The chain length dependence of self-diffusion in melts of polyethylene and polystyrene

The self-diffusion coefficients in melts of polyethylene fractions and polystyrene standards were measured by the NMR pulsed field gradient technique and compared with those measured by other techniques. The data agree very well if one takes into account the molar mass distribution of the samples and the free volume of the matrix. For molar masses much higher than the critical molar massM _c, reptation is confirmed,D M ^–2 holds. BelowM _e=M_c/2 the self-diffusion coefficients corrected for constant free volume show approximately the dependenceD M ^–1 confirming Rouse-like diffusion. This result was also obtained by investigating the self-diffusion of the molecules with different molar masses of a polyethylene fraction with a rather broad molar mass distribution aroundM _e andM _c, i. e. diffusion in a constant matrix. In the molar mass region betweenM _c and about 3 ·M _c the observed molar mass dependence of self-diffusion can be explained by tube formation. The constraint release model of Graessley seems to slightly overestimate the self-diffusion coefficients.     

Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers

The crossover from linear to branched polymer dynamics in highly entangled melts was investigated with a series of asymmetric three-arm stars of poly(ethylene-alt-propylene). Two arms of equal length formed a linear backbone, kept constant through the series, while branches of various length were appended as the third arm. The materials were made by carbanionic polymerization of isoprene and the judicious application of chlorosilane linking chemistry. Subsequent saturation of the polymeric double bonds with deuterium and hydrogen, followed by fractionation, led to a set of structurally matched, nearly monodisperse pairs of deuterium-labeled and fully hydrogenous samples. Dynamic moduli were measured over wide ranges of frequency and temperature. With increasing branch length, the resulting master curves evolve smoothly, but with surprising rapidity, from the relatively narrow terminal spectrum of linear polymers to the much broader spectrum of symmetric stars. The viscosity η_o increases rapidly with branch length, and the diffusion coefficient D, obtained by forward recoil spectrometry, decreases even more rapidly. The product η_oD, however, distinguishes the transition from linear to branched polymer dynamics most clearly: for a backbone with about 38 entanglements, the crossover is already approaching completion for a single mid-backbone branch with only about three entanglements. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1943–1954, 1997     

Effect of bending and torsion rigidity on self-diffusion in polymer melts: a molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for NNe (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for NNe. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.     

NMR self-diffusion studies in heterogeneous systems

The principles and main limitations of the application of the NMR field gradient technique to self-diffusion measurements are discussed. Due to their higher sensitivity for small diffusion coefficients and due to several advantages with the analytical treatment of the experimental data, the pulsed gradient methods are of special importance for the investigation of heterogeneous systems. Examples of the application of these techniques to diffusion studies in multicomponent systems and bounded media are given.     

NMR relaxation and pulsed-gradient diffusion study of polyethylene nanocomposites

We performed pulsed-gradient spin-echo nuclear-magnetic-resonance (NMR) experiments on zinc oxide filled polyethylene. The molecular weights of the polyethylene samples ranged between 808 and 33,000 gmol, and four different zinc oxide samples were used: 27-, 33-, 51-, and 2500-nm-diameter particles. The results of these experiments showed that the diffusion coefficients of the polyethylene chains did not change with nanofiller content, but a drastic change is observed in the NMR relaxation spectrum in spin-spin-relaxation experiments. At fixed zinc oxide content and polyethylene molecular weight (close to entanglement), the system with the smallest zinc oxide showed the most rigid environment. At high polyethylene molecular weights, this effect was still observable but the difference between the three investigated systems was very small, suggesting that the system was dominated by entanglements.     

Viscoelastic properties of branched polyethylene melts

The dynamic mechanical properties of branched polyethylenes in the molten state were determined in the frequency range 10^?3–10 radians/sec. The materials tested have remarkably similar rheological properties even though they vary greatly in molecular weight and molecular weight distribution. The similarity in properties is attributed to the influence of long chain branching on the relaxation spectra. A mechanistic argument is proposed to relate the observed behavior to molecular entanglement coupling. The concept of entanglement coupling involving long-chain branching leads to the expectation that the quasi-Newtonian and non-Newtonian viscosities of branched polymers may be either greater or less than those of linear polymers of the same species, which have comparable molecular weights. This is borne out by experiment.     

