Bulk Chain Research Articles

Confinement effect of chain dynamics in micrometer thick layers of a polymer melt below the critical molecular weight

Polymer melts confined in micrometer thick layers were examined with the aid of field-cycling NMR relaxometry. It is shown that chain dynamics under such moderate confinement conditions are perceptibly different from those observed in the bulk material. This is considered to be a consequence of the corset effect, which predicts a crossover between Rouse and reptationlike dynamics for molecular weights below the critical value at confinement length scales much larger than 10RF, where RF is the Flory radius of the bulk polymer coil [Fatkullin et al., New J. Phys. 6, 46 (2004)]. For the polymer species studied, a perfluoropolyether with a molecular weight of 11 000, the Flory radius is of the order 10 nm, so that the experiment refers to the far end of the predicted crossover region from confined to bulk chain dynamics. Remarkably the confinement effect is shown to reach polymer-wall distances of the order 100 Flory radii.

Polymer chain dynamics under nanoscopic confinements

It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands were varied to a certain degree. The chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale, 10(-2)-10(0) s) and field-cycling NMR relaxometry (time scale, 10(-9)-10(-4) s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation (i.e., T1 approximately nu(3/4)) showed up in all samples. A "tube" diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This corset effect is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the crossover from confined to bulk chain dynamics is expected.

Transitional flow behavior of entangled polyisoprene solutions

AbstractA contradiction has recently appeared between the current understanding of entangled polymers in nonlinear shear flow and new experimental observations based on highly entangled monodisperse 1,4‐polybutadiene solutions. Using entangled polydisperse solutions, we have examined the universality of the new revelation that any sufficiently entangled and relatively monodisperse polymeric fluids undergo a flow transition in simple shear when the applied stress is comparable to the plateau modulus. Indeed, a similar flow transition, marking the onset of bulk chain disentanglement, as previously observed for polybutadiene solutions in controlled‐stress experiments, can also be observed in less entangled and more polydisperse polyisoprene solutions, whereas controlled‐rate experiments do not reveal any transitional behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4132–4138, 2004

Polymer dynamics under nanoscopic constraints: the "corset effect" as revealed by NMR relaxometry and diffusometry.

A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined in nanoscopic strands, which in turn are embedded in a quasi-solid methacrylate matrix impenetrable to PEO. Both the molecular weight of the PEO and the mean diameter of the strands are variable to a certain degree. Chain dynamics of the PEO in the molten state were examined with the aid of field-gradient NMR diffusometry and field-cycling NMR relaxometry. The dominating mechanism for translational displacements in the nanoscopic strands is shown to be reptation. A formalism for the evaluation of NMR diffusometry is presented, which permits the estimation of the mean PEO strand diameter. Samples of different composition revealed diameters in the range 9-58 nm, in reasonable agreement with electron micrographs. The time scale of the diffusion measurements was 10-300 ms. On the much shorter time scale of field-cycling NMR relaxometry, 10(-9)-10(-4)s, a frequency dispersion of the spin-lattice relaxation time characteristic for reptation clearly showed up in all samples. An effective tube diameter of only 0.6 nm was found even when the strand diameter was larger than the radius of gyration of the PEO chain random coils. The finding that the tube diameter effective on the short time scale of field-cycling NMR relaxometry is much smaller than the diameter of the confining structure is termed the "corset effect", and is traced back to the lack of local free-volume fluctuation capacity under nanoscale confinements. The order of magnitude of the 'pore' diameter, at which the cross-over from confined to bulk chain dynamics is expected, is estimated.

Different diffusion behavior of cyclic chains under confinement

Molecular dynamics simulations of merging process of two isolated cyclic chains and that of linear chains have been performed, in order to find the difference between the two kinds of chain in bulk and in vacuum, where surface of the system restrains thousands of configurations showing up. Analysis indicates that in such confinement the chain ends at most moments float on the surface layer, and their mobility is much larger than the mean value of all atoms in linear chains, or that in cyclic chains. Comparison of the merging processes of cyclic chains and their linear counterparts was intensively carried out by several means of analyzing the trajectory files in statics and in dynamics. It was found that the segments of cyclic chains showed almost the same behavior of motion with that of linear chains. This is different diffusion behavior from that in bulk systems, where the cyclic chain has much higher diffusion rate. This modeling therefore indicates that in these confined systems because of the surface energy, the end groups are involuntarily kept on the surface, and lost the capacity of leading chain reptation through the other polymer chains, which is possibly the origin that the difference of diffusion behavior between the linear chain and the cyclic chain in the bulk almost disappears in the case of the confinement.

