Dual Relativity and Lorentz Transformations for Liquid-Like Media and Statistics from Scaling Concepts for Geometry

A dual class of Lorentz transformations (dual LT) for linear and Brownian motions in liquid-like media, is presented and discussed. It descends from two LT groups, for self-diffusion in simple liquids (BLT) and its geometrical analogy (GLT), which turned out to represent promising basic tools to deal with statistics at different length scales. Time dilation and length contraction of BLT occur upon ordering the originally indistinguishable molecular disorder in the liquid medium (i.e., a diffusivity lowering), giving rise to universality and scaling laws in polymer solutions. Dual LT exhibit a rich phenomenology, leading to a scale-dependent motion concept, where Brownian and quantum movements somewhat correspond. Density correlations in simple liquids, for instance, are suggested on this basis to behave like radial wave functions at the atomic scale. We also report some remarks on statistics in general, and its connection towards geometry.     

Conformational Polymer Statistics from the Geometrical Scaling of Monomeric Units and the Characteristic Ratio from Circle Maps. Application to Carbohydrate Macromolecules

Summary: Basic results on conformational chain statistics were formerly derived from scaling concepts for geometry and a relativistic picture of Brownian self‐diffusion in liquids. A polymer conformation was interpreted as a geometrical scaling law of its monomer shape, where the concept of characteristic ratio identifies a mean metric coefficient, originating topologically from rotational degrees of freedom internal to single molecules. Here, we add the former theoretical results to first numerical calculations. They are performed for three polysaccharides, provided with different chain topologies and constrained conformationally to identical square‐well energy states with increasing width. The spatial coil dilation‐contraction has been described satisfactorily by dihedral sine‐like rotations on a circle at dimeric length scales. New intrinsic quantities, like inner characteristic ratio and angular Kuhn step, both belonging to the shape of single molecules, have been finally defined. The geometrical mechanism bringing them at larger scales, to point out the chain shape size, is still unknown and under consideration.

Conformational energy landscape of nigerose.     

Wetting properties of the multiscaled nanostructured polymer and metallic superhydrophobic surfaces

A superhydrophobic surface is produced from industrial grade polymer materials. The surface comprises partly disordered triple-scaled arrays of polyvinylidene fluoride (PVDF) globules. An inherently superhydrophobic metallic surface is produced with polymer template. The mathematical model based on the Cassie-Baxter hypothesis of air trapping under a water drop is built, which gives the apparent contact angle on the manifold-scaled interface. The presence of several scales itself is not a sufficient condition of hydrophobicity of inherently wettable surfaces. The geometrical features favoring the increase of the vapor-water interface fraction are necessary for this phenomenon.     

Statistics of Polymer Solutions from Scaling Concepts for Geometry and Relativistic Self-Diffusion in Liquids

Basic results on conformational statistics of polymer solutions are derived from recent scaling concepts for geometry and a relativistic picture for Brownian self-diffusion in liquid media. Any chain conformation is interpreted as a geometrical state affected by its end-to-end dimension, which here denotes the mean deviation between geodesic paths diffusing in the relativistic liquid phase. Statistical polymer length distributions solve an ondulatory equation in non-Euclidean manifolds for coil extension and shape. When length scale is vanishing, the size scaling is found again in terms of parallelism angle rotations. The characteristic chain ratio identifies instead an average metric coefficient, originating topologically from rotational degrees of freedom internal to single molecules.     

Characterisation of roof tile coating degradation using nano-indentation test and surface profilometry

Nano-science and nano-technology have been extensively explored to develop functional and smart coating systems. In this context, it is important to investigate novel characterisation methodologies for surface feature measurement and evaluation of diverse coating systems at nano and micrometrical scales which cannot be implemented by conventional tests. In this study, nano-indentation test have been carried out to characterise the environmental degradation of a polymer coating on a building material substrate. Multiple locations were selected for nano-indention for analysis and evaluation. It has shown that the coating weathering led to a reduction in deformation depth and an increase of hardness and modulus. Furthermore, the weathering resulted in surface quality degradation, which was characterised by hugely reduced surface homogeneity in terms of standard deviations in deformation, hardness and modulus. The coating degradations were also characterised by surface roughness measurement by profilometry. There were significant differences in surface roughness at the micrometrical scale for coatings with varying environmental degradations. They were quantified in terms of surface roughness statistics. The micro morphologies of the coating were observed by SEM which showed a good agreement with results from nano-indentation test and surface roughness measurement. This study demonstrates that nano-indentation test and surface roughness measurement are viable methodologies to evaluate specialised polymer coating systems and to characterise their degradations at the nano and micrometrical scales.     