Viscoelastic behavior of linear polyethylene and of paraffin mixtures

Summary The complex shear modulus of a linear polyethylene (Marlex 50), of which samples were either crystallized from the melt at various temperatures or precipitated from a dilute xylene solution, has been measured as a function of temperature at fixed frequencies between 10⁵ and 10^–1 c/s. The three relaxation regions, , can be distinguished, and activation energies are determined from the relaxation map. The-process shows a frequency-temperature characteristic which has been divided into three parts _I, _II, _III. Further experimental evidence for the kink model, proposed in an earlier paper (reference 4) is taken from the investigation of suitable paraffin mixtures. Measurements on six n-alkane systems, each consisting of an even n-paraffin mixed with a few percent of a paraffin with a chain longer by two C-atoms, are reported.

---

Zusammenfassung Es wurde die TemperaturabhÄngigkeit des komplexen Schubmoduls eines linearen PolyÄthylens (Marlex 50) bei festen Frequenzen zwischen 10^–1 und 10⁵ Hz untersucht, wozu die Proben entweder aus der Schmelze bei verschiedenen Temperaturen kristallisiert oder aus verdünnter Xylollösung bei 80 C gefÄllt, in Methanol ausgewaschen und gepre\t worden waren. Drei Dispersionsgebiete, , können unterschieden werden. Die/max-1/T- Charakteristik des -Relaxations-prozesses wird in drei Bereiche _I, _II, _III unterteilt. Aktivierungsenergien werden aus geradlinigen Kurvenstücken dieser Charakteristiken bestimmt.Eine erneute experimentelle Stütze für das in einer früheren Arbeit (4) vorgeschlagene Kinkenmodell stellen Messungen an 6 weiteren n-Paraffin-Mischungssystemen dar, wobei die KettenlÄngen der Mischungspartner sich jeweils um zwei CH₂-Gruppen unterscheiden.

---

---

Parts of this paper were read at the 4th International Congress on Rheology, Providence R. I., 1963.     

NMR study of diffusion of butane in linear polyethylene

The diffusion coefficient of butane in linear polyethylene at room temperature as a function of the vapor pressure of butane was measured by the spin-echo method with a pulsed magnetic field gradient. For the Special morphology of randomly oriented stacks of parallel lamellas the detour factor is 1/3. As long as the blocking factor and migration through the lamellas can be neglected, the local diffusion coefficient D_a of the small molecules through the amorphous layers in the direction parallel to the lamellas is three times the apparent diffusion coefficient D derived from the decay of the amplitude of the spin echo under the assumption of an infinitely extended homogeneous medium. The diffusion coefficient and the spin–spin relaxation time both increase exponentially with increasing pressure, i.e., butane concentration in the polymer, while the spin-lattice relaxation time is pressure independent and seems to be determined by interaction with the amorphous polyethylene matrix.     

Network fraction and molecular motions in polymer composites: An NMR relaxation and self-diffusion study

We have used NMR T₂ relaxation and pulsed-gradient spin-echo diffusion techniques to study properties of Arco R45M hydroxyl-terminated polybutadiene, either unfilled or containing 65 wt.% filler particles (SiO₂, NaCl, Al) and cured with isophorone diisocyanate (IPDI), as functions of IPDI content. A short T₂ relaxation component arises from the network (gel) whose amount is greatest (up to 92%) near NCO/OH stoichiometry. Gel fraction and stoichiometry concentration both are affected slightly by filler surface reactivity but principally by filler particle size. The diffusion rate of the nonnetwork (sol) molecules has a range of 1–2 orders of magnitude. This range is narrowest near stoichiometry for the smallest filler (SiO₂), i.e., the situation in which the sol molecules are least mobile. Branching theory and the hypothesis of a layer of reduced mobility in a wide vicinity of the filler particles provides semiquantitative explanations of these observations.     

