Polymer with competing hydrogen-like bonding and simple nearest-neighbors interactions.
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We discuss the phase diagram for a lattice-model of polymers with
competing hydrogen-like interactions (hb) and next-neighbors contacts (nn)
in two and three dimensions. The formation of hydrogen bonds is modeled by
short-range interactions between straight segments of the polymers.
In two dimensions interacting segments must be oriented parallel to
each other, while in three dimensions they can be oriented parallel
or orthogonal to each other. The energy and partition function are then given by:
equation
E(\phi)=-m_hb\cdot\epsilon_hb-m_nn\cdot\epsilon_nn,
equation
where $m_hb$ and $m_nn$ is the sum of hydrogen-like bonding and next-neighbor interaction, respectively.
equation
Z_n(\beta_nn,\beta_hb)=
\sum_m_nn,m_hb C_n,m_nn,m_hb\; e^\beta_nn m_nn+\beta_hb m_nn
equation
with $C_n,m_nn,m_hb$ being the density of states and
$\beta_hb=\beta\epsilon_hb$ and $\beta_nn=\beta\epsilon_nn$.
While hydrogen-like bonding at low
temperature induce a ordered phase, the next-neighbors interactions
drive the system to a compact-globule state.
Thus we observe three different phases: two collapsed (ordered, and
liquid droplet like), and a swollen coil. In figure 1 we see the
the plot of the logarithm of the largest eigenvalue of the matrix
of second derivatives of the free energy with respect to number of hb-contacts and
nn-contacts for size of the chain n=128 in three dimension. We see as well three lines, which
show three different scenario. The upper line present situation, when the strength
of the hb-contacts is much bigger then strength of nn-contacts and we observe a first-order
transition from swollen coil to ordered phase. The bottom line presets the opposite situation, the
nn-contacts are preferred, and we have the second order transition. The intermediate line presents
(when decreasing temperature) pseudo-second order transition to the globule state and then next transition to
the ordered phase for finite length. Along this line we find differences in two and three dimension.
In two dimension the transition between those collapsed phases seems to be second order, while in three
we find indication for first-order transition. Since the hb-interaction include an effective stiffness two
the polymer we study as well the similarity of those phase-diagram to
the case of semi-stiff-polymer both dimension.
All results are from simulations
on the square and simple cubic lattices. We perform
simulations using FlatPERM, a
flat histogram stochastic growth algorithm.