Phase transitions of single polymer chains and of polymer solutions: insights from Monte Carlo simulations

Binder, Kurt; Paul, Wolfgang; Strauch, Thomas; Rampf, Federica; Иванов, В. А.; Luettmer-Strathmann, Jutta

doi:10.1088/0953-8984/20/49/494215

Cited by 19 publications

(31 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…agree with the theoretical predictions. We fully confirm the estimates for T Θ given in [12][13][14][15][16], but due to the much longer chains and higher statisitics we can give much smaller error bars in spite of the theoretical uncertainty:…”

supporting

confidence: 85%

See 1 more Smart Citation

Polymer collapse and crystallization in bond fluctuation models

Grassberger¹

2013

EPL

View full text Add to dashboard Cite

While the Θ-collapse of single long polymers in bad solvents is usually a continuous (tri-critical) phase transition, there are exceptions where it is preempted by a discontinuous crystallization (liquid ↔ solid) transition. For a version of the bond-fluctuation model (a model where monomers are represented as 2 × 2 × 2 cubes, and bonds can have lengths between 2 and √ 10) it was recently shown by F. Rampf et al. that there exist distinct collapse and crystallization transitions for long but finite chains. But as the chain length goes to infinity, both transition temperatures converge to the same T * , i.e. infinitely long polymers collapse immediately into a solid state. We explain this by the observation that polymers crystallize in the Rampf et al. model into a non-trivial cubic crystal structure (the 'A15' or 'Cr3Si' Frank-Kasper structure) which has many degenerate ground states and, as a consequence, Bloch walls. If one controlls the polymer growth such that only one ground state is populated and Bloch walls are completely avoided, the liquid-solid transition is a smooth cross-over without any sharp transition at all.In spite of having been studied for several decades, the phase transitions of a single long polymer in a bad solvent are still a subject of active research with occasional big surprises. When temperature is lowered, most polymers undergo a Θ-collapse, which is typically a continuous (tri-critical) phase transition. At the transition point, repulsive entropic effects and attractive energetic forces would cancel exactly for an infinitely long chain. For finite chain length N theory [1, 2] predicts logarithmic corrections which are also seen in simulations [2][3][4] and in experiments [5], and which also affect the unmixing transition of long polymers [6]. Qualitatively, the Θ-transition resembles a gas-liquid transition, with the open coil resembling the gas and the dense globule being analogous to a liquid. At even worse solvent conditions, in many models (e.g. in off-lattice polymers with Lennard-Jones interactions between monomers [7]) there occurs a second 'liquid-solid' transition that is similar to crystallization. Since it is a discontinuous transition, its properties are usually not universal and are not described by perturbative renormalization group methods.But there are well known cases where this Θ-collapse is preempted by a discontinuous 'freezing' or crystallization transition. One example is semi-stiff polymers [8], another is provided by (off-lattice) monomers with hard core repulsion and attractive interactions which extend only very little beyond the core [9,10]. Still another is the cooperative one-step collapse of some proteins [11] A very surprising behavior which falls between these two possibilities -Θ-collapse with subsequent liquid-solid transition, and immediate gas-solid freezing -was observed by . In their model, the specific heats of finite chains show rounded peaks at distinct temperatures T crys (N ) < T Θ (N ), but as the chain length N diverges,Thus, while finite...

show abstract

supporting

confidence: 85%

“…It is these Bloch walls which are responsible for the discontinuity and high temperature of the freezing transition. In contrast to [12][13][14][15][16], where Markov chain Monte Carlo methods were used, we used PERM [4] and "flat PERM" [22]. PERM is a growth algorithm with importance sampling and re-sampling, i.e.…”

mentioning

confidence: 99%

Polymer collapse and crystallization in bond fluctuation models

Grassberger¹

2013

EPL

View full text Add to dashboard Cite

show abstract

“…This monotonic trend of collapse transition is similar to the trend usually observed in linear homopolymers as a function of chain length [35,36] . Collapse transition appears to be driven by the collapse of individual arm, rather than a cooperative collapse observed in the presence of functional end groups, especially The lines joining the points are meant only as a guide to the eye.…”

Section: Collapse Transition Of Telechelic Star Polymersupporting

confidence: 85%

Collapse Transition of Branched Polymers in Dilute Solutions: Telechelic Star vs. H‐Polymer

Dasmahapatra

Reddy

Sanka

2015

Macromolecular Symposia

View full text Add to dashboard Cite

Summary: Self-assembly in polymeric material is facilitated by the presence of active hetero-atoms either along the backbone or as pendant groups. Self-assembly leads to a rich variety of morphological pattern influencing various properties of polymeric materials. Presence of branching along the backbone chain also imparts remarkable change in polymeric properties. We report dynamic Monte Carlo (DMC) simulation study on solution behavior of branched polymers. We take multi-arm telechelic star polymers (TSP, one branch point with terminal active groups) and H-shaped branched polymers (homopolymers with two branch points), elucidating the driving mechanisms of collapse transition and morphological development. The presence of terminal active groups in TSP drives the collapse transition producing segregated and compact globule structure, on deteriorating solvent quality. On the other hand, presence of two branch points in H-shaped polymers incorporates conformational heterogeneity (viz., entropically originated) and produces segregated globule structures. The terminal functional groups in TSP form aggregate, resembles to "watermelons" (WM) and double watermelon (DWM) depending on the number of arms and mode of cooling. In H-polymers, conformational heterogeneity leads to the formation of segregated backbone and branch units (resembles to "Sandwich" or "Janus" morphology) rather an evenly distributed structure consisting of all the units, accompanying with a larger size of branches compared to the backbone.

show abstract

“…In the present model there are two main competing interactions: on the one hand there is the LJ attractive interactions among the beads that tend to collapse the chain when the temperature is lowered 22,23 and, on the other hand, there is the magnetic interaction which is known from ferrofluid studies 55,56 to favour the formation of rod-like chains and rings in which dipoles tend to align in a nose-tail conformation. Nosetail conformations are those in which two dipole i and j satisfy µ µ µ i · µ µ µ j = µ 2 , and µ µ µ i · r r r i j = µ µ µ j · r r r i j = ±µ r i j .…”

Section: Resultsmentioning

confidence: 99%

“…Several studies have shown semiflexible chains to possess toroidal or disklike phases. 22,[24][25][26][27][28] Helix structures have also been found for some very specific square-well potentials. 29 Related to this, helical long-lived transient states have also been identified for chains with truncated Lennard-Jones potentials.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram for a single flexible Stockmayer polymer at zero field

et al. 2013

View full text Add to dashboard Cite

The equilibrium conformations of a flexible permanent magnetic chain that consists of a sequence of linked magnetic colloidal nanoparticles with short-ranged Lennard-Jones attractive interactions (Stockmayer polymer) are thoroughly analysed via Langevin dynamics simulations. A tentative phase diagram is presented for a chain of length $N=100$. The phase diagram exhibits several unusual conformational phases when compared with the non-magnetic chains. These phases are characterised by a large degree of conformational anisotropy, and consist of closed chains, helicoidal-like states, partially collapsed states, and very compact disordered states. The phase diagram contains several interesting features like the existence of at least two 'triple points'

show abstract

Phase transitions of single polymer chains and of polymer solutions: insights from Monte Carlo simulations

Cited by 19 publications

References 33 publications

Polymer collapse and crystallization in bond fluctuation models

Polymer collapse and crystallization in bond fluctuation models

Collapse Transition of Branched Polymers in Dilute Solutions: Telechelic Star vs. H‐Polymer

Phase diagram for a single flexible Stockmayer polymer at zero field

Contact Info

Product

Resources

About