The phase behaviour of single polyethylene chains with and without fixing one end

The phase behaviour of a single polyethylene chain is studied by using molecular dynamics simulations. A free chain and a chain with fixing one end are considered here, since the atomic force microscope （AFM） tip can play a significant role in polymer crystallization in experiment. For a free chain, it is confirmed in our calculation that the polymer chain exhibits an extended coil state at high temperatures, collapses into a condensed state at low temperatures, i.e. the coil-to-globule transition that is determined by a high temperature shoulder of the heat capacity curve, and an additional liquid-to-solid transition that is described by a low temperature peak of the same heat curve. These results accord with previous studies of square-well chains and Lennard-Jones homopolymers. However, when one of the end monomers of the same chain is fixed the results become very different, and the chain cannot reach an extended coil-like state as a free chain does at high temperatures, i.e. there exists no coil-to-globule-like transition. These results may provide some insights into the influence of AFM tip when it is used to study the phase behaviour of polymer chains. If the interaction force between AFM tip and polymer monomers is strong, some monomers or one of them can be seen as being fixed by the tip, which is similar to our simulation model, and it is also found that AFM tip could induce polymer crystallization.     

A new simulation method for the determination of forces in polymer/colloid systems

We introduce a new simulation method, which we call the contact-distribution method, for the determination of the Helmholtz potential for polymer/colloid systems from lattice Monte-Carlo simulations. This method allows one to obtain forces between finite or semi-infinite objects of any arbitrary shape and dimensions in the presence of polymer chains in solution or physisorbed or chemisorbed at interfaces. We illustrate the application of the method using two examples: (i) the interaction between the tip of an atomic force microscope (AFM) and a single, end-grafted polymer chain and (ii) the interaction between an AFM tip and a polymer brush. Numerical results for the first two cases illustrate how the method can be used to confirm and extend scaling laws for forces and Helmholtz potentials, to examine the effects of the shapes and sizes of the objects and to examine conformational transitions in the polymer chains. Received: 15 May 1998 / Revised: 11 June 1998 / Accepted: 12 June 1998     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Effect of surface property of polyimide substrate on the formation of pentacene thin-film

We investigated the effect of surface property of polyimide substrate on the formation of pentacene thin-film by using atomic force microscopy (AFM) and X-ray reflectivity (XRR) and diffuse scattering (XDS). Two types of polymer films were prepared: (1) polyimide (PAA-PI) from poly(amic acid) (PAA) (2) polyimide hybrid (PAA-PI-H) prepared by hybridizing the PAA and soluble polyimide (PI) with a octadecyl side chain. The hybridization ratio of PI to PAA was 2/98 in wt%. The water contact angle for PAA-PI-H and PAA-PI were around 80° and 64°, respectively. Morphology of pentacene with a ropelike structure and (1 1 0) peak around 1.4 Å in q_z was found when it was deposited on PAA-PI thin-film. Different pentacene morphology was observed when it was deposited on PAA-PI-H thin-film. The different morphology might be due to a 5-6 nm thick additional layer (∼0.95 ρ_film) at the interface between pentacene and PAA-PI-H thin-film caused by a long alkyl side chain introduced to the polymer main chain.     

Surface morphology of cellulose films prepared by spin coating on silicon oxide substrates pretreated with cationic polyelectrolyte

Flat cellulose films were prepared and morphologically modified by spin coating a cellulose/N-methylmorpholine-N-oxide/H₂O solution onto silicon oxide substrates pre-coated with a cationic polyelectrolyte. Spin-coated cellulose films were allowed to stably form on the silicon oxide substrates by pretreatment with either polydiallyldimethylammonium chloride (PDADMAC) or polyvinylamine (PVAm). The film surfaces obtained were analyzed by X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). AFM topographical images of the cellulose film surfaces showed a different morphology depending on the underlying polymer, where PVAm pretreatment brought about an anisotropic surface topology. These results suggest that the specific attraction acting at the cellulose/polymer interface influences both the film formation and surface morphology of the cellulose layer. Differences in the solvent used to precipitate cellulose caused variations in the surface roughness by affecting the cellulose separation behavior. The morphological features of spin-coated cellulose film surfaces could be altered to some extent by these film preparation techniques.     