Chain Extension of Carboxy‐Terminated Aliphatic Polyamides and Polyesters by Arylene and Pyridylene Bisoxazolines

AbstractSummary: The bulk reactions between carboxy‐terminated polyamide‐12 (PA12) or carboxy‐terminated poly(butane‐1,4‐diyl adipate) (PBDA) and 2,2′‐(1,3‐phenylene)bis(2‐oxazoline) (mbox), 2,2′‐(1,4‐phenylene)bis(2‐oxazoline) (pbox), 2,2′‐(2,6‐pyridylene)bis(2‐oxazoline) (pybox) as chain‐coupling agents were studied by size exclusion chromatography, carboxy end‐group titration, and NMR spectroscopy. The chain‐coupling reaction yielded high‐molar mass polymers within 20 to 180 min, depending on reaction temperature, starting oligomer molar mass, bisoxazoline/oligomer molar ratio, and the nature of bisoxazoline. No side‐reactions were observed. Bisoxazoline pybox, used for the first time in the bulk chain extension of carboxy‐terminated polymers, exhibited the highest reaction rates. The thermal properties of the resulting polymers, studied by differential scanning calorimetry and thermogravimetric analysis, are also discussed.The reaction of PBDA and PA12 with mbox, pbox, and pybox to give rise to the polymers studied here.magnified imageThe reaction of PBDA and PA12 with mbox, pbox, and pybox to give rise to the polymers studied here.

A direct comparison of surface and bulk chain-relaxation in polystyrene.

Near-edge X-ray absorption fine-structure (NEXAFS) spectroscopy was used to measure simultaneously the relaxation rates of polystyrene (PS) molecules at the free surface and in the bulk. The samples were uniaxially stretched and annealed at temperatures below the bulk glass transition temperature of PS. The surface and bulk chain relaxation was monitored by measuring the partial-electron and the fluorescence NEXAFS yields, respectively, both parallel and perpendicular to the stretching direction. The decay of the optical birefringence was also measured to provide an independent measure of the bulk relaxation. Relaxation of PS chains was found to occur faster on the surface relative to the bulk. The magnitude of the surface glass transition temperature suppression over the bulk was estimated based on the information on the temperature dependence of the rates.

Mechanistic Studies on the CD Degradation of 193nm Resists during SEM Inspection.

Pattern deformation during SEM inspection has been investigated for different types of 193nm positive resists. The mechanism of the CD changes is discussed based on the slimming rate analyses as well as on the e-beam penetration depth. As a general tendency, the methacrylate resists exhibit faster line width reduction than the cycloolefin-maleic anhydride (COMA) systems; however, other resist components as well as CD SEM settings play an important role. Based on the exposure time vs. CD loss, the line width slimming (LWS) is found to proceed in three steps, which are assigned as: (1) chemical change of outer resist layer, (2) evaporation of volatiles and (3) bulk chain scission or deprotection. Countermeasures for CD degradation are proposed from both the formulation and process sides. A calculation of e-beam penetration depth suggests that deprotection, chain scission and other reactions occur in the first 20-40nm, and these reaction rates combined with thermal effects determine LWS. The CD SEM measurement method has been improved to minimize e-beam exposure and to spread out the thermal load over a larger period of time. An optimized formulation exhibits less than 0.2% LWS per measurement with the improved CD measurement program.

Structure and Molecular Motion of Poly(ethylene oxide) Chains Tethered on Silica, Depended on Grafting Ratio by the Spin Labeled Method

Electron spin resonance (ESR) spectroscopy of spin-labeled poly(ethylene oxide) (SL-PEO) tethered on silica was studied to characterize the conformation and local dynamics of the chain end. The e.s.r. spectra could be interpreted in terms of two components from two different kinds of spin labels attached to “train” and “tail” segments, which were strongly and weakly interacted with the silica surface. The structure and molecular motion of the chains are strongly dependent on the grafting ratio. The fractional amount of the “train” segment decreases remarkably with an increase in the grafting ratio. From the temperature dependence of the e.s.r. spectra, it was found that the molecular mobility of the “tail” segment was higher and that of the “train” segment was extremely lower than the PEO chains in the homopolymer bulk. These facts suggest that the “tail” segments are protruding from the silica surface and having a low segmental density, whereas the “train” segments are trapped near the silica surface. It can be also considered that the fractional amount of the “tail” segment increases abruptly with an increase in the grafting ratio after the tethered chains of a coiled structure form one monolayer.

