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2. POLYMERS

The term "reptation" refers to the motion of a polymer in a highly entangled state, e.g., in a polymer network. The entangled state is regarded as a set of chains between crosslinks, and the chain is considered as being in a tube formed by topological constraints. The chain is longer than the tube, so that as the slack of the chain moves through the tube, the tube itself changes with time. The term is from the Latin reptare (to creep), and was introduced by the physicist P.G. de Gennes in 1971. Many experiments have indicated that reptation dominates the dynamics of polymer chains when they are entangled.

POLYMERS WITHOUT BEGINNING OR END

The following points are made by Tom McLeish (Science 2002 297:2005):

1) Natural polymer molecules dominate biology, while artificial polymers are used as plastics or emulsifiers in countless modern products. Many characteristics of their crystalline, glassy, and fluid states can be traced back to the special properties generated by the ends of the molecules. But what would happen if there were no ends? What would be the properties of polymers composed entirely of closed loops? Answers may be within reach following the discovery reported by Bielawski et al (Science 2002 297:2041) of a polymerization catalyst that releases the polymer in the form of a closed ring.

2) These are not the first ring polymers to be studied. In the 1980s, Roovers synthesized small quantities of monodisperse polystyrene rings by anionic polymerization (1). His motivation was the growing interest in the dynamics of polymer melts, in which topological entanglements between chains dominate the pattern of their motion. Experiments with linear, star-shaped, and H-shaped molecules had shown that the architecture of the molecules had a stronger influence on the viscosity and viscoelasticity than their chemistry or molecular weight. For example, the time scales for stress-relaxation in flow can increase exponentially as a function of molecular weight if the molecules are branched, but only as a power law if they are not. The promising "tube model" (2) explained these effects: The key determinant of relaxation time is the time that the locally trapped region of the melt needs to wait for a chain end to diffuse to it through a maze of tube-like constraints around the polymer contour.

3) But what would happen if there were no ends to be found? Answering this question turns out to be delicate. Roovers found (correctly) that the relaxation times of the ring melts were much lower than those of linear melts of the same molecular weight. But other researchers disagreed. There are several reasons why ring molecules are difficult to study. First, it is essential to synthesize rings that are not interlinked (although such "olympic gels" are themselves interesting as rubbery solids with no molecular cross-links at all). Second, even small amounts of linear polymer contaminants in a melt of rings alter the dynamics, bringing relaxation times rapidly up to linear melt values. Finally, polystyrene, although relatively easy to work with, is composed of very bulky molecules that diminish the effects of entanglement.

4) These experimental challenges did not prevent theoretical speculation, however. Linear chains in dense melts display the statistical properties of ideal random walks, but a melt of rings should not behave in this way. The topological constraint that the rings are not linked is permanently set from their creation. This constraint in turn biases their conformations so that they grow in size more slowly with molecular weight than do linear chains (3). Instead of the snakelike "reptation" of linear chains, theory suggested that the dynamics of rings should resemble the motion of amoebae: Unentangled loops continually thrust out and retract in the complex hedge of constraints imposed by neighboring molecules.

References (abridged):

1) J. Roovers, Macromolecules, 21, 1517 (1988)

2) M. Doi, S. F. Edwards, The Theory of Polymer Dynamics (Oxford Univ. Press, Oxford, 1986)

3) M. E. Cates, J. M. Deutsch, J. Phys. (Paris) 47, 2121 (1986)

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ON THE SYNTHESIS OF CYCLIC POLYMERS

The following points are made by C.W. Bielawski et al (Science 2002 297:2041):

1) Produced at a rate of 40 million tons per year, polyethylene remains one of the most valuable synthetic polymers in the world. It is now used in products ranging from grocery bags and milk containers to high-performance fibers and medical devices. Its versatility stems from our ability to tune the material's crystallinity, mechanical strength, and thermal stability by altering the architecture of the individual polymer chains (1). However, the rising number of applications for polyethylene require its material properties to be broadened even further.

2) Though most efforts have been focused on synthesizing polyethylene with increasing structural complexity, there has been interest in exploring whether unique properties could be obtained through the simplest of topological modifications; for example, tying the ends of a linear precursor together to form a cyclic polymer conceptually varies the structure only minimally. However, the additional physical constraints imposed on such a cyclic polymer would not only restrict conformational freedom but also reduce its overall dimensions and, therefore, may lead to unusual or unexpected properties.

