Can Mono Domain Polar Molecular Crystals Exist?

Abstract

The growth of polar molecular crystals (near thermodynamic equilibrium) is investigated by a stochastic growth model. Two types of growth are considered: (i) layer by layer growth and (ii) a kink attachment model within a square lattice. An analytical treatment is in qualitative agreement with Monte Carlo simulations. Essentially, a polar seed progresses along the unique axis to form a minor number of orientational defects in one direction, whereas in the opposite direction a "global" reversal of dipolar building blocks is predicted. Polarity reversal can start from a single orientational defect, undergoing continuation and growth in consecutive layers/attachments (kink), leading finally to complete reversal of all molecular dipoles. Eventually, this behavior results in crystals featuring two sectors of opposite average polarity. The number of growth steps upon dipole reversal depends on the intermolecular interactions. It is shown that for lateral coupling close to or smaller than estimated by the Onsager theory of a ferromagnetic transition in 2D (external field H = 0), there is only a small number of attachments needed to obtain reversal, whereas for strong parallel couplings, the number of grown layers before dipole reversal increases exponentially. Our analysis shows that molecular crystals (made of dipolar building blocks) nucleating into a polar seed are subject to a fundamental growth instability which is adverse to the formation of mono domain polar crystals in general.

Polarity Formation in Molecular Crystals as a Symmetry Breaking Effect

“…Since the Q m l have parity (−1) l ∀m, it turns out that each term in the sum of Equation (2) has a well definite parity. The interactions of multipoles such that l A + l B is odd are, therefore, the origin of the symmetry breaking in Equation (1). This condition is, however, not sufficient for the onset of a bi-polar state because, as we will show in the following, the translational symmetry of the system should also be broken in one direction at least.…”

“…Since the Hamiltonian (1) is invariant under the transformation S i → −S i , S j → −S j (global spin flip symmetry) the thermal average S i = 0, unless this symmetry is broken. Thus, Equation (1), in this simple form, cannot reproduce a net average polarity. In order to analyze the issue in more detail, consider two non-overlapping charge distributions centered around R A and R B , respectively.…”

“…Given the point symmetry of the lattice and its finite size, the system will thermalize into a bi-polar state featuring zero overall polarity [1].…”

Symmetry Breaking and Polarity Formation in Molecular Crystals

“…In the first case, the system at equilibrium consists of a bi-polar state of general ∞∞ m symmetry. In the case of growth, a polar seed undergoes a reversal transition which also transforms the mono-domain state into a bi-polar one [2].Phenomena to be reported represent a general behavior of condensed molecular matter formed by asymmetrical but not necessarily chiral building blocks, which split into a bi-polar state featuring zero net polarity. This is in agreement with a general statistical mechanical statement that a system in a stationary state does not show an electrical dipole moment [3].…”

“…In the first case, the system at equilibrium consists of a bi-polar state of general ∞∞ m symmetry. In the case of growth, a polar seed undergoes a reversal transition which also transforms the mono-domain state into a bi-polar one [2].…”