By means of sophisticated Monte Carlo methods, we investigate the conformational phase diagram of a simple model for flexible polymers with explicit thickness. The thickness constraint, which is introduced geometrically via the global radius of curvature of a polymer conformation, accounts for the excluded volume of the polymer and induces cooperative effects supporting the formation of secondary structures. In our detailed analysis of the temperature and thickness dependence of the conformational behavior for classes of short tubelike polymers, we find that known secondary-structure segments like helices and turns, but also ringlike conformations and stiff rods are dominant intrinsic topologies governing the phase behavior of such cooperative tubelike objects. This shows that the thickness constraint is indeed a fundamental physical parameter that allows for a classification of generic polymer structures.
In this work we present the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among non-bonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness influences the thermodynamic behavior of simple tubelike polymers significantly, i.e., for given temperature, the formatio…
In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of su…
In their tubelike phase, nanowire-adsorbed polymers exhibit strong structural similarities to morphologies known from single-walled carbon (hexagonal) and boron (triangular) nanotubes. Since boron/boron nitride tubes require some disorder for stability the triangular polymer tubes provide a closer analog to the carbon tubes. By means of computer simulations of both two and three dimensional versions of a coarse-grained bead-spring model for the polymers, we investigate their structural properties and make a detailed comparison with structures of carbon nanotubes.
Generalized-ensemble simulations enable the study of complex adsorption scenarios of a coarse-grained model polymer near an attractive nanostring, representing an ultrathin nanowire. We perform canonical and microcanonical statistical analyses to investigate structural transitions of the polymer and discuss their dependence on the temperature and on model parameters such as effective wire thickness and attraction strength. The result is a complete hyperphase diagram of the polymer phases, whose locations and stability are influenced by the effective material properties of the nanowire and the …
I develop a kinetic mechanism to explain chain folding in polymer crystallization which is based on the competition between the formation of stems, which is due to frequent occupations of trans states along the chains in the supercooled polymer melt, and the random coil structure of the polymer chains. Setting equal the average formation time of stems of length $% d_l$ with the Rouse time of a piece of polymer of the same arc length $d_l$ yields a lower bound for the thickness of stems and bundles. The estimated lamellar thickness is inversely proportional to the supercooling. The present appr…
We present results from molecular dynamics simulations of strictly two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of thickness of the order of the radius of gyration. We find that the dynamics of the 2D melt is qualitatively different from that of the films. The 2D monomer mean-square displacement shows a $t^{8/15}$ power law at intermediate times instead of the $t^{1/2}$ law expected from Rouse theory for nonentangled chains. In films of finite thickness, chain entanglements may occur. The impact of confinement on the entanglement length $N_\mathrm{e}$ has been a…
Dynamics of thin films of poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) have been investigated by dielectric relaxation spectroscopy in the frequency range from 0.1Hz to 1MHz at temperatures from 263K to 423K. The $α$-process, the key process of glass transition, is observed for thin films of PVAc and PMMA as a dielectric loss peak at a temperature $T_α$ in temperature domain with a fixed frequency. For PMMA the $β$-process is also observed at a temperature $T_β$. For PVAc, $T_α$ decreases gradually with decreasing thickness, and the thickness dependence of $T_α$ is almost in…
Dielectric relaxation and thermal expansion spectroscopy were made for thin polystyrene films in order to measure the temperature $T_α$ corresponding to the peak in the loss component of susceptibility due to the $α$-process and the $α$-relaxation time $τ$ as functions of film thickness $d$. While the glass transition temperature $T_{\rm g}$ decreases with decreasing film thickness, $T_α$ and $τ$ were found to remain almost constant for $d>d_{\rm c}$ and decrease drastically for $d<d_{\rm c}$ for high temperatures. Here, $d_{\rm c}$ is a critical thickness. Near the glass transition temperatur…
The $α$-process (segmental motion) of thin polystyrene films supported on glass substrate has been investigated in a wider frequency range from 10$^{-3}$ Hz to 10$^4$ Hz using dielectric relaxation spectroscopy and thermal expansion spectroscopy. The relaxation rate of the $α$-process increases with decreasing film thickness at a given temperature above the glass transition. This increase in the relaxation rate with decreasing film thickness is much more enhanced near the glass transition temperature. The glass transition temperature determined as the temperature at which the relaxation time o…
Glass transition process gets affected in ultrathin films having thickness comparable to the size of the molecules. We observe systematic broadening of glass transition temperature (Tg) as the thickness of the polymer film reduces below the radius of gyration but the change in the average Tg was found to be very small. Existence of reversible negative and positive thermal expansion below and above Tg increased the sensitivity of our thickness measurements performed using energy dispersive x-ray reflectivity. A simple model of Tg variation as a function of depth expected from sliding motion cou…
It is shown that the intrinsic stress in solvent cast polymer coatings plays a key role in the nucleation of holes in the film. Nucleation is important because it is meanwhile clear that heterogeneous nucleation is the only relevant rupture mechanism for the technologically relevant thickness regime well above 100 nm. The most striking feature is that in contrast to what has been widely believed, the number density of holes scales not algebraically, but exponentially with the film thickness.