NMR measurement of self-diffusion coefficients by slice selection

Most of the time, so-called inversion-recovery experiments concern longitudinal nuclear magnetization of the whole sample, the region of interest being limited by the transmitting-receiving coil. Here we address the question of what occurs if the region of interest is purposely limited to a thin slice selected by means of procedures employing magnetic field gradients. Gradients of both magnetic fields (B(0), the static magnetic field, and B(1), the radio-frequency magnetic field) can be used. In this study we resorted essentially to B(1) gradients and novel procedures, based on the natural inhomogeneity of the B(1) field delivered by a saddle coil, are described. It is obvious that molecules leaving and entering the slice during the evolution (recovery) period should influence the magnetization recovery. Molecular self-diffusion is responsible for such effects, experimentally visible and accounted for by an appropriate theory which has been approximated for by permitting an easy physical assessment. This approach should lead to alternative methods for measuring self-diffusion coefficients.     

A 13C CP-MAS NMR study of irradiated polyethylene

Solid-state ¹³C-NMR was used to analyze several polyethylene samples, irradiated at room temperature with gamma rays in vacuum or with electrons in air up to a maximum dose of 200 Mrad. The main observed events were the formation of methyl ends and interior double bonds (vinylenes), as well as the disappearance of the initial vinyl ends. No signals associated with “H” or “Y” crosslinks were found in any of the samples. The partitioning of methyl ends and interior vinylenes between the crystalline and noncrystalline regions was determined only for the irradiated ultrahigh-molecular-weight polyethylene (UHMWPE) samples. Although concentration of methyl ends in the crystalline regions was approximately half that in the noncrystalline regions, the vinylenes had very similar concentrations in the two phases. Although some evidence for both cis and trans vinylenes appears in the spectrum of the noncrystalline regions, only one configuration (trans) seems to exist in the crystalline regions. No appreciable effect on the partitioning was detected after annealing the electron-irradiated UHMWPE samples for 16 h at 130°C.     

NMR study of polyethylene crystallization kinetics under high pressure

Crystallization of polyethylene under hydrostatic pressures of 1–4.5 kbar is directly observed using pulsed proton NMR. The rate of growth of extended-chain polyethylene crystals is measured over this pressure range and to a maximum temperature of 227°C. The observed crystallization isotherms are superimposable on a log time scale; this implies a consistent mechanism for extended-chain growth over this pressure range. Avrami coefficients for high-pressure extended-chain crystallization are determined to be 1.3–1.7. A decrease of crystal nucleus surface free energies with increasing pressure is indicated. Findings are consistent with Wunderlich's model of initial folded-chain crystallization followed immediately by chain extension. Future applications of this NMR technique are briefly considered.     

Characterization of elongation viscosity for polyethylene melts

Elongation viscosity is an important characterization of flow properties for polymer melts. In the present article, a new extensional viscosity equation for polymer melts was established by introducing a relaxation time equation based on the Cross model. The elongation viscosities of a low-density polyethylene (LDPE) melt at 200 °C and a metallocene linear low-density polyethylene (mLLDPE) melt at 130 °C were estimated using this equation; then, the calculations of the melt elongation viscosity were compared with the measured data from the extension experiments of the LDPE melt and the mLLDPE melt reported in the reference. Good agreement was found between the predictions and the measured data from the LDPE and mLLDPE melts. In addition, this equation is easy to use for characterization of elongation viscosity during single shaft elongation flow for polymer melts.     

Fast emulsion droplet sizing using NMR self-diffusion measurements

Emulsion droplet sizing using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) is a well-established technique. Traditionally these measurements require total acquisition times of typically 5-20 min per sample, which severely limits our ability to use this method to study dynamic processes. Here we present the application and verification of an NMR pulse sequence, Difftrain, which enables emulsion droplet size distributions to be measured in 3-10 s. We have previously introduced applications of Difftrain (C. Buckley, K.G. Hollingsworth, A.J. Sederman, D.J. Holland, M.L. Johns, L.F. Gladden, J. Magn. Reson. 161 (2003) 112-117), including the droplet sizing of a single unimodal emulsion sample. In this paper, several model emulsions containing different oils are measured and the results compared directly with sizing provided by laser scattering. In this manner, the Difftrain method is verified and its possibilities and limitations are explored. Guidelines are proposed for the range of droplet sizes for which accurate results can be produced. The Difftrain technique opens up the possibility of studying non-equilibrium emulsions; a study of the in situ emulsification of a 21% v/v water-in-silicone oil emulsion is presented.     

