprises both a Gaussian distribution for the crystalline region, and an exponential decay for the amorphous component. The effects of crystallization conditions and of temperature were determined. In the molten state the T₂ decay is more complex, but can be resolved into three exponentials. The longest (T_2L) component arises as expected from the most mobile, low molecular weight fraction. The T_2S component is due to an entangled but mobile network, as in other polymers. In addition, a short relaxation component T_2X is observed, which is influenced by previous crystallinity and the processing history of the material, and is ascribed to some vestigial degree of structure in the molten phase.     

Linear viscoelastic behaviour of complex polymeric materials: a fractional mode representation

A rheological constitutive equation for complex polymeric materials is derived starting from a special formulation of the relaxation function. This relaxation function contains six parameters and is divided into three regions: the plateau region, an intermediate power-law region and the terminal region of rapid stress decay. Material functions like the complex modulusG ^* and the logarithmic density function of the relaxation time spectrum H and of the retardation time spectrum L respectively are derived. Material parameters like the zero shear viscosity ₀ and the equilibrium shear complianceJ _e are also calculated. The comparison of the measured dynamic moduli of H-shaped polystyrenes, associating terminally functionalized polyisoprenes and randomly associating polybutadienes with the theoretical predictions of the proposed phenomenological model shows an excellent agreement.     

Nuclear magnetic relaxation and phase transitions of diethylene glycol in Vycor porous glasses

The times of longitudinal T ₁ and transverse T ₂ magnetic relaxation of protons of diethylene glycol in the bulk phase and in Vycor porous glasses with average pore radii of 4, 11, and 32 nm are measured by the pulse NMR method in the 172–350 K temperature range. It is found that, for all samples of porous glasses, the crystallization of diethylene glycol is not observed if its content corresponds to the monolayer surface filling. The minimum content of diethylene glycol, which makes it possible to cause its crystallization in porous glass, is determined. By analyzing the dependence of the characteristics of a component with T _2b = 20−40 μs in the transverse magnetization decay on the content of diethylene glycol in porous glasses, the volume of nanopores comparable in size with diethylene glycol molecule is estimated.     

A molecular approach to the spurt effect in polymer melt flow

The Doi-Edwards theory of polymer melts, extended to include relaxation processes associated with chain-length equilibration, is used to make quantitative predictions of a discontinuity in the flow curve of a monodisperse melt in a capillary. A fluid interface between regions of high and low deformation rates is found to propagate from the former into the latter. Our results for the “spurt” and its hysteresis compare favorably with experiment using a molecular weight dependence of the ratio of “reptation time” (T_d) to “equilibration time” (T_eq) in agreement with that determined from nonlinear stress relaxation.     

Solid-state 13C-NMR studies of the aging of poly(vinylidene fluoride)/poly(methyl methacrylate) blends

Solid state ¹³C-NMR was used to investigate the miscibility and subsequent separation of solution-cast blends of poly(vinylidene fluoride) (PVF₂) and poly(methyl methacrylate) (PMMA) with aging for a range of compositions. It was found that one amorphous phase and intimate mixing of the polymer chains in this phase existed for all compositions of the blends, even after 2 months of aging at room temperature as determined by the proton spin lattice relaxation time T_1ρH in the rotating frame, and the time constant T_CH for transfer of magnetization. The T_1ρH is sensitive to the spatial homogeneity of the blend via spin diffusion and would indicate the presence of phases or domains in the amorphous component of the blend larger than approximately 19 Å. The T_CH is proportional to the inverse sixth power of the interatomic distances needed for transfer of magnetization from proton to carbon and would be sensitive to a separation of polymer chains in the amorphous phase with aging on the order of 4–5 Å. There was an increase of the T_1ρH and T_CH values with aging, indicating that a subtle separation between unlike chains in the amorphous phase was occurring although a single amorphous phase was present.     

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 _⊥.     

The effect of degassing on the measurement of transverse relaxation times in molten polymers

Three commercially produced polymer samples (polyethylene, polypropylene, and polystyrene) have been analyzed in the melt state using proton nuclear magnetic resonance (NMR) T₂ relaxation methods using the Carr-Purcell-Meiboom-Gill (CPMG) spin-echo pulse sequence. Samples were run with exposure to air and again after extensive degassing at a vacuum of 10⁻⁴ mmHg for periods of not less than 96 h. The comparison is made by initially considering the presence of microscopic voids in the samples as a source of local field inhomogeneity and how they affect the T₂ relaxation behavior. For PP and PS samples, degassing caused a decrease in all T₂ time constants associated with the multicomponent decays. The component intensities each of the time constants was also significantly altered. For the PE sample, degassing caused a decrease in the time constants associated with the amorphous material in the molten polymer. Examination of the fastest relaxing component of the three component decay showed approximate invariance in the T₂ decay constant. This result supports our previously reported model in which that fast relaxing component is attributable to regions of local order or high segmental density within the molten polyethylene, a remnant of the crystalline material which exists in the premelting bulk polymer. The results of this research are of particular significance to those who wish to use this NMR technique as a quantitative method of determination of NMR distinct morphological regions within heterogeneous polymers. © 1996 John Wiley & Sons, Inc.     

