Effect of Molecular Weight on Enthalpy Relaxation in Syndiotactic Poly(Methyl-Methacrylate)

The structural relaxation behaviour of narrow fractions (M_w/M_n < 1.1) of syndiotactic poly(methyl methacrylate) with molecular masses ranging from 2,000 to 200,000 Daltons have been studied by DSC with two classical procedures, namely: the rate of cooling and the isothermal approaches. The apparent activation energy (Δh*) of enthalpy relaxation was evaluated from the dependence of the glass transition temperature on the cooling rate while a comparison of the apparent relaxation rates was appraised from the enthalpy loss by annealing the different samples at the same level of undercooling (T_a = T_g − 10 °C). As expected, the increase of molecular weights gives rise to both a continuous increase of Δh* and a decrease of the apparent isothermal relaxation rate. More interestingly, both Δh* and the apparent isothermal relaxation rate showed abrupt changes around the syndiotactic PMMA entanglement mass (M_e ).     

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.     

On the theory of the effective nuclear magnetic relaxation time T2e and its application to polymer melts

A general expression for the magnetization decay of a multipulse group is derived. This formula is applied to a three-component model of molecular motions in polymer melts. The influence of the several components on the magnetization decay is discussed. The relation of the effective nuclear magnetic relaxation time T_2e to the Anderson-Weiss formula is also shown, and an analytical expression for the transverse relaxation in melts is derived. Finally T_2e is compared with the relaxation time in the rotating frame T_1ρ in the melt. The theoretical results for T_2e are tested with measurements of frequency dependence in polyethylene melts.     

A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes

We report measurements of the nonlinear relaxation moduli after a step-shear strain of polystyrene solutions with nearly monodisperse and with bidisperse distributions of molecular weight. We find, as have others, that for monodisperse solutions with M/M_e > 60, there are anomalies, such as an unusually low nonlinear modulus and a kink in a plot of shear stress versus time after the step strain. Here M is the polymer molecular weight and M_e is the entanglement molecular weight. We find that in the bidisperse solutions the anomalies persist as long as M_w/M_e > 60, where M_w is the weight-averaged molecular weight of the bidisperse solution. The persistence of the anomalies in bidisperse solutions disagrees with a theory of Marrucci and Grizzuti that attributes the anomalies to strain inhomogeneities similar to shear banding. The Marrucci-Grizzuti theory predicts that as little as 10% short chains in the bidisperse mix should eliminate the anomalies, whereas in the experiments reported here at least 30% is required. Nevertheless the way in which the anomalies disappear at high strains when one increases the fraction of low-molecular-weight component is qualitatively similar to the theoretical predictions and supports the notion that strain inhomogeneities occur in these systems. © 1992 John Wiley & Sons, Inc.     

13C and1H NMR study of molecular motion in the deoxycholic acid-ferrocene solid inclusion compound

Using solid-state ¹³ C NMR spectroscopy and also measurements of proton spin-lattice relaxation times T ₁ and second moments M ₂ , we have investigated molecular motion in solid inclusion compounds of deoxycholic acid with ferrocene in the interval 100–400 K. We have identified various dynamic processes occurring with participation of molecules of the matrix and the included molecules. We have shown that in addition to rapid reorientations of the cyclopentadienyl rings, the ferrocene molecules undergo 180° jumps about the C ₂ axis. We have determined the parameters for all the molecular motions. We discuss the conformational state of the included molecules.A. N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences, Moscow 117813. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 586–593, March, 1992.     

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     

High-resolution solid-state 13C NMR study of ethylcellulose films

Ethylcellulose films cast from concentrated solutions of chloroform, benzene, and carbon tetrachloride were subjected to the NMR relaxation measurements including ¹H spin-lattice relaxation time (T_1H), rotating-frame ¹H spin-lattice relaxation time (T_1ρH), and ¹³C spin-lattice relaxation time (T_1C). The values of T_1ρH for carbons in the glucose units of ethyl-cellulose were of the same order of magnitude as those reported for the crystalline and noncrystalline regions of ramie cellulose. The values of T_1C for unsubstituted C2, C3 carbons were smaller than those for the corresponding carbons in the noncrystalline region of native celluloses. The T_1C values for unsubstituted C2, C3, and substituted C6 carbons showed a small but definite dependence on the solvent from which the films were cast. © 1993 John Wiley & Sons, Inc.     