3) Although cyclic polymers have been synthesized previously, access to high molecular weight material (MW > 100 kD), which is often required for many polymers to show their characteristic physical properties, is exceedingly challenging (2). The typical synthetic route involves intramolecular macrocyclization of linear precursors at extremely low concentrations. Alternatively, the balance between linear and cyclic products that occurs for many polymerizations (e.g., polycondensations, metathesis polymerizations, etc.) may be shifted to maximize formation of cyclic product (which again generally involves using low concentrations). Incomplete cyclizations or undesired side reactions are common for both approaches; therefore, elaborate purification procedures are often required to remove the acyclic contaminants (3). Furthermore, many monomers, including ethylene, are not amenable to these types of polymerizations. As a result, there are very few reported examples of cyclic polyethylenes, especially in the high molecular weight (>10^(4) dalton) regime, and thus the physical properties and potential applications of this material remain largely unexplored (4,5).

4) In summary: The authors report that a new synthetic route to cyclic polymers has been developed in which the ends of growing polymer chains remain attached to a metal complex throughout the entire polymerization process. The approach eliminates the need for linear polymeric precursors and high dilution, drawbacks of traditional macrocyclization strategies, and it effectively removes the barrier to producing large quantities of pure cyclic material. Ultimately, the strategy offers facile access to a unique macromolecular scaffold that may be used to meet the increasing demand of new applications for commercial polymers. As a demonstration of its potential utility, cyclic polyethylenes were prepared and found to exhibit a variety of physical properties that were distinguishable from their linear analogs.

References (abridged):

1. A. J. Peacock, Handbook of Polyethylene: Structure, Properties, and Applications (Marcel Dekker, New York, 2000)

2. J. A. Semlyen, Cyclic Polymers (Kluwer Academic, Dordrecht, The Netherlands, ed. 2, 2000)

3. W. Lee, et al., Macromolecules 35, 529 (2002)

4. H. Höcker and K. Riebel, Makromol. Chem. 178, 3101 (1977)

5. K. S. Lee and G. Wegner, Makromol. Chem.-Rapid 6, 203 (1985)

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BROWNIAN MOTION OF DNA CONFINED WITHIN A TWO-DIMENSIONAL ARRAY

The following points are made by D. Nykypanchuk et al (Science 2002 297:987):

1) Under incessant Brownian motion, mobile macromolecules in gels, membranes, or cytoplasm constantly squeeze through and around molecular-size obstructions. Until recently, neither the surroundings nor the motion of a single molecule could be directly observed, and the understanding of such sterically constrained motions was principally deduced through examination of the macroscopic diffusion coefficient. The dynamics of a single, large macromolecule can now be visually monitored by fluorescence microscopy (1-4), but studies of macromolecular diffusion by this approach have not extended to environments providing well-defined spatial constraints.

2) Three basic mechanisms have emerged to explain how flexible macromolecules diffuse within a constraining medium -- sieving, entropic barriers transport, and reptation (5). The first of these treats each macromolecule as a rigid sphere, assigning a fixed radius equal to the molecule's average size. The medium's smaller pores and constrictions block passage, so with fewer traversable pathways, a larger molecule diffuses more slowly than a smaller one. Entropic barriers transport applies when the configuration of a flexible macromolecule must deform or fluctuate to pass through a medium's spatial constraints. At each position, the number of accessible configurations defines the molecule's local entropy. Entropy differences derived from the medium's spatial heterogeneity drive molecules to partition or localize preferentially in less constrictive spaces, where their enhanced configurational freedom raises entropy. Diffusion then occurs by thermally activated jumps across the intervening entropic barriers. Reptation can be envisioned as imposing lateral confinement on a diffusing linear macromolecule by enveloping the molecule in a fictitious tube. Only end segments can escape as the molecule undergoes random curvilinear motion along the tube axis. The tube's random contour and the molecule's sliding friction combine to hinder center-of-mass displacement. In contrast to entropic barriers transport, the number of configurations accessible to a reptating macromolecule does not depend on position. Which diffusion mechanism prevails under given conditions remains an open question. Sequential transitions from sieving to entropic barriers transport to reptation have been postulated as molecular weight or confinement increases (5). Such transitions, however, may not always be distinct.