Studies on equilibrium structures of complex polymers in condensed systems

The thermodynamic-equilibrium structures of four copolymers with different chain architectures are compared. They are AB diblock, BAB triblock, and ABC triblock copolymers and AB2 star-branched graft copolymers. Their morphological transitions meaningfully differ from one another, reflecting the difference in chain architecture. Two-component polymers barely form bicontinuous structures; however, symmetric ABC triblock copolymers easily form tricontinuous structures composed of two surfaces parallel to a Gyroid minimal surface. All four ABC equilibrium structures have a superlattice structure. Block polymer chains in microphase-separated bulk are elongated in the longitudinal direction in lamellar microphases. Although the deformation manner of the chains restricted in microphases depends on the chain architectures, the volumes of the deformed coils are always the same as those of the unperturbed chains regardless of their architectures. The measured polystyrene/poly(2-vinylpyridine) interfacial thickness is fairly thin, but the observed value is much thicker than the theoretically predicted one. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1645–1655, 2000

Aggregation energies of nonionic micelles calculated via pair potentials

The aggregation energies of two different forms of nonionic isolated micelles belonging to a binary oil-in-water system were calculated by using pairwise central potentials. One of the micelles is an elongated form (the spherocylinder); the other one is a flat form (the square tablet). The spherocylinder and the square tablet degenerate into the same spherical micelle at low aggregation numbers, whereas they form elongated cylinders and lamellae, respectively, at very high aggregation numbers. Both forms are of particular importance in some nematic systems involving a phase transition. The interaction energy among the polar heads of the amphiphilic molecules was calculated using a central Lennard-Jones potential. The interaction energy among the hydrocarbon chains in the micelle bulk was calculated via a phenomenological potential model. The calculations were performed considering a wide range of values of the parameters involved (i.e. polar head diameter, chain length). The entropic contribution to the aggregation free energy is similar for both micelles, and so their relative stability depends principally on the aggregation energy. The micelle aggregation energy depends strongly on the aggregation number and other geometrical parameters for both forms. The present results are consistent with those obtained using the surfactant parameter model, which permits the evaluation of the elastic bending energy of the micelle membrane for both forms.

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

AbstractIt 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 v3/4 on a time scale shorter than the longest Rouse relaxation time τR. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r2>∝ M−1/2t1/2 predicted for τR < t < τd, where τd 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.

Radical Polymerization Initiated from a Solid Substrate. 1. Theoretical Background

From a survey of the literature on grafting free radical polymerization from solid surfaces we suggest kinetic schemes for the process. The system of differential equations in partial derivatives including the diffusion equation based on the classical theory of free radical polymerization and the assumption that surface-bonded free radicals terminate by (1) reactions with bulk free radicals and (2) chain transfer to solvent or monomer are introduced. Computer simulations performed using the equations have shown good agreement with the characteristic features of the grafting process. The rate of grafting is linearly proportional to the surface concentration of the initiator and decreases as the initiation rate in the bulk increases. It follows from the concentration profiles of the bulk free radicals that free radical concentration in the vicinity of the surface can be several times larger than that in the bulk. The concentration profile depends on the distance between two surfaces. For distances less than...

Forces in foam films containing polyelectrolyte and surfactant

Foam films of semi-dilute anionic polyelectrolyte solutions containing additionally the cationic surfactant dodecyltrimethylammonium bromide are investigated. The polyelectrolytes used are polystyrene sulfonate (PSS) and acrylamide-acrylamidesulfonate (AAS) as examples of strongly and weakly charged polyions, respectively. The disjoining pressure isotherm results in film stratification well below the critical micelle concentration (CMC) and the critical aggregate concentration (CAC). These pressure oscillations are related to a network of polyelectrolyte chains in the film bulk, and their period to the mesh size. The network can be described by the theory for semi-dilute polyelectrolyte solutions, which is different for the two polyelectrolytes because of different charge densities along the chain. The surfactant has no observable influence on the network. To obtain information about the film interface surface tension measurements at the water–air interface are carried out. In comparison with the pure polyelectrolyte and the surfactant, respectively, the surface tension is much reduced for the mixed systems as a result of the formation of complexes between the surfactant and the polyelectrolyte. The two polymers show different behaviour in saturation of the surface coverage, which leads us to the conclusion that the complexes are different, although the behaviour of the film bulk is not influenced by changes in the interface.

Analytical Approximation to the Scheutjens−Fleer Theory for Polymer Adsorption from Dilute Solution. 2. Adsorbed Amounts and Structure of the Adsorbed Layer

In part I we adapted the recent analytical mean-field theory of polymer adsorption by Semenov et al. to match the numerical lattice theory of Scheutjens and Fleer (SF). Here we calculate explicitly the contributions of trains, loops, and tails to the adsorbance and their size distributions. We choose conditions in the so-called plateau region, which is most relevant from an experimental point of view. We thus use the plateau approximation, where the two simultaneous equations that determine the proximal length p and the distal length d can be uncoupled. The variations with bulk concentration, chain length, and surface affinity compare quite nicely with the SF numerics. Both a good solvent (at the mean-field level) and Θ solvent are considered; the agreement is better in the former case.