Evidence of two relaxation processes in the photon correlation spectra of poly(methyl methacrylate) above Tg

Photon correlation functions of a high-molecular-weight PMMA (M_w = 1.06 × 10⁷, M_n = 2.2 × 10⁶, T_g = 103°C) have been studied in the temperature range 98 ? 149°C. In contrast to previous results, two relaxation modes are observed in relaxation functions. The observed relaxation functions of PMMA are analyzed for the first time in terms of a continuous spectrum representing the distribution of retardation times. Using a modified computer program originally developed by Provencher, we have computed the spectrum of retardation times at various temperatures. The appearance of two distinct relaxation modes is clearly evident in the distribution of the retardation times and in the time correlation functions below 123°C.     

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.     

Investigation on the dynamics of aromatic polyesters by means of high resolution solid state CPMAS 13C NMR

The dynamics of amorphous aromatic polyesters consisting of poly(ethylene terephthalate) (PET), poly(ethylene isophthalate) (PEI), and poly(ethylene 2,6-naphthalenedicarboxylate) (PEN) has been investigated by means of solid state CPMAS ¹³C NMR. Proton T₂, ¹³C T_1ρ, and proton T_1ρ decays have been measured in particular, and the experimental data fitted to suitable model functions to determine best relaxation parameters. The fitting results show for proton T₂ and ¹³C T_1ρ measurements the presence of two components with different relaxation times and intensities, arising from different motional domains. The proton T_1ρ, on the contrary, shows a single component which limits the dimensions of the two regions to less than 20 Angstroms. The dependence of ¹³C T_1ρ values on two different irradiating field strengths (H₁ = 38 KHz, H₁ = 60 KHz) allowed the assignment of each component to relatively rigid and mobile regions. By comparing the three polymers we observe that PEN and PEI have a similar relaxation behavior, while a higher fraction of mobile components was found for PET. These differences are believed to arise mainly from local motions of the aromatic rings. The relaxation measurements have been evaluated to suggest a correspondence to O₂ and CO₂ gas permeabilities in PET, PEI, and PEN. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1557–1566, 1998     

Systematic Dielectric and NMR Study of the Ionic Liquid 1‐Alkyl‐3‐Methyl Imidazolium

The dynamic behaviors of ionic liquid samples consisting of a series of 1‐alkyl‐3‐methylimidazolium cations and various counteranionic species are investigated systematically over a wide frequency range from 1 MHz to 20 GHz at room temperature using dielectric relaxation (DR) and nuclear magnetic resonance (NMR) spectroscopies. DR spectra for the ionic liquids are reasonably deconvoluted into two or three relaxation modes. The slowest relaxation times are strongly dependent upon sample viscosity and cation size, whereas the relaxation times of other modes are almost independent of these factors. We attribute the two slower relaxation modes to the rotational relaxation modes of the dipolar cations because the correlation times of the cations evaluated using longitudinal relaxation time (T₁ ¹³C NMR) measurements corresponded to the dielectric relaxation times. On the other hand, the fastest relaxation mode is presumably related to the inter‐ion motions of ion‐pairs formed between cationic and anionic species. In the case of the ionic liquid bis(trifluoromethanesulfonyl)imide, the system shows marked dielectric relaxation behavior due to rotational motion of dipolar anionic species in addition to the relaxation modes attributed to the dipolar cations.     

Strain criterion in nonlinear creep and recovery in concentrated polymer solutions

Transient and steady-state rheological data are reported for several anionic polystyrene solutions in tritolylphosphate (1. 6 < cM/ρM_c < 7). Here c is the concentration of the solution, M is the molecular weight, ρ the density of the undiluted polymer, and M_c the molecular weight between entanglements as determined from zero-shear viscosity. The polystyrene used had M_w = 410,000 and M_w/M_n < 1.06. Data are also given for solutions of polyisobutylene and poly(vinyl acetate) with larger M_w/M_n. The results give a critical strain γ′ ∝ c⁻¹ such that linear viscoelastic behavior was obtained in a simple shear deformation with shear less than γ′. A simplified version of the constitutive equation of Bernstein, Kearsley, and Zapas is used with an empirical strain function F (γ) which contains γ′ as a parameter to discuss transient and steady-state behavior in terms of the distribution of relaxation (or retardation) times determined for linear viscoelastic responce. Features of the dependence of the steady-state viscosity η_k, recoverable compliance R_k, the first-normal stress function N_k⁽¹⁾ on shear rate k are discussed in terms of F (γ) and the distribution of relaxation times to conclude that the latter plays a dominant role in the behavior observed in the range of k usually studied. The results predict that the reduced functions η_k/η₀, R_k/R₀, and N_k⁽¹⁾/N₀⁽¹⁾ should depend on η₀R_0k, and that the functional form depends markedly on the distribution of relaxation times, at least in the range η₀R₀k < 10². Comparison with the mechanistic model of Doi and Edwards shows a similar F (γ) but substantial differences in the reduced functions caused by a very narrow distribution of relaxation times in the model.     