Poly-benzyl domains grown on porous silicon and their I-V rectification

Microwave-irradiated polymerization of benzyl chloride and triphenyl chloromethane on hydride-terminated porous silicon (PS) was achieved through the use of Zn powder as a catalyst. Transmission infrared Fourier-transform spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS) analyses confirmed the poly-benzyl membranes grafted on PS. Topographical images by AFM revealed crystal-like domains rather than homogenous monolayers on the surface. The current-voltage measurements in nano-scale by current sensing atomic force microscopy (CS-AFM) showed the rectification behavior of this polymer membrane. Finally, mechanism of a radical initiation on the surface and a following Friedel-Crafts alkylation was proposed for the covalent assembly of poly-benzyl domains.     

Factors affecting phase and height contrast of diblock copolymer PS-b-PEO thin films in dynamic force mode atomic force microscopy

Asymmetric PS-b-PEO block copolymer exhibits well-ordered cylindrical morphology with nanoscale domain sizes due to microphase separation. Since the PS and PEO blocks have large stiffness difference, this polymer system represents an ideal candidate for studies of the phase contrast behavior in atomic force microscopy (AFM). In this paper, PS-b-PEO films are investigated under different scanning conditions using two different atomic force microscopes. It is found that the phase contrast of the film can be well described in terms of energy dissipation, though the exact phase image may also depend on the scanning parameters (e.g., the repulsive versus attractive regimes) as well as the settings of the microscope. Height variation on sample surface does not have significant effect on phase contrast. However, in order to obtain true topography of the polymer film, care has to be taken to avoid damage to the sample by AFM. Under certain conditions, true topography can be obtained during the first scan in spite of the surface-damaging forces are used.     

Correlation of atomic force microscopy detecting local conductivity and micro‐Raman spectroscopy on polymer–fullerene composite films

Thin hetero‐junction composite films of polymer (electron donor) and fullerene (electron acceptor) are prepared on indium‐tin‐oxide coated glass by spin‐coating from solution in dichlorobenzene. Optimized atomic force microscopy (AFM) parameters allowed us to scan these soft composite films in contact mode and to measure their local conductivity with high lateral resolution by current‐sensing AFM. The morphology and local conductivity data are correlated with Kelvin force microscopy and micro‐Raman mapping and discussed with view to their photovoltaic properties. Regions with both compounds present are compared to areas where the components segregated, acting as shunts of the junction. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Surface analytical studies of Ar-plasma etching of thin heptadecafluoro-1-decene plasma polymer films

An audio-frequency plasma polymerization set-up with a planar plasma source was used to deposit thin heptadecafluoro-1-decene (HDFD) plasma polymer films. The morphology and chemical structure of the films after deposition were compared with the state of the film after a subsequent Ar-plasma treatment by means of in situ Fourier transform infrared reflection absorbance spectroscopy (FT-IRRAS), X-ray photoelectron spectroscopy (XPS), time-of-flight secondary ion mass spectrometry (ToF-SIMS) and atomic force microscopy (AFM) as well as contact angle measurements. The results revealed the correlation of wettability of the model Teflon-like films with change of surface chemistry and surface topography as a result of Ar-plasma treatment.     

Influence of surface energy and relative humidity on AFM nanomechanical contact stiffness

The effects of surface functionality and relative humidity (RH) on nanomechanical contact stiffness were investigated using atomic force acoustic microscopy (AFAM), a contact scanned-probe microscopy (SPM) technique. Self-assembled monolayers (SAMs) with controlled surface energy were studied systematically in a controlled-humidity chamber. AFAM amplitude images of a micropatterned, graded-surface-energy SAM sample revealed that image contrast depended on both ambient humidity and surface energy. Quantitative AFAM point measurements indicated that the contact stiffness remained roughly constant for the hydrophobic SAM but increased monotonically for the hydrophilic SAM. To correct for this unphysical behavior, a viscoelastic damping term representing capillary forces between the tip and the SAM was added to the data analysis model. The contact stiffness calculated with this revised model remained constant with RH, while the damping term increased strongly with RH for the hydrophilic SAM. The observed behavior is consistent with previous studies of surface energy and RH behavior using AFM pull-off forces. Our results show that surface and environmental conditions can influence accurate measurements of nanomechanical properties with SPM methods such as AFAM.     

