Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userForce-induced desorption of 3-star polymers in two dimensions
64
0
0.0
(
0
)
Added by
Esaias J Janse van Rensburg
Publication date
2019
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a ballistic phase, an adsorbed phase and a mixed phase where part of the 3-star is adsorbed and part is ballistic. We use both rigorous arguments and Monte Carlo methods to map out the phase diagram, and investigate the location and nature of the phase transition boundaries. In two dimensions, only two of the arms can be fully adsorbed in the surface and this alters the phase diagram when compared to 3-stars in three dimensions.
rate research
Read More
We consider a simple cubic lattice self-avoiding walk model of 3-star polymers adsorbed at a surface and then desorbed by pulling with an externally applied force. We determine rigorously the free energy of the model in terms of properties of a self-avoiding walk, and show that the phase diagram includes 4 phases, namely a ballistic phase where the extension normal to the surface is linear in the length, an adsorbed phase and a mixed phase, in addition to the free phase where the model is neither adsorbed nor ballistic. In the adsorbed phase all three branches or arms of the star are adsorbed at the surface. In the ballistic phase two arms of the star are pulled into a ballistic phase, while the remaining arm is in a free phase. In the mixed phase two arms in the star are adsorbed while the third arm is ballistic. The phase boundaries separating the ballistic and mixed phases, and the adsorbed and mixed phases, are both first order phase transitions. The presence of the mixed phase is interesting because it doesnt occur for pulled, adsorbed self-avoiding walks. In an atomic force microscopy experiment it would appear as an additional phase transition as a function of force.
We analyze the phase diagrams of self-avoiding walk models of uniform branched polymers adsorbed at a surface and subject to an externally applied vertical pulling force which, at critical values, desorbs the polymer. In particular, models of adsorbed branched polymers with homeomorphism types stars, tadpoles, dumbbells and combs are examined. These models generalize earlier results on linear, ring and $3$-star polymers. In the case of star polymers we confirm a phase diagram with four phases (a free, an adsorbed, a ballistic, and a mixed phase) first seen in the paper by Janse van Rensburg EJ and Whittington SG 2018 J. Phys. A: Math. Theor. 51 204001 for $3$-star polymers. The phase diagram of tadpoles may include four phases (including a mixed phase) if the tadpole is pulled from the adsorbing surface by the end vertex of its tail. If it is instead pulled from the middle vertex of its head, then there are only three phases (the mixed phase is absent). For a dumbbell pulled from the middle vertex of a ring, there are only three phases. For combs with $t$ teeth there are four phases, independent of the value of $t$ for all $t ge 1$.
We investigate self-avoiding walk models of linear block copolymers adsorbed at a surface and desorbed by the action of a force. We rigorously establish the dependence of the free energy on the adsorption and force parameters, and the form of the phase diagram for several cases, including $AB$-diblock copolymers and $ABA$-triblock copolymers, pulled from an end vertex and from the central vertex. Our interest in block copolymers is partly motivated by the occurrence of a novel mixed phase in a directed walk model of diblock copolymers cite{Iliev} and we believe that this paper is the first rigorous treatment of a self-avoiding walk model of the situation.
We study crystal melting in two-dimensional antiferromagnets, by analyzing the statistical mechanics of the six-state clock model on a lattice in which defects (dislocations and disclinations) are allowed to appear. We show that the elementary dislocations bind to fractional magnetic vortices. We compute the phase diagram by mapping the system into a Coulomb gas model. Surprisingly, we find that in the limit of dominant magnetic interactions, antiferromagnetism can survive even in the hexatic and liquid phases. The ensuing molten antiferromagnets are topologically ordered and are characterized by spontaneous symmetry breaking of a non-local order parameter.
These notes focus on the description of the phases of matter in two dimensions. Firstly, we present a brief discussion of the phase diagrams of bidimensional interacting passive systems, and their numerical and experimental measurements. The presentation will be short and schematic. We will complement these notes with a rather complete bibliography that should guide the students in their study of the development of this very rich subject over the last century. Secondly, we summarise very recent results on the phase diagrams of active Brownian disks and active dumbbell systems in two dimensions. The idea is to identify all the phases and to relate, when this is possible, the ones found in the passive limit with the ones observed at large values of the activity, at high and low densities, and for both types of constituents. Proposals for the mechanisms leading to these phases will be discussed. The physics of bidimensional active systems open many questions, some of which will be listed by the end of the Chapter.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