We consider the continuum limit of a recently-introduced model for discretized thick polymers, or tubes. We address both analytically and numerically how the polymer thickness influences the decay of tangent-tangent correlations and find how the persistence length scales with the thickness and the torsional rigidity of the tube centerline. At variance with the worm-like chain model, the phase diagram that we obtain for a continuous tube is richer; in particular, for a given polymer thickness there exists a threshold value for the centerline torsional rigidity separating a simple exponential de…
The glass transition temperature $T_{\rm g}$ and the temperature $T_α$ corresponding to the peak in the dielectric loss due to the $α$-process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in $T_{\rm g}$ was observed with decreasing film thickness, while $T_α$ was found to remain almost constant for $d>d_{\rm c}$ and to decrease drastically with decreasing d for $d<d_{\…
Polybutene-1 (PB-1), a typical semicrystalline polymer, in its stable form I shows a peculiar temperature dependent strain-whitening behavior when being stretched at different temperatures where the extent of strain-whitening weakens with the increasing of stretching temperature reaching a minima value followed by an increase at higher stretching temperatures. Correspondingly, a stronger strain-hardening phenomenon was observed at higher stretching temperatures. The strain-whitening phenomenon in semicrystalline polymers has its origin of cavitation process during stretching. In this work, the…
Atactic polystyrene of two different molecular weights (560900 g.mol-1 and 212400 g.mol-1) have been studied as spin-coated films of thickness varying from ~30 nm to ~250 nm, i.e., ~2Rg to ~12Rg where Rg is the unperturbed radius of gyration of polystyrene, using x-ray reflectivity and transmission UV-spectroscopy. Electron density profiles along depth of the films show formation of layers parallel to the substrate surface, when the film thickness is below 4Rg, with layer spacing ~2Rg. The pure electronic singlet 1A1g -> 1E1u indicates exciton interaction throughout film thickness, as evidence…
We present a modified version of our "sliding model", where chain arcs, between two contacts at the surface, may move if all the barriers along the arc are weaker than a certain threshold.An important advance of the revised model is that the high limiting chain lengths N* observed in the experiments are naturally accoundted for. In this model, a film of thickness h, smaller than the coil size, can show either a "sandwich" structure with two mobile sublayers (at low temperatures T<T(h)), or a single mobile layer at T>T(h). But the accident occurring at T=T(h), does not necessarily coincide with…
The equilibrium properties of block copolymer micelles confined in polymer thin films are investigated using self-consistent field theory. The theory is based on a model system consisting of AB diblock copolymers and A homopolymers. Two different methods, based on the radius of gyration tensor and the spherical harmonics expansion, are used to characterize the micellar shape. The results reveal that the morphology of micelles in thin films depends on the thickness of the thin films and the selectivity of the confining surfaces. For spherical (cylindrical) micelles, the spherical (cylindrical) …
We consider solutions where the surface tension of the solvent is smaller than the surface tension of the polymer. In an evaporating film, a plume of solvent rich fluid, then induces a local depression in surface tension, and the surface forces tend to strengthen the plume. We give an estimate (at the level of scaling laws) for the minimum thickness required to obtain this instability. We predict that the thickness a) is a decreasing function of the solvent vapor pressure b) should be very small (<1 micron) provided that the initial solution is rather dilute. The overall evaporation time for t…
Dewetting of ultra-thin polymer films near the glass transition exhibits unexpected front morphologies [G. Reiter, Phys. Rev. Lett., 87, 186101 (2001)]. We present here the first theoretical attempt to understand these features, focusing on the shear-thinning behaviour of these films. We analyse the profile of the dewetting film, and characterize the time evolution of the dry region radius, $R_{d}(t)$, and of the rim height, $h_{m}(t)$. After a transient time depending on the initial thickness, $h_{m}(t)$ grows like $\sqrt{t}$ while $R_{d}(t)$ increases like $\exp{(\sqrt{t})}$. Different regim…
This paper is an attempt to predict the thickness and modulus at the nanometric interphase region with the knowledge on the macroscopic Young's modulus in the polymer-clay nanocomposites. First, a systematic design of 20160 linear elastic finite element simulations are used to derive an analytical equation between the interphase thickness, the interphase modulus, the nanoclay content and the macroscopic Young's modulus of the nanocomposite. Four calibration parameters in this equation are calculated based on the reported data about NYLON6-MMT nanocomposite. Next, an analytical nanoscale equati…