3) In summary: The authors report that linear DNA molecules are visualized while undergoing Brownian motion inside media patterned with molecular-sized spatial constraints. The media, prepared by colloidal templating, trap the macromolecules within a two-dimensional array of spherical cavities interconnected by circular holes. Across a broad DNA size range, diffusion does not proceed by the familiar mechanisms of reptation or sieving. Rather, because of their inherent flexibility, DNA molecules strongly localize in cavities and only sporadically "jump" through holes. Jumping closely follows Poisson statistics. By reducing DNA's configurational freedom, the holes act as molecular weight-dependent entropic barriers. Sterically constrained macromolecular diffusion underlies many separation methods and assumes an important role in intracellular and extracellular transport.

References (abridged):

1. T. W. Houseal, C. Bustamante, R. F. Stump, M. F. Maestre, Biophys. J. 56, 507 (1989)

2. M. Matsumoto, et al., J. Polym. Sci. B Polym. Phys. 30, 779 (1992)

3. J. Käs, H. Strey, E. Sackmann, Nature 368, 226 (1994)

4. T. T. Perkins, D. E. Smith, S. Chu, Science 264, 819 (1994)

5. D. L. Smisek and D. A. Hoagland, Science 248, 1221 (1990)

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SELF-ALIGNED, VERTICAL-CHANNEL, POLYMER FIELD-EFFECT TRANSISTORS

The following points are made by N. Stutzmann et al (Science 2003 299:1881):

1) Many advanced electronic device configurations, such as vertical transistors (1) and vertical-cavity surface-emitting lasers, require the formation of well-defined vertical sidewalls in functional multilayer structures. Most conventional techniques for fabrication of such sidewalls are based on photolithographic patterning followed by either reactive ion etching or anisotropic wet chemical etching. Application of these techniques to polymer multilayer structures is difficult because of plasma-induced degradation of electroactive polymers and the lack of anisotropic etching techniques for polymers.

2) Different patterning techniques for low-cost fabrication of solution-processible polymer field-effect transistors (FETs) have been demonstrated, including photolithographic patterning (2), screen printing (3), soft lithographic stamping (4), micromolding in capillaries (5), and high-resolution inkjet printing. These techniques allow accurate definition of polymer patterns with micrometer resolution, but they do not permit the formation of vertical sidewalls and, with some exceptions such as near-field photolithography, their extension to submicron resolution patterning is complex and becomes more expensive the higher the required resolutions.

3) Embossing is a nonlithographic patterning technique that has found widespread industrial use in the manufacture of diffraction gratings, compact disks, and security features such as holograms, but that is also capable of imprinting nanoscale patterns into single, sacrificial polymer layers that can be transferred subsequently into a functional layer by conventional etching. The LIGA technique (a German abbreviation for lithographic galvanic deposition) that is widely used for fabrication of micro-electrical-mechanical structures is based on the embossing of high-aspect-ratio structures in poly(methyl methacrylate) (PMMA). Direct laser-assisted imprinting of silicon surface layers has been demonstrated.

4) In summary: The manufacture of high-performance, conjugated polymer transistor circuits on flexible plastic substrates requires patterning techniques that are capable of defining critical features with submicrometer resolution. The authors used solid-state embossing to produce polymer field-effect transistors with submicrometer critical features in planar and vertical configurations. Embossing is used for the controlled microcutting of vertical sidewalls into polymer multilayer structures without smearing. Vertical-channel polymer field-effect transistors on flexible poly(ethylene terephthalate) substrates were fabricated, in which the critical channel length of 0.7 to 0.9 micrometers was defined by the thickness of a spin-coated insulator layer. Gate electrodes were self-aligned to minimize overlap capacitance by inkjet printing that used the embossed grooves to define a surface-energy pattern.