Nuclear relaxation in atactic polystyrenes: T1 and T1ρ measurements

Measurements have been made on a series of linear atactic polystyrenes whose molecular weights range from 900 to 1.8 × 10⁶, where M _w/M _n ? 1.2. Spin lattice relaxation times have been measured in the laboratory frame (T₁) and in the rotating frame (T_1ρ) in the temperature range 90–500°K. Two major relaxation minima were observed in both sets of measurements. The high temperature process corresponds to the glass transition (α process), the position of the minimum depending on the chain length. The low temperature process appears to originate from the n-butyl endgroups in the polymer, its position being independent of chain length while its intensity is inversely proportional to molecular weight. No other minima were observed, in contrast to some other observations made by broadline and pulsed NMR techniques. Relaxation was exponential in all cases except in the region of the high temperature T_1ρ minimum and above. This nonexponential behavior is possibly connected with the transition at T > T_g observed by a number of other techniques and which is thought to correspond to a transition between two types of liquid state. A correlation frequency diagram has been drawn for all the processes observed in polystyrene by other techniques, (α, β, αβ, γ, and δ) which shows that the T₁ and T_1ρ minimum positions correlate well with the α process and that there is a possible contribution to the relaxation due to the γ process on the low temperature side of the α process. At these measurement frequencies the α and β processes are merged into an αβ process. There is no evidence for a contribution from the mechanical δ process. The effect of the endgroups is observed to very high molecular weights (4.98 × 10⁵), and it seems that a three-dimensional diffusion model would be more adequate than the one-dimensional model used to interpret similar behavior of paraffins and polyethylenes. Measurements of T₁ in the low-temperature region would constitute a method for a rough measurement of the molecular weight of these polymers.     

Enthalpy relaxation of low molecular weight amorphous styrene oligomers measured with an adiabatic calorimeter

Herein, we measured the enthalpy relaxation of three styrene oligomers with different molecular weights (styrene oligomer with M_w?=?4.53?×?10²: PSA-300, styrene oligomer with M_w?=?5.89?×?10²: PSA-500, and styrene oligomer with M_w?=?1.01?×?10³: PSA-1000) near their respective glass transition temperatures (T_g) using an adiabatic calorimeter. We determined the relaxation rates and the amounts of configurational enthalpy released from the temperature dependence of the temperature drift rates around T_g. Based on our experimental findings, we found the amounts of configurational enthalpy release per monomer unit to be 0.8, 3.5, and 1.6 kJ mol^?1 for PSA-300, PSA-500, and PSA-1000, respectively. These values were 3.9–18 times larger than that of glycerol, which is a typical glass-forming liquid.

     

Dynamic light scattering from bulk poly(n-hexylmethacrylate) near and above the glass transition

Photon correlation spectra of polarized scattered light from poly(n-hexylmethacrylate) PHMA (M_w = 1.6·10⁵, T_g = ?5°C) have been studied in the temperature range of ?2–25°C. The experimental time correlation functions over the time range 10^?6?10² s were represented by the Kohlrausch-Williams-Watts (KWW) function exp{?(t/τ)^β} with a virtually temperature-independent distribution parameter β = 0.27 ± 0.02. The observed relaxation functions were also analyzed in terms of a continuous distribution of retardation times L(τ) by means of a direct inverse Laplace transformation. The computed L(τ) distributions reveal a broad single peak structure in agreement with the results of the single KWW fit. The temperature dependence of τ is very similar to that of the shift factors obtained from measurements of the shear modulus and the stress relaxation modulus in the glass-rubber region. Conversely, the values of τ compare well with those extracted from the experimental dielectric loss peaks consistently represented in the time domain by the KWW function. These findings suggest that the slow density fluctuations in bulk PHMA are associated with the primary glass-rubber or α-relaxation, which, however, displays an unusual low apparent Arrhenius activation energy and a rather low β value. PHMA exhibits significant dynamic light scattering with correlation times faster than 10^?6 s near T_g. © 1992 John Wiley & Sons, Inc.     