Simulation of aggregate structure and SANS-spectra in filled elastomers

We report preliminary simulations of anisotropic scattering from aggregates of small hard spherical particles embedded in an elastic polymer matrix, using simple geometrical methods. First we build several types of aggregates in three dimensions: crystalline, amorphous compact, fractals, of different numbers of particles and varying polydispersity. We then turn to the spectra of deformed samples simulated in two dimensions. We impose an affine displacement inside the matrix to the fillers, which can be isolated particles or small aggregates, and account for the collisions which arise due to lateral shrinking of the material. The two-dimensional scattering spectra are shown and discussed. They reproduce experimentally observed isointensity curves: ellipses, banana-shaped maxima and splitting of these maxima in four spots. Finally, we explore the consequences of the reduction to two dimensions via statistics of the number of collisions. It is found that even if collisions are more important in 3 dimensions, the behavior is qualitatively similar in two and three dimensions.     

Physical and mechanical properties of polyvinyl alcohol and polypropylene composite materials reinforced with fibril aggregates isolated from regenerated cellulose fibers

Natural fibers in micro and nano scales may be a potential alternative for man-made fibers because of the comparable mechanical properties to those of glass, carbon, and aramid fibers. Cellulose fibril and fibril aggregate are generally prepared by physical treatments, e.g., high-pressure homogenizer, or chemical treatments, e.g., acid hydrolysis. In this study, fibril aggregates were generated from a regenerated cellulose fiber by a novel mechanical treatment. The geometrical characteristics of the fibers and the fibril aggregates were investigated using scanning electron microscopy (SEM) and polarized light microscopy (PLM), and its crystallinity was investigated by wide angle X-ray diffraction (WAXD). The degree of fibrillation of the fibers was indirectly evaluated by water retention value (WRV). Nano-biocomposites reinforced with fibril aggregates were prepared by film casting and compression molding and evaluated by tensile test. The morphological characteristics of the nanocomposites were investigated with SEM and PLM. As reference, commercial microfibrillated cellulose was also used to reinforce biodegradable polymer.     

Variations in molecular compactness and chain entanglement during the compression of grafted polymers

Characterizing the effect of geometrical confinement on mean polymer shape is an important step towards understanding and controlling molecular behaviour at interfaces. In this work, we study the configurational transitions and molecular shape changes that take place when a grafted polymer (or “mushroom”) is compressed by a hard plane. The polymer is modelled as a single, permanently‐grafted chain with a Lennard‐Jones interaction between monomer beads. For this model, we have monitored molecular size, asphericity, and chain entanglements as a function of compression, from the regime of self‐avoiding walks to the regime of collapsed polymers. With these tools, we show that strong confinement can produce chain compactization and disentanglement even in the presence of a mild attractive interaction. Our results provide limit values to the degree of compression and monomer attraction that is necessary to deform strongly collapsed polymer mushrooms.     

C120异构富勒烯分子的AM1半经验量子化学研究

以哑铃状2C60聚合体、花生壳状2C60聚合体以及C120富勒烯分子为研究对象,采用AM1半经验量子化学方法,计算了3种C120异构富勒烯分子的几何构型、电子结构、分子能量、疏水常数、极化率与偶极矩;然后,根据计算结果,分析对比了3种C120异构体分子的化学稳定性与物理化学特性.研究结果表明,3种C120分子的形成均为吸热反应,它们的稳定性排序为:C120富勒烯>花生壳状2C60>哑铃状2C60分子.     

Mobility of Spherical Probe Objects in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement ?Δr(2)? of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (?Δr(2) (t)? ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (?Δr(2) (t)? ~ t(1/2)) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ(e) of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ(e)) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τ(rep). At longer times t > τ(rep), the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.     

Reptation theory: geometrical and topological aspects

This paper discusses topological and geometrical aspects of reptation theory which are common to all versions of reptation theory. These are: the postulated existence of the tube, the functional relationship between the tube diameter a and the polymer/monomer density p, the crossover from the Rouse to reptation regime. Statistical mechanics of the geometrically confined polymer chain is reanalyzed by careful separation of the diffusive motion of the chain into the longitudinal and transversal parts. Connection between old results and the new formalism is established. It is shown that the longitudinal motion resembles that known for directed polymers. This provides a source of the effective rigidification of the reptating chain's backbone thus facilitating the viscosity exponent to be larger than 3. The transversal motion is also reanalyzed. It is shown that the diffusion on the Bethe lattice used before to describe the transversal (planar) motion (conformational statistics) of the trapped chain is actually the diffusion on the universal covering of the corresponding Riemannian surface. This fact allows to reanalyze the tube stability using topological arguments. Detailed numerical comparison of the obtained new theoretical results with available experimental and Monte Carlo data is provided. Very good agreement between theory and experiment is found. It is also shown that the emerging physical picture of the tube destruction is isomorphic to that which was developed earlier with the help of the quantum Hall effect analogy (J. Phys. I 4 , 843 (1994)). Remarkable connections between the reptation theory and the theory of quantum chaotic/mesoscopic systems are established thus making the reptation theory part of the more general theory of quantum chaotic systems.     