Adsorption of polymer chains by disordered traps

We study the adsorption cross-over of ideal polymer chains in an environment of disordered traps. Starting from the assumption of an optimal cluster size of traps (optimal fluctuation method) we derive a general scaling form of the free energy function for arbitrary spatial dimensions. For small concentrations of traps we find a cross-over from localized (adsorbed) behavior to delocalized behavior depending on the chain's length and on the depth of the traps; this is connected with the non-monotonic behavior of the chain's extension. In terms of the free energy of the chain this cross-over resembles a first order transition scenario, the chain gets localized at many traps at once. Received 18 November 1998     

Deformation of a tethered polymer in uniform flow

Static properties of a single polymer fixed at one end and subjected to a uniform flow field are investigated for several polymer models: the Gaussian chain, the freely jointed chain, and the FENE (Finitely Extensible Nonlinear Elastic) chain. By taking into account first the excluded-volume interaction and subsequently also the hydrodynamic interaction, the polymer models are gradually completed and the relevance of each effect for the polymer deformation can be identified. Results from computer simulations of these bead spring chains are compared with analytical calculations using either the conformational distribution function or blob models. To this end, in contrast to the blob model with non-draining blobs introduced for a tethered polymer by Brochard-Wyart, we here develop also a model with free-draining blobs. It turns out that a limited extensibility of the polymer – described by nonlinear spring forces in the model – leads to a flow velocity dependence of the end-to-end distance, segment density, etc. which agrees with the power law predictions of the blob model only for very long chains and in a narrow range of flow velocities. This result is important for comparison with recent experiments on DNA molecules which turn out to be still rather short in this respect. The relative importance of finite extensibility, the excluded-volume effect, and hydrodynamic interactions for polymers in flow is not fully understood at present. The simulation of reasonably long chains becomes possible even when fluctuating hydrodynamic interactions are taken into account without employing averaging procedures by introducing efficient numerical approximation schemes. At medium velocity of the uniform flow the polymer is partially uncoiled and simulations show that the effects of excluded-volume and hydrodynamic interactions are position-dependent. Both are stronger near the free end than near the tethered end of the polymer. A crossover from a nearly non-draining polymer at small flow velocities to a free-draining almost uncoiled chain at large velocities is found in the simulations. Accordingly, models assuming the polymer to be composed of either free- or non-draining subunits, like the two blob models, cannot correctly describe the extension and shape of a tethered polymer in flow, and simple power laws for the polymer extension, etc. cannot be expected. Received 21 June 1999     

Specific heat study of quasi-one-dimensional antiferromagnetic model for an organic polymer chain

The specific heat of an infinite one-dimensional polymer chain bearing periodically arranged side radicals connected to the even sites is studied by means of quantum transfer-matrix method based on a Ising-Heisenberg model. In the absence of the exchange interactions between side radicals and the main chain, the curves of specific heat show a round peak due to the antiferromagnetic excitations for the all antiferromagnetic interactions along the polymer chain. Considering the exchange interactions between the side radicals and the main chain, the curves of the specific heat show double-peak structure for ferromagnetic interactions between the radicals and main chain, indicating that a competition between ferromagnetic and antiferromagnetic interactions and the possibility of the occurrence of the stable ferrimagnetic state along the polymer chain.     

AFM‐Based Single Molecule Force Spectroscopy of Polymer Chains: Theoretical Models and Applications

Abstract

In recent years, remarkable advances in research of the mechanical and structural properties of single polymer chains have been achieved thanks to atomic force microscope (AFM)‐based single molecule force spectroscopy (SMFS). This technique offers great possibilities to investigate the mechanical properties of a single polymer chain by static/dynamic force‐extension measurements at the mesoscale level. Data are analyzed with the help of appropriate theoretical models, such as statistical mechanics models for freely jointed chains (FJC) or worm‐like chains (WLC), which can well describe the moderate entropy‐controlled stretch of most polymers, and with semiclassical models, which are being modified using quantum mechanics principles to account for entropic and enthalpic contributions to stretching in the high‐force Hookean regime. In this article we review the theoretical models of single chain stretching, the latest progress in force‐extension measurements by static and dynamic AFM modes for polymer chains dispersed in different solvents and subjected to a force that may induce their conformational transformations, as well as relevant applications.     

