Can Nematic Transitions Be Predicted By Atomistic Simulations? A Computational Study of The Odd–Even Effect

Abstract

Computer simulations at the atomistic level are often called realistic as they offer, in principle, the possibility of reproducing in full the properties of a molecular system. Unfortunately, the number of atomic centers for molecules forming liquid-crystalline phases is normally so large, and correspondingly the number of molecules considered so low, that the proof of true realism, for example, the approximate reproduction of transition temperatures and of the relevant observables (such as order parameters together with their temperature dependence) has to our knowledge never been given to date. This is understandable in view of the complexity of liquid crystal molecules and probably depends on at least three issues: interaction potentials, sample size, and equilibration time. The force fields available have not been developed to reproduce liquid crystal properties, and only recently have some recommendations on the most appropriate choice amongst the many force fields available [1] been made. Sample sizes have varied from a number of particles N 50, [2±4] to 64 N 75, [5±10] to 100 N 125, [8, 11±15] and to N 200 molecules. [16] In a few recent cases, larger samples with N % 10 3 [17,18] particles have been simulated but without really studying the full temperature dependence and identifying transitions.At atomistic resolution, the observation time window in molecular dynamics (MD) calculations has also been quite short, ranging from less than % 600 ps [2, 3, 5±7, 10, 11, 14±18] to 1 or 2 ns. [4,9,13,15,16] Recently, a few simulations lasting up to 8 and 12 ns have appeared, [8,12] but these have involved the study of one, or very few, state points: again not sufficient to assess the ability of the methodology to predict transitions. The rather short runs are probably also connected to the contradictory preliminary findings on size dependence: thus in a recent study comparing N 118 and N 994 simulations, no size dependence was found: [18] in contrast to what was found on going from N 125 to 1000. [17] These strong limitations have been paralleled by the development of molecular-level models, where molecules are considered as simple objects, either just hard or endowed with attraction and repulsion, as in the Gay ± Berne models.[19] These approximate models have proven extremely useful in studying the general properties of liquid crystals (LC), such as phase transitions and correlations, and in discussing the existence of new and yet undiscovered phases such as the biaxial [20] and the ferroelectric nematic, [21] suggesting design hints to the synthetic chemist.However, there is a class of problems and observations that are very important for the understanding of anisotropic fluids, and completely depends on an atomistic level description. The foremost example is probably the prediction of the nematic ± isotropic (NI) transition temperature T NI , a crucial element in the design of viable LC display materials that have to exist and operate in a certain temperature range, that is now tackled empirically. [22,23...

Atomistic Simulations of a Thermotropic Biaxial Liquid Crystal

“…To our knowledge this is the first time growth of a liquid crystal phase has been achieved for an all-atom liquid crystal model. The time scale for the orientational transition is very similar to that seen in the work of Berardi et al who considered the orientational melting of a nematic to an isotropic phase close to the clearing point [21]; and is considerably longer than that required for united-atom [22] or coarse-grained simulation models [23]. The value of hS ZZ 2 i at the end of the run are typical of those expected experimentally for a nematic system.…”

Molecular simulation of liquid crystals: progress towards a better understanding of bulk structure and the prediction of material properties

“…Here, it was discovered that there is a strong coupling between molecular structure and phase behaviour. 14,15 For example, the dihedral angles for an alkyl chain attached to a phenyl ring exhibit an odd-even effect, such that gauche conformations of even dihedral angles normally allow the chain to lie along the molecular axis (favoured in a nematic), while gauche conformations of odd dihedrals lead to the chain lying at an angle to the molecular axis (disfavoured in a nematic). Such an effect was predicted by molecular field theory and often manifests itself in a similar odd-even effect in transition temperatures seen experimentally.…”

“…Such an effect was predicted by molecular field theory and often manifests itself in a similar odd-even effect in transition temperatures seen experimentally. 14 Recent atomistic work has benefited by the huge increases in computer power seen over the last decade. It is now possible to grow a nematic phase from an isotropic liquid, thereby demonstrating thermodynamic stability.…”

Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation

“…Simulations of single site potentials ͑where longer simulation runs are possible͒ point to some hystersis in cooling/heating through the phase transition, particularly with small system sizes. The most detailed atomistic study of the nematic-isotropic transition conducted top date, for the first three homologs of the phenylalkyl-4-(4Ј cyanobenzylidene)-aminocinnamates, was able to predict transitions temperatures to within 10Ϯ5 K. 4 The order parameters found from the dipole moment are significantly lower than those found from the inertia tensor as well as being lower than the Raman scattering results for temperatures below T NI expt. .…”

“…Of particular interest has been the progress made in the simulation of complicated self-ordering systems such as liquid crystal phases. [1][2][3][4][5][6] Here changes in molecular alignmnent can occur on relatively long times scales (Ͼ1 ns) and accurate force fields are required for simulations to reproduce the stability of the phases. [7][8][9][10] In principle the bulk material properties of a system should be available from accurate atomistic simulations.…”