The glass transition temperature $T_g$ and the temperature $T_α$ corresponding to the peak in the dielectric loss due to the $α$-process have been simultaneously determined as functions of film thickness $d$ through dielectric measurements for thin films of polystyrene. A decrease of $T_g$ was observed with decreasing film thickness, while $T_α$ was found to remain almost constant for $d > d_c$ and decrease drastically for $d < d_c$. Here, $d_c$ is a critical thickness dependent on molecular weight. The thickness dependence of $T_g$ is related to the distribution of relaxation times of the $α$…
Two-dimensional semiflexible polymer rings are studied both by imaging circular DNA adsorbed on a mica surface and by Monte Carlo simulations of phantom polymers as well as of polymers with finite thickness. Comparison of size and shape of the different models over the full range of flexibilities shows that excluded volume caused by finite thickness induces an anisotropic increase of the main axes of the conformations, a change of shape, accomplished by an enhanced correlation along the contour.
The glass transition temperature ($T_g$) of polymer thin films has been a subject of controversy in the last two decades. (Pseudo)thermodynamic determinations of $T_g$ generally suggest a significant depression, whereas the molecular mobility is found to be unchanged. The present study clarifies this apparent controversy by assuming that the $T_g$ in thin films is determined not only by the molecular mobility but also by the thickness of the film. This hypothesis is supported by the analysis of literature results on polystyrene thin films showing that the $T_g$ dependence on the cooling rate o…
Theory is presented for the phase stability of mixtures containing nanospheres and non-adsorbing reversible supramolecular polymers. This was made possible by incorporating the depletion thickness and osmotic pressure of reversible supramolecular polymer chains into generalized free-volume theory, recently developed for investigating the phase behaviour of colloidal spheres mixed with interacting polymers [Adv. Colloid Interface Sci. 143 (2008) 1-47]. It follows that the fluidfluid phase stability region where reversible supramolecular polymer chains can be mixed with nanospheres is sensitive …
We perform molecular dynamics simulations of an idealized polymer melt surrounding a nanoscopic filler particle to probe the effects of a filler on the local melt structure and dynamics. We show that the glass transition temperature $T_g$ of the melt can be shifted to either higher or lower temperatures by appropriately tuning the interactions between polymer and filler. A gradual change of the polymer dynamics approaching the filler surface causes the change in the glass transition. We also find that while the bulk structure of the polymers changes little, the polymers close to the surface te…
Density of the polyacrylamide ultrathin films has been studied using X-ray reflectivity technique. Two sources (one powder and another aqueous solution) of polyacrylamide were used to prepare spin coated films on silicon substrate. Light scattering measurements show that the polymer chains were unentangled in a concentrated (4 mg/ml) as well as in a dilute (2 mg/ml) solution prepared from the powder, whereas the solution (4 mg/ml) prepared by diluting the solution source shows entangled chain morphology. Three sets of films of different thicknesses were prepared using the three solutions by sp…
We study the effect of surface fields on the interfacial properties of a binary polymer melt confined between two parallel walls. Each wall attracts a different component of the blend by a non-retarded van der Waals potential. An interface which runs parallel to the surfaces is stabilized in the center of the film. Using extensive Monte Carlo simulations we study the interfacial properties as a function of the film thickness, the strength of the surface forces and the lateral size over which the profiles across the film are averaged. We find evidence for capillary wave broadening of the appare…
Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $ξ$, the chain size parallel to the walls diverges logarithmically, $R^2/…
Ionic electro-active polymers (E.A.P.) can be used as sensors or actuators. For this purpose, a thin film of polyelectrolyte is saturated with a solvent and sandwiched between two platinum electrodes. The solvent causes a complete dissociation of the polymer and the release of small cations. The application of an electric field across the thickness results in the bending of the strip and vice versa. The material is modelled by a two-phase continuous medium. The solid phase, constituted by the polymer backbone inlaid with anions, is depicted as a deformable porous media. The liquid phase is com…