FTIR spectroscopic and NMR studies of hard elastic polypropylene

The variation of amorphous orientation and crystalline regularity of hard elastic polypropylene (HEPP) films during cyclic deformation and stress relaxation processes were studied using a FTIR spectrometer. The result proves entropic elasticity and shows the orientational hysteresis in the amorphous region or within the microfibrils, and also shows that the amorphous orientation increases, but that the crystalline regularity decreases with the increase of extension rate.Three spin-spin relaxation timesT _2f,T _2m, andT _2s and associated mass fractionsF _f,F _m, andF _s of HEPP fibers were measured with a solid echo of NMR method at different elongations and after relaxation or recovery for a long time A new possible interpretation was proposed that, while the microfibrils are formed in HEPP, the medium decay component should be ascribed to inner molecules of the microfibrils, and the slow decay component to the surface molecules of the microfibrils. According to this interpretation, the results implied that subfibrillation is the main process when HEPP is stretched up to 15% strain, and that at above 15% strain thinning and lengthening of the microfibrils become the main process. Thickening of the microfibrils was found in the recovery and relaxation processes.     

Dielectric relaxation and glass transition temperature of copolymers

Dielectric relaxation measurements were made on methyl methacrylate—styrene and methyl methacrylate–p-chlorostyrene copolymers at temperatures higher than the glass transition temperature T_g. It was found that the temperature dependence of the relaxation time can be described satisfactorily by an expression derived recently for chain motion in amorphous polymers. The temperature T_g obtained from the expression agrees well with that determined by differential thermal analysis.     

Studies on crude oil‐water biphasic mixtures by low‐field NMR

Low‐field ¹H NMR was used in this work for the analysis of mixtures involving crude oils and water. CPMG experiments were performed to determine the transverse relaxation time (T₂) distribution curves, which were computed by the inverse Laplace transform of the echo decay data. The instrument's ability of quantifying water and petroleum in biphasic mixtures following different methodologies was tested. For mixtures between deionized water and petroleum, one achieved excellent results, with root mean squared error of cross‐validation (RMSECV) of 0.8% for a regression between the water content (wt %) and the relative area of the water peak in the T₂ distribution curve, or a standard deviation of 0.9% for the relationship between the water content and the relative water peak area, corrected by the relative hydrogen index of the crude. In the case of biphasic mixtures of Mn²⁺‐doped water and crude oils, the best result of RMSECV = 1.6% was achieved by using the raw magnetization decay data for a partial least squares regression. Copyright © 2012 John Wiley & Sons, Ltd.     

Carbon-13 NMR of polyethylenes: Correlation of the crystalline component T1 with structure

The carbon-13 spin-lattice relaxation times T₁ of the crystalline portion of a set of polyethylenes have been studied. Chain structure and crystallization conditions have been varied over the widest possible extremes so that large differences are developed in the level of crystallinity, the supermolecular structure, and the crystallite thickness. Concomitantly, the observed crystalline T₁ values cover the extraordinarily wide range of about 40–4500 s. They bear a one-to-one relation with the crystallite thickness, which is found to be the key structural variable determining this property. A correlation with the temperature for the α-transition can be established, which implies a similar type of segmental motions for the two phenomena. Major changes in the interfacial structure can also have a drastic influence on the value for the crystalline T₁. Analysis of the magnetization decay curve also allows for a quantitative determination of the degree of crystallinity, which is found to be in excellent agreement with the corresponding value found from Raman spectroscopy.     

Atomic level picture of stress relaxation in polymer melts

We have been developing a physical picture on the atomic level of stress relaxation in polymer melts by means of computer simulation of the process in model systems. In this article we treat a melt of freely jointed chains, each with N = 200 bonds and with excluded-volume interactions between all nonbonded atoms, that has been subjected to an initial constant-volume uniaxial extension. We consider both the stress relaxation history σ(t) based on atomic interactions, and the stress history σ_e(t; N_R) based on subdividing the chain into segments with N_R bonds each, with each segment regarded as an entropic spring. It is found that at early times σ(t) > σ_e(t; N_R) for all N_R, and that, for the remainder of the simulation, there is no value of N_R for which σ(t) = σ_e(t; N_R) for an extended period; by the end of the simulation σ(t) has fallen just below the value σ_e(t; 50). The decay of segment orientation, 〈P₂(t; N_R)〉, and of bond orientation 〈P₂(t; 1)〉, is computed during the simulation. It is found that the decay of the atom-based stress σ(t) is closely related to that of 〈P₂(t; 1)〉. This result may be understood through the concept of steric shielding. The change in local structure of the polymer melt during relaxation is also studied. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 143–154, 1998     

How does tack depend on time of contact and contact pressure?