NMR self-diffusion measurements in inverse micellar cubic phases

Abstract

We have measured self-diffusion coefficients of amphiphile and water molecules in novel inverse micellar lyotropic cubic phases using the pulsed field gradient NMR technique. We investigated two different ternary lyotropic systems: oleic acid/sodium oleate/water, and dioleoylglycerol/dioleoylphosphatidylcholine/water. Both of these systems have previously been shown by one of us to form a cubic phase of space group Fd3m, whose structure is a complex packing of two types of disconnected quasi-spherical inverse micelles embedded in a 3D hydrocarbon matrix. The amphiphile translational diffusion coefficients determined for the first time by ¹H NMR in both systems are surprisingly large. Thus the self diffusion coefficients of amphiphiles may not provide a reliable way of distinguising inverse micellar from inverse bicontinuous phases. The water self-diffusion coefficient has been determined to have a value of 2·4 × 10^?12 m² s^?1, a value which is more than two orders of magnitude lower than that typically observed for inverse bicontinuous cubic phases. This confirms unambiguously the inverse micellar topology of the Fd3m cubic phase, and indicates that the value of the water diffusion coefficient should permit inverse micellar and inverse bicontinuous structures to be reliably distinguished, even for systems where the structure has not been previously determined by diffraction.     

Characterization of fractionated asphaltenes by UV-vis and NMR self-diffusion spectroscopy

Asphaltenes have been fractionated by liquid/liquid extraction, yielding four subfractions. The characteristics of fractionated asphaltenes were studied with respect to solubility, aromaticity, heteroatom content, and diffusion behavior. It was observed that asphaltenes from the four subfractions showed variations in their tendency to flocculate and also distinct differences in aromaticity. Furthermore, NMR self-diffusion studies showed that the average diffusion coefficients varied for asphaltenes from the different subfractions. The results suggest a variation in average size and stability between asphaltenes, depending on what subfraction they belong to. The subfraction that consisted of asphaltenes with the largest average size and the highest aromaticity was also found to contain the asphaltenes that had the strongest tendency to flocculate.     

Properties of polyethylene glycol (23) lauryl ether with cetyltrimethylammonium bromide in mixed aqueous solutions studied by self-diffusion coefficient NMR

NMR self-diffusion coefficient measurements have been used to study the properties of polyethylene glycol (23) lauryl ether (Brij-35) with cetyltrimethylammonium bromide (CTAB) in the mixed aqueous solutions with different mole fractions of CTAB. By fitting the self-diffusion coefficients to the two-state exchange model, the critical micelle concentrations of the two solutes in the mixed solutions (cmc*1 and cmc*2) were obtained. The critical mixed micelle concentrations (cmc*) were then evaluated by the sum of cmc*1 and cmc*2, which are in good agreement with the results measured by the surface tension method. The cmc* values are lower than those of the ideal case of mixing, which indicates that the behavior of the CTAB/Brij-35 system is nonideal. Moderate interactions between CTAB and Brij-35 in their mixtures can be deduced from the interaction parameters (betaM) based on the cmc* obtained by the NMR self-diffusion method. The compositions (x1) of the mixed micelles at different total surfactant concentrations were also evaluated. By using these results, a possible mechanism of mixed micellar formation and a picture of the formation of nonsimultaneous CTAB/Brij-35 binary mixed micelle were proposed. In contrast to the case of CTAB/TX-100 system, Brij-35 molecules have a tendency to form micelles first at any mole fraction of CTAB. The mixed micellar self-diffusion coefficients (Dm) increase slightly at lower CTAB molar ratios, and then speed up with increasing CTAB mole fraction.