Ionic electro-active polymers (E.A.P.) is an active material consisting in a polyelectrolyte (for example Nafion). Such material is usually used as thin film sandwiched between two platinum electrodes. The polymer undergoes large bending motions when an electric field is applied across the thickness. Conversely, a voltage can be detected between both electrodes when the polymer is suddenly bent. The solvent-saturated polymer is fully dissociated, releasing cations of small size. We used a continuous medium approach. The material is modelled by the coexistence of two phases; it can be considere…
The structural features of polystyrene brushes grafted on spherical silica nanoparticles immersed in polystyrene are investigated by means of a Monte Carlo methodology based on polymer mean field theory. The nanoparticle radii (either 8 nm or 13 nm) are held constant, while the grafting density and the lengths of grafted and matrix chains are varied systematically in a series of simulations. The primary objective of this work is to simulate realistic nanocomposite systems of specific chemistry at experimentally accessible length scales and study the structure and scaling of the grafted brush. …
Nanoscale polymeric thin films are widely used in diverse applications such as energy devices, flexible electronics and biosensors, where a satisfactory mechanical performance is of vital importance to realize their full functionality. It has been evidenced that the elastic properties of polymer films are often strongly affected by their thickness; however, the underlying mechanism of this phenomenon, especially a thorough understanding at the microscopic level, has yet to be achieved. Here we established a coarse-grained molecular dynamics (CGMD) based computational framework, combining with …
We characterize the equilibrium thermodynamics of a thick polymer confined in a spherical region of space. This is used to gain insight into the DNA packaging process. The experimental reference system for the present study is the recent characterization of the loading process of the genome inside the $ϕ$29 bacteriophage capsid. Our emphasis is on the modelling of double-stranded DNA as a flexible thick polymer (tube) instead of a beads-and-springs chain. By using finite-size scaling to extrapolate our results to genome lengths appropriate for $ϕ$29, we find that the thickness-induced force ma…
In frameworks of the scaling theory of phase transitions and critical phenomena the quantitative dependence of macroscopic properties on nanostructural parameters in a polymeric material is revealed. The draw ratios at neck and at break are referred to the macroscopic properties. The structure is characterized by an average thickness of amorphous layers in isotropic melt-crystallized linear high density polyethylene which is chosen as an example. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the chain ends collision probability. This pro…
Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native state structures and is not incompatible with the existence of structured building blocks such as $α$-helices and $β$-strands. We present a discussion on how the notion of the thickness of a polymer chain, besides being useful in describing a chain molecule in the continuum limit, plays a vital role in interpolating between conventional polymer physics and th…
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by a special three body interaction and impacts on the behaviour both locally and non-locally. When thick polymers undergo compaction due to an attractive self-interaction, we find a new type of phase transition between a compact phase and a swollen phase at zero temperature on increasing the thickness. In the vicinity of this transition, short tubes form space…
We study the interplay between wetting and miscibility of a symmetric polymer mixture via MC simulations and SCF calculations. The film surfaces interact with the monomers via short ranged potentials and the wetting transition is of first order. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point. The crossover be…
The behavior of a strongly charged polymer adsorbed on an oppositely charged surface of low-dielectric constant is formulated by the functional integral method. By separating the translational, conformational, and fluctuational degrees of freedom, the scaling behaviors for both the height of the polymer and the thickness of the diffusion layer are determined. Unlike the results predicted by scaling theory, we identified the continuous crossover from the weak compression to the compression regime. All teh analytical results are found to be consistent with Monte-Carlo simulations. Finally, an al…