References (abridged):

1. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, ed. 2, 1981)

2. C. J. Drury, C. M. J. Mutsaers, C. M. Hart, M. Matters, D. M. d. Leeuw, Appl. Phys. Lett. 73, 108 (1998)

3. Z. Bao, Y. Feng, A. Dodabalapur, V. R. Raju, A. J. Lovinger, Chem. Mater. 9, 1299 (1997)

4. J. A. Rogers, Z. Bao, A. Makhija, P. Braun, Adv. Mater. 11, 741 (1999)

5. J. A. Rogers, Z. Bao, V. R. Raju, Appl. Phys. Lett. 72, 2716 (1998)

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TEMPLATING ORGANIC SEMICONDUCTORS VIA SELF-ASSEMBLY OF POLYMER COLLOIDS

The following points are made by R. Mezzenga et al (Science 2003 299:1872):

1) Doped pi-conjugated polymers have attracted considerable attention in past decades because of their broad applicability (1-5) and their ease of processing when compared to inorganic semiconductors. For applications requiring both conductivity and good mechanical properties, these polymers are blended with tougher insulating polymer matrices, resulting in mechanically resistant and easy-to-process semiconducting polymer blends. In these blends, conductivity is achieved by percolation of the dispersed doped pi-conjugated polymer phase hosted in an insulating polymer matrix. The doped pi-conjugated polymer volume fraction at the percolation threshold plays an important role in determining the blend's electrical conductivity.

2) In summary: A route for producing semiconducting polymer blends is demonstrated in which a doped pi-conjugated polymer is forced into a three-dimensionally continuous minor phase by the self-assembly of colloidal particles and block copolymers. The resulting cellular morphology can be viewed as a high-internal phase polymeric emulsion. Compared with traditional blending procedures, this process reduces the percolation threshold for electrical conductivity by a factor of 10, increases the conductivity by several orders of magnitude, and simultaneously improves thermal stability. Following this route, new applications can be envisaged for semiconducting polymer blends that require only minimal concentrations of doped pi-conjugated polymer.

References (abridged):

1. Y. Yang and A. J. Heeger, Nature 372, 344 (1994)

2. M. Granstrom, M. Berggren, O. Inganas, Science 267, 1479 (1995)

3. P. K. H. Ho, D. S. Thomas, R. H. Friend, N. Tessler, Science 285, 233 (1999)

4. H. Sirringhaus, et al., Science 290, 2123 (2000)

5. B. Crone, et al., Nature 403, 521 (2000)

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POLYMER REPLICAS OF PHOTONIC POROUS SILICON FOR SENSING AND DRUG DELIVERY APPLICATIONS

The following points are made by Y.Y. Li et al (Science 2003 299:2045):

1) Synthesis of materials using nanostructured templates has emerged as a useful and versatile technique to generate ordered nanostructures (1). Templates consisting of microporous membranes (2,3), zeolites (4), and crystalline colloidal arrays (5) have been used to construct elaborate electronic, mechanical, or optical structures. Porous Si is an attractive candidate for use as a template because the porosity and average pore size can be tuned by adjusting the electrochemical preparation conditions that allow the construction of photonic crystals, dielectric mirrors, microcavities, and other optical structures. For many applications, porous Si is limited by its chemical and mechanical stability. The use of porous Si as a template eliminates these issues while providing the means for construction of complex optical structures from flexible materials that are compatible with biological systems or harsh environments.

2) Multilayered porous Si templates containing nanometer-scale pores are prepared by an anodic electrochemical etch of crystalline silicon wafers with the use of a pseudosinusoidal current-time waveform, according to published procedures. The thickness, pore size, and porosity of a given layer is controlled by the current density, duration of the etch cycle, and etchant solution composition. The multilayer templates possess a sinusoidally varying porosity gradient, providing sharp features in the optical reflectivity spectrum that approximate a rugate filter. The porous Si is converted to porous SiO2 by thermal oxidation, and the oxidized nanostructure is used as a template for solution-cast or injection-molded thermoplastic polymers.

3) In summary: The authors report that elaborate one-dimensional photonic crystals are constructed from a variety of organic and biopolymers, which can be dissolved or melted, by templating the solution-cast or injection-molded materials in porous silicon or porous silicon dioxide multilayer (rugate dielectric mirror) structures. After the removal of the template by chemical dissolution, the polymer castings replicate the photonic features and the nanostructure of the master. The authors demonstrate that these castings can be used as vapor sensors, as deformable and tunable optical filters, and as self-reporting, bioresorbable materials.

