Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 \div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time declines with growing contour length $L$ as $\propto L^{-0.17}$, and with side chain length as $\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.Comment: 15 pages, 7 figure

About disposition of energy levels

The unique properties of central potential of the form $-\beta e^{-r}r^{\gamma}$ were studied using the recently developed critical parameter technique. The particular cases of $\gamma=0$ and $\gamma=-1$ yield, respectively, the exponential and Yukawa potentials widely used in the atomic, molecular and nuclear physics. We found different behavior of the energy levels of this potential for three different ranges of the value of $\gamma$. For $\gamma\geq0$ it was found that the energy of bound states with the same principal quantum number $N$ decreases with increasing angular momentum $\ell$. The Gaussian and Woods-Saxon potentials also show this behavior. On the contrary, for $-2\leq\gamma\leq-1$ increasing $\ell$ gives a higher energy, resembling the Hulthen potential. However, a potential with $-1<\gamma<0$ possesses mixed properties, which give rise to several interesting results. For one, the order of energy levels with different quantum numbers is not preserved when varying the parameter $\beta$. This leads to a quantum degeneracy of the states, and in fact, for a given value of $\gamma$ we can find the values $\beta_{thr}$ for which two energy levels with different quantum numbers coincide. Another interesting phenomena is the possibility, for some values of $\gamma$ in this range, for two new energy levels with different quantum numbers to appear simultaneously when $\beta$ reaches their common critical value.Comment: 10 pages, 3 table