Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation

We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated rigorously, tube renewal is taken into account in an approximation motivated by random walk theory. We find microstructure effects to be present for remarkably large times and long chains, affecting essentially all present day computer experiments. The various asymptotic power laws, commonly considered as typical for reptation, hold only for extremely long chains. Furthermore, for an arbitrary segment even in a very long chain, we find a rich variety of fairly broad crossovers, which for practicably accessible chain lengths overlap and smear out the asymptotic power laws. Our analysis suggests observables specifically adapted to distinguish reptation from motions dominated by disorder of the environment.Comment: 38 pages in latex plus 8 ps figures, submitted to J. Stat. Phys. on September 18, 1997, please note part II on cond-mat/971006

Segment Motion in the Reptation Model of Polymer Dynamics. II. Simulations

We present simulation data for the motion of a polymer chain through a regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths range from N=20 to N=640, and time up to $10^{7}$ Monte Carlo steps. For $N \geq 160$ we for the central segment find clear $t^{1/4}$-behavior as an intermediate asymptote. The also expected $t^{1/2}$-range is not yet developed. For the end segment also the $t^{1/4}$-behavior is not reached. All these data compare well to our recent analytical evaluation of the reptation model, which shows that for shorter times (t \alt 10^{4}) the discreteness of the elementary motion cannot be neglected, whereas for longer times and short chains (N \alt 100) tube renewal plays an essential role also for the central segment. Due to the very broad crossover behavior both the diffusion coefficient and the reptation time within the range of our simulation do not reach the asymptotic power laws predicted by reptation theory. We present results for the center-of-mass motion, showing the expected intermediate $t^{1/2}$-behavior, but again only for very long chains. In addition we show results for the motion of the central segment relative to the center of mass, where in some intermediate range we see the expected increase of the effective power beyond the $t^{1/4}$-law, before saturation sets in. Analysis and simulations agree on defining a new set of criteria as characteristic for reptation of finite chains.Comment: 19 pages in latex plus 13 ps figures, submitted to J. Stat. Phys. on September 18, 199

Dynamics of unbinding of polymers in a random medium

We have studied the aging effect on the dynamics of unbinding of a double stranded directed polymer in a random medium. By using the Monte Carlo dynamics of a lattice model in two dimensions, for which disorder is known to be relevant, the unbinding dynamics is studied by allowing the bound polymer to relax in the random medium for a waiting time and then allowing the two strands to unbind. The subsequent dynamics is formulated in terms of the overlap of the two strands and also the overlap of each polymer with the configuration at the start of the unbinding process. The interrelations between the two and the nature of the dependence on the waiting time are studied.Comment: 7 pages, latex, 3 figures, To appear in J. Chem. Phy

Insertion and hairpin formation of membrane proteins: a Monte Carlo study

Some particular effects of a lipid membrane on the partitioning and the concomitant folding processes of model proteins have been investigated using Monte Carlo methods. It is observed that orientational order and lateral density fluctuations of the lipid matrix stabilize the orientation of helical proteins and induce a tendency of spontaneous formation of helical hairpins for helices longer than the width of the membrane. The lateral compression of the lipids on a hairpin leads to the extrusion of a loop at the trans side of the membrane. The stability of the hairpin can be increased by the design of appropriate groups of hydrophilic and hydrophobic residues at the extruded loop. It is shown that in the absence of lipids the orientation of proteins is not stable and the formation of hairpins is absent. Some analogies between the formation of helical hairpins in membranes and the formation of hairpins in polymer liquid crystals are discussed. The simulations indicate that the insertion process follows a well-defined pattern of kinetic steps

On the orientational ordering of long rods on a lattice

We argue that a system of straight rigid rods of length k on square lattice with only hard-core interactions shows two phase transitions as a function of density, rho, for k >= 7. The system undergoes a phase transition from the low-density disordered phase to a nematic phase as rho is increased from 0, at rho = rho_c1, and then again undergoes a reentrant phase transition from the nematic phase to a disordered phase at rho = rho_c2 < 1.Comment: epl.cl

Intra-chain correlation functions and shapes of homopolymers with different architectures in dilute solution