References (abridged):

1. S. Polarz and M. Antonietti, J. Chem. Soc. Chem. Commun. 2002, 2593 (2002)

2. M. Wirtz, M. Parker, Y. Kobayashi, C. R. Martin, Chem. Eur. J. 16, 3572 (2002)

3. J. C. Hulteen and C. R. Martin, J. Mater. Chem. 7, 1075 (1997)

4. K. Moller and T. Bein, Chem. Mater. 10, 2950 (1998)

5. C. E. Reese, M. E. Baltusavich, J. P. Keim, S. A. Asher, Anal. Chem. 73, 5038 (2001)

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POLYMER VESICLES

The following points are made by D.E. Discher1 and A. Eisenberg (Science 2002 297:967):

1) Vesicles and biomembranes have existed since the first biological cells and play critical roles in compartmentalization functions as varied as nutrient transport and DNA protection (1). Whereas phospholipids are the natural amphiphiles of cell membranes, vesicle-forming materials used in products ranging from cosmetics to anticancer agents can be synthetic as well as biological (2). When suitably mixed in water or similar solvents, the oily parts of the amphiphiles tend to associate while the more hydrophilic parts face inner and outer solutions, helping to delimit the two interfaces of the membrane.

2) Despite the molecularly thin nature of these membranes, the vesicles that form by the relatively weak solvent-associated forces can effectively entrap dissolved compounds and can also accumulate, within the membrane cores, hydrophobic or fatty substances. Several skin-rejuvenating products, for example, not only encapsulate the water-soluble antioxidant vitamin C within lipid vesicles but also dissolve skin-healing vitamin E within the cores. Aggregation of more than 100,000 small amphiphiles such as lipids (with molecular weight MW less than 1 kD) into the molecularly thin membranes also manifests itself in a dynamic, physical softness (1). As a consequence, many lipid vesicle properties such as encapsulant retention, membrane stability, and degradation are not particularly well controlled.

3) A polymer approach to vesicle formation broadens the range of properties achievable through a widened choice of amphiphile MW and chemistry. To be clear, the systems are not polymerized vesicles in which amphiphiles are polymerized or cross-linked after vesicle formation; such an approach has generally started with lipid-size, reactive amphiphiles, and (if successful) generates membranes of the same basic architecture as lipid bilayers (3,4). Instead, the authors focus on linear polymers with the intrinsic ability to self-direct their own assembly into membranes. Being lipid-like only in the latter sense, vesicle-forming polymers offer fundamental insight into natural design principles for biomembranes.

4) In summary: Vesicles are microscopic sacs that enclose a volume with a molecularly thin membrane. The membranes are generally self-directed assemblies of amphiphilic molecules with a dual hydrophilic-hydrophobic character. Biological amphiphiles form vesicles central to cell function and are principally lipids of molecular weight less than 1 kilodalton. Block copolymers that mimic lipid amphiphilicity can also self-assemble into vesicles in dilute solution, but polymer molecular weights can be orders of magnitude greater than those of lipids. Structural features of vesicles, as well as properties including stability, fluidity, and intermembrane dynamics, are greatly influenced by characteristics of the polymers. Future applications of polymer vesicles will rely on exploiting unique property-performance relations, but results to date already underscore the fact that biologically derived vesicles are but a small subset of what is physically and chemically possible.

References (abridged):

1. R. Lipowsky, E. Sackmann, Eds., Structure and Dynamics of Membranes--from Cells to Vesicles (Elsevier Science, Amsterdam, 1995)

2. D. D. Lasic, D. Papahadjopoulos, Eds., Medical Applications of Liposomes (Elsevier Science, Amsterdam, 1998)

3. H. Ringsdorf, B. Schlarb, J. Venzmer, Angew. Chem. Int. Ed. 27, 113 (1988)

4. S. C. Liu, D. F. O'Brien, J. Am. Chem. Soc. 124, 6037 (2002)

5. A. D. Bangham, Chem. Phys. Lipids 64, 275 (1993)

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ADHESION AND FRICTION MECHANISMS OF POLYMER-ON-POLYMER SURFACES

The following points are made by N. Maeda et al (Science 2002 297:379):

1) Polymers are often used as adhesive and lubricant coatings to produce both high and low adhesion or friction. Characterization of tribological and adhesive properties and dynamics has been of great interest for many years. Most tribological studies have, however, been limited to macroscopic or microscopic systems, because of a lack of experimental nanoscale techniques and the molecular-level complexity of these systems. With the miniaturization of machinery and computer-related devices, there is now a practical need to understand these phenomena at the molecular level.

