Collapse transition of linear polymers on a family of truncated n-simplex lattices

Critical behavior of magnetic polymers on the three-dimensional Sierpiński Gasket

We present the (numerically) exact phase diagram of a magnetic polymer on the Sierpińsky gasket embedded in three dimensions using the renormalization group method. We report distinct phases of the magnetic polymer, including paramagnetic swollen, ferromagnetic swollen, paramagnetic collapsed, and ferromagnetic collapsed states. By evaluating critical exponents associated with phase transitions, we located the phase boundaries between different phases. If the model is extended to include a four-site interaction which disfavors configurations with a single spin of a given type, we find a rich variety of critical behaviors. Notably, we uncovered a phenomenon of reentrance, where the system transitions from a collapsed (paramagnetic) state to a swollen (paramagnetic) state followed by another collapse (paramagnetic) and ultimately reaching a ferromagnetic collapsed state. These findings shed new light on the complex behavior of (lattice) magnetic polymers.

Pyrolysis of long chain hydrocarbon-based plastics via self-exothermic effects: The origin and influential factors of exothermic processes

Converting plastic wastes into value-added products through energy-efficient pyrolysis is essential, and it requires lower pyrolysis temperatures and shorter processing times than that of other processes. An exothermic phenomenon was observed during the process high-pressure polyethylene pyrolysis. It was proven for the first time that the exotherm is caused by a pressure-induced phase transition, in which colossal heat release can be driven by relatively small pressures. A large temperature change (> 100 °C) leads to the deep cracking of polyethylene, although the set temperature is far lower than the required temperature for thermal cracking. Importantly, the heat input stops immediately when the set temperature is reached; thus, the external heating time is short. Polyethylene can be completely converted into liquid products in ~90 wt% yield and with a small number of gases. The self-exothermic phase transition only occurs within a certain range of material thickness, which is related to the corresponding phase behavior. In the self-exothermic pyrolysis process, with an increase in the thickness of polyethylene, the proportion of low-value olefins in oil products decreases gradually, while alkanes, isoalkanes and aromatics show an increasing trend, making the product composition closer to the fuel standard. This work provides a viable approach for plastic recycling at low pyrolysis temperatures and short external heating times with the help of a self-exothermic phase transition in the absence of a catalyst.

Dynamics of a polymer chain translocating through varying cone-shaped channels

By employing the exact enumeration technique, we study consequences of different apex angles of a wedge-shaped channel on the mean first passage time and free-energy profile of a linear polymer chain translocating from the cis- to the trans-side through an interacting pore. We investigate effects of asymmetry arising in the free-energy profile due to the change in apex angles and its dependence on the first passage time. We report the combined effect of entropy (arising due to apex angles) and pore interaction on the nonmonotonic behavior of the translocation time. The effect of different solvent quality across the channel has also been explored. We show that the increase in monomer-monomer interaction leads to the formation of globules near the pore, which drives the process faster.

Single polymer gating of channels under a solvent gradient

We study the effect of a gradient of solvent quality on the coil-globule transition for a polymer in a narrow pore. A simple self-attracting, self-avoiding walk model of a polymer in solution shows that the variation in the strength of the interaction across the pore leads the system to go from one regime (good solvent) to the other (poor solvent) across the channel. This may be thought to be analogous to thermophoresis, where the polymer goes from the hot region to the cold region under the temperature gradient. The behavior of short chains is studied using exact enumeration while the behavior of long chains is studied using transfer matrix techniques. The distribution of the monomer density across the layer suggests that a gatelike effect can be created, with potential applications as a sensor.

Force induced unfolding of biopolymers in a cellular environment: a model study

Effect of molecular crowding and confinement experienced by protein in the cell during unfolding has been studied by modeling a linear polymer chain on a percolation cluster. It is known that internal structure of the cell changes in time, however, they do not change significantly from their initial structure. In order to model this we introduce the correlation among the different disorder realizations. It was shown that the force-extension behavior for correlated disorder in both constant force ensemble and constant distance ensemble is significantly different than the one obtained in absence of molecular crowding.

Effects of molecular crowding on stretching of polymers in poor solvent

We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the simplest representation of biopolymers in a cell. We show the existence of intermediate states during stretching arising as a consequence of molecular crowding. In the constant distance ensemble the force-extension curves exhibit oscillations. We observe the emergence of two or more peaks in the probability distribution curves signaling the coexistence of different states and indicating that the transition is discontinuous unlike what is observed in the absence of molecular crowding.

Stretching of a single-stranded DNA: evidence for structural transition

Recent experiments have shown that the force-extension (F-x) curve for single-stranded DNA (ssDNA) consisting only of adenine [poly(dA)] is significantly different from thymine [poly(dT)]. Here, we show that the base stacking interaction is not sufficient to describe the F-x curves as seen in the experiments. A reduction in the reaction coordinate arising from the formation of helix at low forces and an increase in the distance between consecutive phosphates of unstacked bases in the stretched state at high force in the proposed model qualitatively reproduce the experimentally observed features. The multistep plateau in the F-x curve is a signature of structural change in ssDNA.

Role of pulling direction in understanding the energy landscape of proteins

Single-molecule force spectroscopy provide details of the underlying energy surfaces of proteins which are essential to the understanding of their unfolding process. Recently, it has been observed experimentally that by pulling proteins in different directions relative to their secondary structure, one can gain a better understanding of the shape of the energy landscape. We consider simple lattice models which are anisotropic in nature to study the response of a force in unfolding of a polymer. Our analytical solution of the model, supported by extensive numerical calculations, reveal that the force temperature diagrams are very different depending on the direction of the applied force. We find that either unzipping or shearing kind transitions dominate the dynamics of the unfolding process depending solely on the direction of the applied force.

Scaling of Hamiltonian walks on fractal lattices

We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e., self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling forms for open HWs on three-simplex lattice, Sierpinski gasket, and their generalizations: Given-Mandelbrot (GM), modified Sierpinski gasket (MSG), and n -simplex fractal families. For GM, MSG and n -simplex lattices with odd values of n , the number of open HWs Z(N), for the lattice with N>>1 sites, varies as omega(N)}N(gamma). We explicitly calculate the exponent gamma for several members of GM and MSG families, as well as for n-simplices with n=3, 5, and 7. For n-simplex fractals with even n we find different scaling form: Z(N) approximately omega(N)mu(N1/d(f), where d(f) is the fractal dimension of the lattice, which also differs from the formula expected for homogeneous lattices. We discuss possible implications of our results on studies of real compact polymers.