The tack of polymer melts on rigid substrates under conditions of short contact times and low pressures is examined. The substrate is modeled as a random rough surface with a distribution of asperities heights. The true contact area between the adhesive and the substrate is calculated for a given total load and elastic modulus of the substrate. The dependence of tack on contact time is accounted for by introducing the relaxation of the adhesive through a time-dependent elastic modulus. For relatively high pressures the tack is predicted to scale with 1/E so that for short contact times, t_c, the tack is predicted to scale with (t_c/τ_e)^1/2, where τ_e is the entanglement time. For lower pressures this simple scaling law is no longer valid and we predict a complex variation of tack with contact time and molecular parameters. © 1996 John Wiley & Sons, Inc.     

Intra- and inter-chain fluctuations in entangled polymer melts in bulk and confined to pore channels

It is known that topological restraints by “chain entanglements” severely affect chain dynamics in polymer melts. In this field-cycling NMR relaxometry and fringe-field NMR diffusometry study, melts of linear polymers in bulk and confined to pores in a solid matrix are compared. The diameter of the pore channels was 10 nm. It is shown that the dynamics of chains in bulk dramatically deviate from those observed under pore constraints. In the latter case, one of the most indicative signatures of the reptation model is verified 28 years after its prediction by de Gennes: The frequency and molecular mass dependencies of the spin-lattice relaxation time obey the power law T_! ∝ M⁰ v^3/4 on a time scale shorter than the longest Rouse relaxation time τ_R. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r²>∝ M^−1/2t^1/2 predicted for τ_R < t < τ_d, where τ_d is the so-called disengagement time. Contrary to these findings, bulk melts of entangled polymers show frequency and molecular mass dependencies significantly different from what one expects on the basis of the reptation model. The data can however be described with the aid of the renormalized Rouse theory.     

Quantitative nuclear magnetic resonance imaging of liquids in swelling polymers

The variation of nuclear magnetic resonance (NMR) relaxation parameters (T₁, T₂) within a polymer during swelling, limits the absolute accuracy with which liquid concentration profiles can be obtained using NMR imaging. In this article a study of the diffusion of decalin into ultra-high molecular weight polyethylene (UHMWPE) is reported. The study illustrates the use of a method of analysis whereby quantitative solvent profiles can be obtained from data influenced by both T₁ and T₂ contrast effects. A T₁ and T₂ map are obtained at a point in the uptake of liquid where the greatest range in liquid concentration is obtained at a point in the uptake of liquid where the greatest range in liquid concentration is observed. The intensity of signal corresponding to liquid in the polymer is compared to that of pure liquid in a reference sample, and correlations for T₁ and T₂ values versus signal intensity are used to deconvolve relaxation contrast, to yield the true liquid concentration. The technique was used to study the effect of degree of crosslinking of UHMWPE on the swelling kinetics and decalin transport within the polymer. A spin-echo imaging technique was used with a recycle delay approximately equal to the average spin-lattice relaxation time of the liquid, and an echo time approximately half the average spin-spin relaxation time. Under these conditions the relaxation contrast was significant, yet the mass uptake data derived from the concentration profiles obtained, using the method of analysis described, agreed well with gravimetric data. © 1995 John Wiley & Sons, Inc.     

A Nuclear Singlet Lifetime of More than One Hour in Room‐Temperature Solution

Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are supremely important techniques with numerous applications in almost all branches of science. However, until recently, NMR methodology was limited by the time constant T₁ for the decay of nuclear spin magnetization through contact with the thermal molecular environment. Long‐lived states, which are correlated quantum states of multiple nuclei, have decay time constants that may exceed T₁ by large factors. Here we demonstrate a nuclear long‐lived state comprising two ¹³C nuclei with a lifetime exceeding one hour in room‐temperature solution, which is around 50 times longer than T₁. This behavior is well‐predicted by a combination of quantum theory, molecular dynamics, and quantum chemistry. Such ultra‐long‐lived states are expected to be useful for the transport and application of nuclear hyperpolarization, which leads to NMR and MRI signals enhanced by up to five orders of magnitude.