2) A close correlation exists between adhesion hysteresis, where the work needed to separate two surfaces or molecules is generally greater than that originally gained on bringing them together, and friction forces. Such correlations have been experimentally demonstrated in studies of the adhesion and friction of adsorbed surfactant layers with each other (symmetric system) (1) and of polymer surfaces with mica (asymmetric system) (2,3). These correlations can be understood from simple thermodynamic considerations (4), as well as more sophisticated theories and simulations (5).

3) For surfaces composed of chain molecules, their adhesion hysteresis is largely determined by the rearrangement or restructuring of surface molecular groups to enhance the number and/or strength of contacting bonds (e.g., interdigitating chain segments) across the interface. Earlier work with surfactant-coated surfaces containing short hydrocarbon chains indicated that the state of the outermost molecular groups plays a crucial role in determining the extent and dynamics of these processes, and that even a small amount of interdigitation can significantly enhance their adhesion hysteresis and friction (1).

4) In summary: The authors report that the adhesion and friction of smooth polymer surfaces were studied below the glass transition temperature by use of a surface forces apparatus. The friction force of a crosslinked polymer was orders of magnitude less than that of an uncrosslinked polymer. In contrast, after chain scission of the outermost layers, the adhesion hysteresis and friction forces increase substantially. The authors suggest these results demonstrate that polymer-polymer adhesion hysteresis and friction depend on the dynamic rearrangement of the outermost polymer segments at shearing interfaces, and that both increase as a transition is made from crosslinked surfaces to surfaces with long chains to surfaces with quasi-free ends. The authors suggest the results indicate new ways for manipulating the adhesion and friction of polymer surfaces by adjusting the state of the surface chains.

References (abridged):

1. Y.-L. Chen, C. A. Helm, J. N. Israelachvili, J. Phys. Chem. 95, 10736 (1991)

2. M. Heuberger, G. Luengo, J. Israelachvili, J. Phys. Chem. B 103, 10127 (1999)

3. G. Luengo, M. Heuberger, J. Israelachvili, J. Phys. Chem. B 104, 7944 (2000)

4. J. Israelachvili, A. Berman, Origin of Energy Dissipation and Other Tribological Processes at the Molecular Level, Proceedings of the International Tribology Conference III, 30 October to 2 November 1995, Yokohama, Japan (Japanese Society of Tribologists, 1996)

5. B. N. J. Persson, Sliding Friction: Physical Principles and Applications (Springer-Verlag, Berlin, 1998)

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POLYMER NANOTUBES BY WETTING OF ORDERED POROUS TEMPLATES

The following points are discussed by M. Steinhart et al (Science 2002 296:1997):

1) The authors report they have developed a simple technique for the fabrication of polymer nanotubes with a monodisperse size distribution and uniform orientation. When either a polymer melt or solution is placed on a substrate with high surface energy, it will spread to form a thin film, known as a precursor film, similar to the behavior of low molar mass liquids (1,2). Similar wetting phenomena occur if porous templates are brought into contact with polymer solutions or melts: A thin surface film will cover the pore walls in the initial stages of wetting. This is because the cohesive driving forces for complete filling are much weaker than the adhesive forces. Wall wetting and complete filling of the pores thus take place on different time scales. The latter is prevented by thermal quenching in the case of melts or by solvent evaporation in the case of solutions, thus preserving a nanotube structure.

2) If the template is of monodisperse size distribution, aligned or ordered, so are the nanotubes, and ordered polymer nanotube arrays can be obtained if the template is removed. Any melt-processible polymer, such as polytetrafluoroethylene (PTFE), blends, or multicomponent solutions can be formed into nanotubes with a wall thickness of a few tens of nanometers. The authors suggest that owing to its versatility, this approach should be a promising route toward functionalized polymer nanotubes.