We present results of Monte Carlo study of the monomer-monomer correlation functions, static structure factor and asphericity characteristics of a single homopolymer in the coil and globular states for three distinct architectures of the chain: ring, open and star. To rationalise the results we introduce the dimensionless correlation functions rescaled via the corresponding mean-squared distances between monomers. For flexible chains with some architectures these functions exhibit a large degree of universality by falling onto a single or several distinct master curves. In the repulsive regime, where a stretched exponential times a power law form (de Cloizeaux scaling) can be applied, the corresponding exponents $\delta$ and $\theta$ have been obtained. The exponent $\delta=1/\nu$ is found to be universal for flexible strongly repulsive coils and in agreement with the theoretical prediction from improved higher-order Borel-resummed renormalisation group calculations. The short-distance exponents $\theta_{\upsilon}$ of an open flexible chain are in a good agreement with the theoretical predictions in the strongly repulsive regime also. However, increasing the Kuhn length in relation to the monomer size leads to their fast cross-over towards the Gaussian behaviour. Likewise, a strong sensitivity of various exponents $\theta_{ij}$ on the stiffness of the chain, or on the number of arms in star polymers, is observed. The correlation functions in the globular state are found to have a more complicated oscillating behaviour and their degree of universality has been reviewed. Average shapes of the polymers in terms of the asphericity characteristics, as well as the universal behaviour in the static structure factors, have been also investigated.Comment: RevTeX 12 pages, 10 PS figures. Accepted by J. Chem. Phy

Phase Transitions of Single Semi-stiff Polymer Chains

We study numerically a lattice model of semiflexible homopolymers with nearest neighbor attraction and energetic preference for straight joints between bonded monomers. For this we use a new algorithm, the "Pruned-Enriched Rosenbluth Method" (PERM). It is very efficient both for relatively open configurations at high temperatures and for compact and frozen-in low-T states. This allows us to study in detail the phase diagram as a function of nn-attraction epsilon and stiffness x. It shows a theta-collapse line with a transition from open coils to molten compact globules (large epsilon) and a freezing transition toward a state with orientational global order (large stiffness x). Qualitatively this is similar to a recently studied mean field theory (Doniach et al. (1996), J. Chem. Phys. 105, 1601), but there are important differences. In contrast to the mean field theory, the theta-temperature increases with stiffness x. The freezing temperature increases even faster, and reaches the theta-line at a finite value of x. For even stiffer chains, the freezing transition takes place directly without the formation of an intermediate globule state. Although being in contrast with mean filed theory, the latter has been conjectured already by Doniach et al. on the basis of low statistics Monte Carlo simulations. Finally, we discuss the relevance of the present model as a very crude model for protein folding.Comment: 11 pages, Latex, 8 figure

Barriers and Challenges for Visually Impaired Students in PE - An Interview Study With Students in Austria, Germany, and the USA

Physical education (PE) is an important part of school education worldwide, and at the same time, almost the only subject that explicitly deals with body and movement. PE is therefore of elementary importance in the upbringing of young people. This also applies to children with visual impairments. However, existing findings on participation and belonging in PE as well as on physical and motor development reveal that this group of children and adolescents is noticeably disadvantaged in this respect. Against this background, this paper aims to explore fundamental barriers and challenges across different types of schools, types of schooling, and countries from the perspective of visually impaired children. The qualitative interview study with 22 children with visual impairments at different types of schools in three countries (Austria, Germany, USA) reveals that none of the respondents could escape the power of social distinctions and related problematic and existing hierarchies. Hence, ideas of normality and associated values remain the main challenge for all of them. However, the type-forming analysis provides important insight across settings on how visually impaired children differ on this, allowing for greater sensitivity to the concerns of children with visual impairments

...And After That Came Me . Subjective Constructions of Social Hierarchy in Physical Education Classes Among Youth with Visual Impairments in Germany

The aim of this study was to reconstruct subjective constructions of experiences in PE and feelings of being valued within PE classes in Germany by students with visual impairment (VI). Two female and two male students (average age: 19.25 years) participated in the study from the upper level. For the reconstruction of experiences of feeling valued, episodic interviews with a semi-structured interview guide were used. The data analysis was conducted with MAXQDA 2020 based on content-related structuring of qualitative text analysis with deductive-inductive category formation. To structure the analysis, the main category, feelings of being valued, was defined by two poles (positive feelings of being valued as opposed to bullying). As a main finding, respondents primarily reported negative feelings and experiences characterized by instances of bullying, discrimination, and physical and social isolation, perpetuated by both their peers and teachers. In search of a deeper understanding, we identified social hierarchy as an underlying structure determining the students\u27 perceived positioning within the social context and thus directing their feelings of being (de-)valued. It became evident that it is not the setting per se that determined social hierarchy, but that it is more about the concrete manifestation of social hierarchy