Manning condensation in two dimensions

We consider a macroion confined to a cylindrical cell and neutralized by oppositely charged counterions. Exact results are obtained for the two-dimensional version of this problem, in which ion-ion and ion-macroion interactions are logarithmic. In particular, the threshold for counterion condensation is found to be the same as predicted by mean-field theory. With further increase of the macroion charge, a series of single-ion condensation transitions takes place. Our analytical results are expected to be exact in the vicinity of these transitions and are in very good agreement with recent Monte-Carlo simulation data.Comment: 4 pages, 4 figure

Segmental Dynamics in Poly(Methyl Acrylate)-d3 on Strongly and Weakly Adsorbing Silica Surfaces

The segmental dynamics of a polymer on a solid surface appears to be significantly different than that in bulk. The strength of the interaction between polymer segments and a solid surface is likely to be an important factor affecting the segmental mobility of the polymers. Studies of polymers on a weakly adsorbing surface would provide additional understanding of their motional characteristics on surfaces. In a recent NMR study by Rivillon et al., chain dynamics was seen to be different for samples, even when there was no specific interaction with the surface. Peanasky et al. have found a restricted segmental dynamics for the polyphenylmethylsiloxane samples at weakly adsorbing surfaces. Zheng et al. Observed a significant difference from bulk dynamics on both strongly and weakly interacting interfaces for poly(styrene) (PS) and poly(2-vinylpyridine). Mechanical properties of weakly interacting poly(methyl acrylate) (PMA)- silica composites were seen to become poorer than the ones with stronger interactions. Contrasting results for PS on silicon surfaces with X-ray reflectivity also highlighted the importance of the surface-polymer interaction for thin films.5,6 Wallace et al. explained that the contrasting results were due to a difference in the surface characteristics. A stronger surface-polymer interaction on a hydrogen-terminated silicon resulted in an increase in glass transition temperature (Tg) for thin films of PS, while Keddie et al.â s work on a silicon native-oxide surface with the same polymer indicated a decrease in Tg for thin films due to a weaker interaction. The segmental dynamics of PMA-d3 on a strongly adsorbing surface was previously studied using the deuterium (2H) quadrupole-echo NMR and modulated differential scanning calorimetry. In this study, the segmental dynamics of PMA on a weakly adsorbing surface was investigated with 2H quadrupole-echo NMR and compared to that in bulk and on a strongly adsorbing surface

Molecular Mass and Dynamics in PMA-d₃ in the Glass Transition Region

The segmental dynamics through the glass transition region, by which the glassy polymer becomes rubbery, are not well understood. Free volume, thermodynamic and kinetic theories have been used to describe the phenomenon behind the glass transition and some of those theories were tested with computer simulations. Different experimental techniques, such as NMR, thermo-mechanical analysis (TMA), differential scanning calorimetry (DSC), dilatometry and dynamic mechanical analysis (DMA) have all been also used to probe this important phenomena. Deuterium (2H) NMR has been a valuable tool for the investigation of the dynamics of macromolecules. Deuteration of macromolecules at specific locations on the chains does not significantly affect the properties of polymers. Spiess et al. Investigated motions in the glass transition region using 1D and 2D exchange NMR experiments on deuterated polystyrene. Rössler et al. studied the molecular dynamics in deuterated binary liquids close to the glass transition temperature (Tg) using 2D Exchange NMR. Blum et al. studied the effect of molecular mass on dynamics through glass transition for poly(methyl acrylate) (PMA). They found a “homogeneity” of the dynamics in the glass transition region for high molecular mass sample, but heterogeneity for the low molecular mass sample. In addition, the polydispersities of the samples were large. In this paper, we report studies of the dynamics of more monodisperse poly(methyl acrylate)-d3 (PMA)-d3 samples around the glass transition region using 2H quadrupole echo NMR and modulated DSC (MDSC)

Segmental Mobility of Chain Ends in Poly(Methyl Acrylate)-d3

Better control of polymeric materials can be achieved with a thorough understanding of the dynamics of their constituents. In the present study, we consider polymer chains as composed of chain middles and chain ends. Even though chain ends do not comprise much of the sample by mass, they may play a crucial role in the ultimate properties of the polymers. Although chain ends have been assigned a higher mobility, as compared to chain middles, there have not been a large number of experimental studies that directly probe their mobility. Among those, the studies of Kitahara et al.1 and Miwa et al.2 demonstrated the higher mobility of chain ends using ESR for polyethylene and polystyrene (PS), respectively. They observed that the transition temperatures for the onset of rapid molecular motion at the chain ends were 5 K lower than those inside the chains. A molecular mass dependence was also observed for the transition for the chain ends. A specular neutron reflectivity (SNR) study3 indicated that segments in the center sections of PS have a lag in mobility across a welded interface, as compared to chain ends. Previous deuterium NMR studies,4,5 by our group, have shown the a molecular-mass dependence on segmental dynamics through the glasstransition region. More heterogeneous segmental dynamics were observed in the NMR spectra of lower molecular mass poly(methyl acrylate) (PMA) compared to those of higher molecular mass. This heterogeneity was attributed to the presence of a higher concentration of more-mobile chain ends. In this study, the segmental dynamics of the PMA samples, with methyl-groupdeuterated chain ends, was studied using the 2H quadrupole-echo NMR technique. These results provided significant insight into the role of chain ends in the glass transition region of polymers