3) The authors used ordered porous alumina and oxidized macroporous silicon templates with narrow pore size distribution (3). Extended regular pore arrays were prepared by lithography. The pores are well-defined, straight, with a smooth inner surface and with diameters DP between 300 and 900 nm. To process melts, the authors placed the polymer on a pore array at a temperature well above its glass transition temperature, in the case of amorphous polymers, or its melting point, in the case of partially crystalline polymers. The liquid polymer forms a thin wetting film covering the entire pore surface on a time scale ranging from a few minutes to half an hour. Polymer solutions were dropped on the templates at ambient conditions. The resulting nanotubes obtained from either method had wall thicknesses between 20 and 50 nm and lengths of up to 100 æm.(4)

References (abridged):

1. P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985)

2. S. F. Kistler, in Wettability, Surfactant Science Series, vol. 49, J. C. Berg, Ed. (Dekker, New York, 1993), chap. 6.

3. R. B. Wehrspohn and J. Schilling, MRS Bull. 8, 623 (2001)

4. M. Bognitzki, et al., Adv. Mater. 12, 637 (2000)

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ON CHARGE INVERSION IN POLYMERS

The following points are made by T.T. Nguyen and B.I. Shklovskii (Phys. Rev. Lett. 2002 89:018101):

1) The inversion of the negative charge of a DNA double helix by its complexation with a positive polyelectrolyte (PE) is used for gene delivery. The positive charge of a DNA-PE complex facilitates DNA contact with a typically negative cell membrane, making penetration into the cell hundreds of times more likely [1]. Charge inversion of DNA-PE complexes was confirmed recently by electrophoresis [2]. At a given concentration of long DNA helices, when the concentration of shorter PE molecules increases, at some critical concentration the electrophoretic mobility of a DNA-PE complex changes sign from negative to positive.

2) The challenging and counterintuitive phenomenon of charge inversion of a macroion by an oppositely charged PE and other multivalent ions has attracted significant attention [3-5]. Intuitively, one can think that, when a PE completely neutralizes a large macroion such as the DNA double helix, new molecules of a PE do not attach to the macroion. Indeed, the Poisson-Boltzmann approximation for the description of screening of a macroion by any counterions including PE does not lead to charge inversion. Charge inversion can be explained if one takes into account that the surface potential of an already-neutralized macroion is locally affected by a new approaching PE molecule or, in other words, it can be explained if one takes into account correlations between PE molecules.

3) For quantitative consideration, the charges of a macroion are always assumed to be uniformly smeared. This approach ignores the interference between the structure of the macroion surface and that of a PE and clearly is not fully satisfactory. More importantly, it is not clear whether or not charge inversion is an artifact of the assumption of uniformly smeared charge.

4) In summary: The authors model one strand of DNA by a one- dimensional lattice (ODL) of negative charges and consider the problem of inversion of its charge by a positive polyelectrolyte (PE). In the neutral state of the ODL-PE complex, each of the ODL charges is locally compensated by a PE charge. When an additional PE molecule is adsorbed by ODL, its charge gets fractionalized into monomer charges of defects (tails and arches) on the background of the perfectly neutralized ODL. Defects spread all over the ODL, eliminating the self-energy of PE. For DNA this fractionalization mechanism leads to a substantial inversion of charge, a phenomenon which is widely used for gene delivery.

References (abridged):

1. A.V. Kabanov and V.A. Kabanov, Bioconjug. Chem. 6, 7 (1995); Adv. Drug Delivery Rev. 30, 49 (1998).

2. V.A. Kabanov, A. A. Yaroslavov, and S.A. Sukhisvili, J. Controlled Release 39, 173 (1996).

3. T. Wallin and P. Linse, J. Phys. Chem. 100, 17 873 (1996).

4. E.M. Mateescu, C. Jeppersen, and P. Pincus, Europhys. Lett. 46, 454 (1999).

5. S. Y. Park, R. F. Bruinsma, and W. M. Gelbart, Europhys. Lett. 46, 493 (1999).

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