One measure of geometrical complexity of a spatial curve is the number of crossings in a planar projection of the curve. For $N$-noded ring polymers with a fixed knot type, we evaluate numerically the average of the crossing number over some directions. We find that the average crossing number under the topological constraint are less than that of no topological constraint for large $N$. The decrease of the geometrical complexity is significant when the thickness of polymers is small. The simulation with or without a topological constraint also shows that the average crossing number and the av…
The formation of chain-folded structures from the melt is observed in molecular dynamics simulations resembling the lamellae of polymer crystals. Crystallization and subsequent melting temperatures are related linearly to the inverse lamellar thickness. Analysis of the single chain conformations in the crystal shows that most chains reenter the same lamella by tight backfolds. Simulations are performed with a mesoscopic bead-spring model including a specific angle bending potential. They demonstrate that chain stiffness alone, without an attractive inter-particle potential, is a sufficient dri…
We study the conformational behavior of a polymer adsorbed at an attractive nanostring and construct the complete structural phase diagram in dependence of the binding strength and effective thickness of the string. For this purpose, Monte Carlo optimization techniques are employed to identify lowest-energy structures for a coarse-grained hybrid polymer-wire model. Among the representative conformations in the different phases are, for example, compact droplets attached to the string and also nanotube-like monolayer films wrapping the string in a very ordered way. We here systematically analyz…
Using extensive Monte Carlo simulations we study the phase diagram of a symmetric binary (AB) polymer blend confined into a thin film as a function of the film thickness D. The monomer-wall interactions are short ranged and antisymmetric, i.e, the left wall attracts the A-component of the mixture with the same strength as the right wall the B-component, and give rise to a first order wetting transition in a semi-infinite geometry. The phase diagram and the crossover between different critical behaviors is explored. For large film thicknesses we find a first order interface localisation/delocal…
The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both linear dimensions and on the nature of boundary conditions and statistical ensembles applied. These phenomena generic for systems in confined geometry are demonstrated by Monte-Carlo simulations of the bond fluctuation model of symmetric polymer mixtures. Both the canonical and semi-grand-canonical ensemble are studied. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as t…
Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this relaxed structure after the compression is released can be slowed to the scale of tens of minutes and that the recovery time grows rapidly with molecular weight. We argue that the arrested state of the free layer before relaxation can be described as a Guiselin brush structure1, in which the surface excess lies at heights of the order of the layer thickness, unlike an adsorbed layer. This brush structure predicts an exponential falloff of …
A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed characteristics of protein structures. The authors show here that proteins may be regarded as tubes of nonzero thickness. This approach allows one to bridge the conventional compact polymer phase with a novel phase employed by Nature to house biomolecular structures. The continuum description of a tube (or a sheet) of arbitrary thickness entails using appropriately c…
The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^ν$, where $ν\approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.
Surface segregation of the low-molecular weight component in a polymeric mixture leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer and oligomer-gel systems following a temperature quench. We compute equilibrium and time varying migrant density profiles and wetting layer thickness using coarse grained molecular dynamics and mesoscale hydrodynamics simulations to demonstrate that surface migration in oligomer-gel systems is significantly reduced due to network elasticity. Further, phase separation proces…
Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has …
In frameworks of scaling theory of phase transitions and critical phenomena the structure of melt-crystallized polymers is discussed. The model constructed follows drawing polymeric materials and dissipating the energy during the transition from isotropic to oriented state. It is possible to estimate temperatures of secondary relaxation transitions. The entropic parameters of the model are: the space dimension; the number of components of an ordering field; the polymerization degree. The Kuhn segment, the melting temperature and the difference of energies of two rotating isomers can be regarde…