Molecular Mass and Dynamics of Poly(Methyl Acrylate) in the Glass Transition Region

The segmental dynamics of bulk poly(methyl acrylate) (PMA) were studied as a function of molecular mass in the glass-transition region using 2H NMR and modulated differential scanning calorimetry (MDSC). Quadrupole-echo 2H NMR spectra were obtained for four samples of methyl-deuterated PMA-d3 with different molecular masses. The resulting spectra were fit using superpositions of simulated spectra generated from the MXQET simulation program, based on a model incorporating nearest-neighbor jumps from positions on the vertices of a truncated icosahedron (soccer-ball shape). The lower molecular-mass samples, influenced by the presence of more chain ends, showed more heterogeneity (broader distribution) and lower glass transitions than the higher molecular-mass samples. The MDSC experiments on both protonated and deuterated samples showed behavior consistent with the NMR results, but temperature shifted due to the different frequency range of the measurements in terms of both the position and breadth of the glass transition as a function of molecular mass

Segmental Dynamics in Poly(Methyl Acrylate) on Silica: Molecular-mass Effects

The effect of molecular mass on the segmental dynamics of poly(methyl acrylate) (PMA) adsorbed on silica was studied using deuterium quadrupole-echo nuclear magnetic resonance (NMR) and modulated differential scanning calorimetry. Samples adsorbed on silica (all about 1.5 mg PMA/m2 silica) were shown to have more restricted segmental mobility, and higher Tg\u27s, than the corresponding bulk PMA samples. Around the glass-transition region, adsorbed samples exhibited segmental mobility, which could be classified as heterogeneous due to a superposition of more-mobile and less-mobile components present in the deuterium NMR spectra. This heterogeneity was consistent with a motional gradient with more-mobile segments near the polymer-air interface and the less-mobile species near the polymer-silica interface. The mobility of the adsorbed 77 kDa PMA sample was the lowest among the four different molecular-mass samples studied. Samples studied with masses both larger and smaller than 77 kDa had larger mobile-component fractions in the adsorbed polymer. The additional mobility was attributed to the presence of either longer tail and loop conformations in the higher molecular-mass samples or the inherent mobility of the tails in the lower molecular-mass samples on the surface

NMR and Modulated Differential Scanning Calorimetry of Adsorbed Poly(Methyl Acrylate) on Silica

The interaction between polymers and solid substrates can be studied by a variety of techniques. The results from different experiments can be affected by the nature of the polymer, surface, polymer-surface interactions and, also, the experiment. A great deal has been learned about the behavior of polymers at interfaces, but there is also much to be learned about the interactions and how they affect the physical properties of adsorbed polymers. In the present study, we report both deuterium nuclear magnetic resonance (NMR) and modulated differential scanning calorimetry (MDSC) of poly(methyl acrylate) (PMA) adsorbed on Cab-O-Sil silica. The focus of this study is on the dynamics of polymer segments and the interfacial glass transition temperature (Tg). In our case, very small amounts of polymer were adsorbed, and we can view behavior of polymer segments in close proximity to the silica surface. We found that both NMR and MDSC experiments provide consistent insight into the dynamics of adsorbed polymers. Both experiments show the heterogeneous nature of the adsorbed polymers, with the polymer segments closer to the solid surface being the most motionally restricted resulting in a higher Tg for those segments

Discrete aqueous solvent effects and possible attractive forces

We study discrete solvent effects on the interaction of two parallel charged surfaces in ionic aqueous solution. These effects are taken into account by adding a bilinear non-local term to the free energy of Poisson-Boltzmann theory. We study numerically the density profile of ions between the two plates, and the resulting inter-plate pressure. At large plate separations the two plates are decoupled and the ion distribution can be characterized by an effective Poisson-Boltzmann charge that is smaller than the nominal charge. The pressure is thus reduced relative to Poisson-Boltzmann predictions. At plate separations below ~2 nm the pressure is modified considerably, due to the solvent mediated short-range attraction between ions in the the system. For high surface charges this contribution can overcome the mean-field repulsion giving rise to a net attraction between the plates.Comment: 12 figures in 16 files. 19 pages. Submitted to J. Chem. Phys., July 200

Dispersion control for matter waves and gap solitons in optical superlattices

We present a numerical study of dispersion manipulation and formation of matter-wave gap solitons in a Bose-Einstein condensate trapped in an optical superlattice. We demonstrate a method for controlled generation of matter-wave gap solitons in a stationary lattice by using an interference pattern of two condensate wavepackets, which mimics the structure of the gap soliton near the edge of a spectral band. The efficiency of this method is compared with that of gap soliton generation in a moving lattice recently demonstrated experimentally by Eiermann et al. [Phys. Rev. Lett. 92, 230401 (2004)]. We show that, by changing the relative depths of the superlattice wells, one can fine-tune the effective dispersion of the matter waves at the edges of the mini-gaps of the superlattice Bloch-wave spectrum and therefore effectively control both the peak density and the spatial width of the emerging gap solitons.Comment: 8 pages, 9 figures; modified references in Section 2; minor content changes in Sections 1 and 2 and Fig. 9 captio