Simultaneous measurements of T1 and T2 during fast polymerization reaction using continuous wave‐free precession NMR method

Continuous wave‐free precession (CWFP) pulse sequence employing time domain nuclear magnetic resonance spectroscopy (TD‐NMR) was used to measure longitudinal (T₁) and transverse relaxation times (T₂), during the cure of a commercial epoxy resin (Araldite^TM) with a 10‐min solidification time. The intensity of the NMR signal after the first pulse and in the CWFP regime were used to monitor the concentration of the monomers, and the relaxation times were used to monitor the chain mobility. The main advantage of CWFP over the standard methods to measure relaxation times, inversion recovery (inv‐rec) for T₁ and Carr‐Purcell‐Meiboom‐Gill (CPMG) for T₂, is that the measurement of both relaxation times can be performed in a fast and single NMR experiment and, therefore, using a single reaction batch. CWFP is also as fast as the CPMG measurement but at least fivefold faster than the method to obtain T₁ using null point approximation in the inv‐rec method. Therefore, the CWFP sequence can be used as a fast and general method to measure relaxation times in polymerization reactions, even with fast solidification time. As a TD‐NMR technique, CWFP can be employed in any low‐cost bench top TD‐NMR equipment commonly used in an academic or industrial laboratory. Copyright © 2012 John Wiley & Sons, Ltd.     

Dispersion of T1 and T2 Nuclear Magnetic Resonance Relaxation in Crude Oils

Crude oils, which are complex mixtures of hydrocarbons, can be characterized by nuclear magnetic resonace diffusion and relaxation methods to yield physical properties and chemical compositions. In particular, the field dependence, or dispersion, of T₁ relaxation can be used to investigate the presence and dynamics of asphaltenes, the large molecules primarily responsible for the high viscosity in heavy crudes. However, the T₂ relaxation dispersion of crude oils, which provides additional insight when measured alongside T₁, has yet to be investigated systematically. Here we present the field dependence of T₁‐T₂ correlations of several crude oils with disparate densities. While asphaltene and resin‐containing crude oils exhibit significant T₁ dispersion, minimal T₂ dispersion is seen in all oils. This contrasting behavior between T₁ and T₂ cannot result from random molecular motions, and thus, we attribute our dispersion results to highly correlated molecular dynamics in asphaltene‐containing crude oils.     

Polyisobutylene: A most unusual polymer

The influence of molecular weight, M, on the fragility and fast dynamics in polyisobutylene (PIB) was studied using dielectric and mechanical relaxation spectroscopies, calorimetry, and Raman spectroscopy. The measurements indicate a decrease in fragility with increasing M for shorter chains, in the range of M where T_g is M‐dependent. Such behavior is not observed for other polymers and is at odds with traditional theoretical models that predict an increase in fragility with chain length. These results confirm the unusual character of PIB, as evident in various properties including extremely low gas permeability, a low fragility, and a segmental relaxation spectrum much broader than expected for a low‐fragility material. The reason for this anomalous behavior remains unclear, but might be related to the symmetric structure of the PIB repeat unit, together with comparable flexibility of both structural components, the backbone and side groups. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1390–1399, 2008     

Relaxation dynamics of salt‐free polyelectrolyte solutions using flow birefringence and rheometry

Relaxation dynamics of salt‐free, aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) were investigated by mechanical rheometry and flow birefringence measurements. Two semidilute concentration regimes were studied in detail for a range of polymer molecular weights. At solution concentrations c < 10 mg mL, limiting shear viscosity η₀ was found to scale with molecular weight and concentration as η₀ ∼ c^0.5M_w over nearly two decades in concentration. At higher solution concentrations, c > 10 mg mL, a change in viscosity scaling was observed η₀ ∼ c^1.5M, consistent with a change from simple Rouse dynamics for unentangled polyions to near‐perfect reptation dynamics for entangled chains. Characteristic relaxation times τ deduced from shear stress and birefringence relaxation measurements following start‐up of steady shearing at high rates reveal very different physics. For c < 10 mg mL, both methods yield τ ∼ c^−0.42M and τ ∼ c⁰M for c > 10 mg mL. Curiously, the concentration scalings seen in both regimes are consistent with theoretical expectations for salt‐free polyelectrolyte solutions undergoing Rouse and reptation dynamics, respectively, but the molecular weight scalings are not. Based on earlier light scattering studies using salt‐free NaPSS solutions, we contend that the unusual relaxation behavior is likely due to aggregation and/or coupled polyion diffusion. Simultaneous stress and birefringence measurements suggest that in concentrated solution, NaPSS aggregates are likely well permeated by solvent, supporting a loose collective of aggregated chains rather than the dense polymer aggregates previously supposed. Nonetheless, polyion aggregates of either variety cannot account for the inverse dependence of relaxation time on polymer molecular weight for c < 10 mg mL. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 825–835, 1999