Short repulsive binary-alloy chains as a model for disordered quantum wells

Quantum confinement in one-dimensional disordered quantum wells is verified by means of resonant tunneling signatures in the transmission probability of an electron through barrier-well-barrier structures. The wells are simulated by short repulsive binary-alloy chains. These chains are interesting disordered systems, showing both localized and delocalized states. Bona fide confined states in the energy range where the bulk chain presents states with a localization length that exceeds at least three times the quantum-well width are found. These bona fide quantum-well states show clear symmetry properties for the envelope probability density in spite of disorder. In addition, the inadequacy of mean-field approximations to understand the quantization rules of disordered heterostructures is discussed.

Concentration dependence of static chain properties 2, off-lattice Monte Carlo simulations

Monte Carlo simulations of polymer chains in off-lattice systems under theta and athermal conditions have been performed in order to support results obtained for cubic lattice chains in assemblies of varying concentration. Global as well as local quantities are investigated in detail in order to point out the differences as well as the similarities of the results and the reliability of the two models, especially with respect to local packing effects. Furthermore, the results are discussed with reference to theoretical predictions of the scaling theory. Probably the most important finding is the fact that an isolated θ chain and a chain in bulk exhibit totally different microscopic structures (which is in full concordance with our previous lattice simulations), although the global dimensions of bulk polymers tend to converge to the values of an isolated θ chain.

End Group Effects on Surface Properties of Polymers: Semiempirical Calculations and Comparison to Experimental Surface Tensions for α,ω-Functional Poly(dimethylsiloxanes)

Current theoretical models for the surface behavior of polymers have stressed the importance of several factors such as the chain length (r), local chain stiffness, and the surface energy difference between chain ends and middle segments, χs. Here we assert that the critical parameter, which is affected by all of these factors, that controls thermodynamic properties is the surface composition of the different moieties in the macromolecular system. Composite surface properties, such as the surface tension, are calculated directly by assuming that the end group and repeat unit segments contribute to surface properties weighted by the composition in the lattice layer, which is immediately adjacent to the surface. We utilize the Scheutjens−Fleer lattice self-consistent mean-field model and Monte Carlo simulations to determine the surface composition of end groups for end-functionalized polymer chains. We find that end group segregation is primarily controlled by surface energetic differences between the chain ends and chain middle moieties and that entropic effects are effectively irrelevant in this context. Within the range of surface energy differences that are expected to be encountered in practice, the predicted surface segregation of chain ends is so small that the molecular weight dependence of the surface tension of an end-functionalized polymer melt is for all practical purposes determined by the direct relationship between the bulk end group concentration and chain length represented by φe = 2/r. Group contribution methods are employed to estimate the surface tensions of the end and middle groups, and no adjustable parameters are required. The simple model provides a facile method for determining the variation of surface tension with molecular weight and end group type and reproduces well experimental surface tension data for several α,ω-functional poly(dimethylsiloxanes).

Van der Waals Interactions in Nonionic Micelles

The aggregation energies of prolate and oblate ellipsoidal neutral micelles in a binary oil/water system were calculated by using a semiempirical model. The interactions among the polar heads of the amphiphilic molecules at the micelle interface were evaluated via a central potential of the Lennard−Jones 6−12 type. The interactions among the hydrophobic chains in the micelle bulk were evaluated via a phenomenological model. The results, which refer only to micelles of low eccentricity, show that the prolate and oblate micelles of equal volumes (containing the same number of molecules) have approximately the same aggregation energies.

Stick−Slip Transition in Capillary Flow of Polyethylene. 2. Molecular Weight Dependence and Low-Temperature Anomaly

The present study focuses on molecular characteristics and temperature dependence of a superfluid-like stick−slip transition in a series of highly entangled high-density polyethylene (PE) resins and their rheological behavior in pressure-driven capillary flow. It is found that at sufficiently high stresses the capillary flow characteristics are largely dictated by the stick−slip transition occurring at the PE/die wall interfaces. The transition magnitude is found to have an explicit and strong molecular weight Mw dependence reminiscent of bulk chain entanglement, i.e., the extrapolation length bc ∝ Mw3.4. In addition to its normal temperature dependence for T ≥ 200 °C as described in paper 1, the critical stress for the stick−slip transition ceases to scale linearly with T from 200 down to 160 °C for all four molecular weights studied. The extrapolation length bc at the transition also becomes much larger at a lower T. The anomaly is clearly interfacial in nature and may involve a flow-induced ordered mes...