Quantification of entanglement from magnetic susceptibility for a Heisenberg spin 1/2 system

We report temperature and magnetic field dependent magnetization and quantification of entanglement from the experimental data for dichloro (thiazole) copper (II), a Heisenberg spin chain system. The plot of magnetic susceptibility vs. temperature indicates an infinite spin chain. Isothermal magnetization measurements (as functions of magnetic field) were performed at various temperatures below the antiferromagnetic (AFM) ordering, where the AFM correlations persist significantly. These magnetization curves are fitted to the Bonner–Fisher model. Magnetic susceptibility is used as an entanglement witness to quantify the amount of entanglement in the system.     

Analysis of infrared reflectivity of conducting polymers: example of camphor-sulphonic-acid-doped polyaniline

The reflectivity spectrum of a polyaniline CSA-doped in presence of m-cresol has been measured over the wide wavenumber range of 15- 9 000 cm ^-1 (0.002-1.1 eV) at room temperature. Experimental data compare well with similar experiments performed by another group. The conductivity spectrum of this conducting polymer has been deduced from the reflectivity spectrum by means of two methods, Kramers-Kronig transformation and best fit of an “extended Drude” model to the reflectivity spectrum. Whereas the deviation from Drude behavior was interpreted in terms of Anderson localization or by inhomogeneous disorder by other groups, it is shown here that a different model developed for conducting oxides that also exhibit non-Drude behavior, applies very well to this example of conducting polymer. Received 11 February 1999 and Received in final form 26 April 1999     

A two-leg spin ladder model for fumarate-bridged chain-like polymer of Cu(II)

In this paper, the transfer matrix renormalization group method is used to study the thermodynamic and the magnetic properties of a novel one-dimensional fumarate-bridged Cu(II) chain by a two kinds of models. One simplified model is that of the dominant ferromagnetic and antiferromagnetic alternating chain, which is only in rough agreement with the experimental results. Further research shows a possible mechanism of alternating strong ferromagnetic and weak antiferromagnetic interaction among one chain. Considering the weak antiferromagnetic interaction existing in the actual materials, we propose a two-leg spin ladder model with intrachain ferromagnetic and weak interchain antiferromagnetic interaction. The obtained theoretical results are in quite good agreement with experimental curves, which indicates the two-leg spin ladder model is appropriate to describe the fumarate-bridged chain-like polymer of Cu(II).     

Speed dependence of atomic stick-slip friction in optimally matched experiments and molecular dynamics simulations

The atomic stick-slip behavior of a Pt tip sliding on a Au(111) surface is studied with atomic force microscopy (AFM) experiments and accelerated (i.e., reduced sliding speed) molecular dynamics (MD) simulations. The MD and AFM conditions are controlled to match, as closely as possible, the geometry and orientation, load, temperature, and compliance. We observe clear stick-slip without any damage. Comparison of both MD and AFM results with the thermally activated Prandtl-Tomlinson model shows that MD results at the highest speeds are not in the thermally activated regime. At lower speeds, within the thermally activated regime, AFM and MD provide consistent energetics, but attempt frequencies differ by orders of magnitude. Because this discrepancy lies in attempt frequencies and not energetics, atomistic details in MD simulations can be reliably used in interpreting AFM data if the MD speeds are slow enough.     

Adsorption of polyampholytes on charged surfaces

We have studied the adsorption of neutral polyampholytes on model charged surfaces that have been characterized by contact angle and streaming current measurements. The loop size distributions of adsorbed polymer chains have been obtained using atomic-force microscopy (AFM) and compared to recent theoretical predictions. We find a qualitative agreement with theory; the higher the surface charge, the smaller the number of monomers in the adsorbed layer. We propose an original scenario for the adsorption of polyampholytes on surfaces covered with both neutral long-chain and charged short-chain thiols. Received 22 February 2002 and Received in final form 23 April 2002