Unmixing of polymer blends confined in ultrathin films: crossover between two-dimensional and three-dimensional behavior

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.     

NMR study of poly-p-isopropyl-α-methylstyrene

220 MHz NMR spectra of sample of poly-p-isopropyl-α-methylstyrene prepared through anionic (A) and cationic (B) polymerizations are studied. Peaks at τ values of 9.07, 9.41, and 9.71 are assigned to isotactic (i), heterotactic (h), and syndiotactic (s) α-methyl triads, respectively. From the α-methyl triads and the β-proton tetrads it is found that polymer A deviates little from Bernoullian statistics and that first-order Markov configurational statistics applies to polymer B. Isopropyl methine and methyl proton resonances are also analyzed in terms of the configurational statistics of the polymer. Resonances of the phenyl protons are assigned with increasing field to s, h, i meta and ortho protons.     

Two different one-dimensional structural motifs in the same coordination polymer: a novel interpenetration of infinite ladders by bundles of infinite chains

A coordination polymer with a novel structural motif consisting of stacks of infinite ladders interpenetrated by bundles of infinite chains is described; geometrical arguments are made for the requirements that can lead to such interpenetration as a function of ligand dimensions.     

Structure of the Polymer Obtained from Bisphenol-A and Cl 2 P(O)CH 3

Using the step-by-step build-up approach, the possible conformations of compound PhOP(O)(Me)OPh(Me) 2 Ph were constructed and geometrically optimized. Among the obtained structures 32 conformations belonging to low, comparable energy levels were used to construct the most stable dimers and tetramers of the title polymer. The results allowed us to estimate the geometrical structure of the polymer.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Some metrological aspects of the comparison between two ordinal measuring systems

The usage of ordinal scales (sometimes called ‘semi-quantitative’ scales) for performing measurements in the area of applied chemical metrology and quality assurance is widespread. This paper presents a method for handling actions such as calibration, measuring systems’ capabilities comparison and reproducibility evaluation as a comparison between two measuring systems (MSs) referring to a known/unknown reference standard. The strength of the agreement between these MSs is evaluated through two known versions of Cohen’s kappa statistics (the traditional one and the modified one). The effectiveness of these statistics from the metrological point of view is examined, and the preferability of the modified kappa statistics is demonstrated via an example.     

Dynamics and scaling of polymers in a dilute solution: analytical treatment in two and higher dimensions

We consider the dynamical scaling of a single polymer chain in good solvent. In the case of two-dimensional systems, Shannon and Choy [Phys. Rev. Lett. 79, 1455 (1997)] have suggested that the dynamical scaling for a dilute polymer solution breaks down. Using scaling arguments and analytical calculations based on the Zimm model, we show that the dynamical scaling of a dilute two-dimensional polymer system holds when the relevant dynamical quantities are properly extracted from finite systems. Most important, the polymer diffusion coefficient in two dimensions scales logarithmically with system size, in excellent agreement with our extensive computer simulations. This scaling is the reason for the failure of the previous attempts to resolve the dynamical scaling of dilute two-dimensional polymer systems. In three and higher dimensions our analytic calculations are in agreement with previous results in the literature.     

A polymer in an ionic liquid: Structural properties of a system during attraction between the polymer and cations of the ionic liquid

In terms of the polymer integral equation theory, structuring in ionic liquids containing flexiblechain polymers under the conditions of good solubility is studied for the first time. The influence of the polymer concentration on the structural properties of system components is studied at different lengths of polymer molecules. The structural organization of the ionic liquids is shown to be fairly stable after addition of the polymer. When there is attraction between the polar groups of cations of the ionic liquid and polymer molecules, the calculated structural factors suggest intermediate-range scales of polymer-component ordering. Given this, for any considered length of polymer molecules, there is a range of polymer concentrations in which the characteristic scale of ordering decreases with an increase in polymer density according to a power law.