Computer simulation of the liquid crystal formation in a semi-flexible polymer system

Molecular dynamic simulations are reported for system of semi-flexible linear rod-like molecules. The molecules are composed of N_c tangent soft spheres, connected by elastic springs. Rigidity is introduced by additional springs between all pairs of spheres along the molecule. The formation of only a nematic LC phase is shown for all systems with N_c = 8 and different flexibility. The effect of flexibility on the order parameter and the volume fraction at the LC phase transition is compared with theoretical predictions by Khokhlov-Semenov and with available simulation data. The dependence of the anisotropy of diffusion on chain flexibility in LC phase was studied. The polymer brushes consisting of flexible and semi-flexible (composed of linear rod-like segments) chains were simulated at different grafting densities. Height of brush, order parameter, distribution of density and chain ends in brush were obtained in both cases and compared with theoretical predictions.     

Conformational Entropy as a Means to Control the Behavior of Poly(diketoenamine) Vitrimers In and Out of Equilibrium

Control of equilibrium and non‐equilibrium thermomechanical behavior of poly(diketoenamine) vitrimers is shown by incorporating linear polymer segments varying in molecular weight (MW) and conformational degrees of freedom into the dynamic covalent network. While increasing MW of linear segments yields a lower storage modulus at the rubbery plateau after softening above the glass transition (T_g), both T_g and the characteristic time of stress relaxation are independently governed by the conformational entropy of the embodied linear segments. Activation energies for bond exchange in the solid state are lower for networks incorporating flexible chains; the network topology freezing temperature decreases with increasing MW of flexible linear segments but increases with increasing MW of stiff segments. Vitrimer reconfigurability is therefore influenced not only by the energetics of bond exchange for a given network density, but also the entropy of polymer chains within the network.     

Universal scaling behaviour of surface tension of molecular chains

We use and extend the universal relationship recently proposed by Galliero [G. Galliero, J. Chem. Phys. 133, 074705 (2010)], based on a combination of the corresponding-states principle of Guggenheim [E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945)] and the parachor approach of Macleod [J. Macleod, Trans. Faraday Soc. 19, 38 (1923)], to predict the vapour-liquid surface tension of fully flexible chainlike Lennard-Jones molecules. In the original study of Galliero, the reduced surface tension of short-chain molecules formed by up to five monomers is expressed as a unique function of the difference between the liquid and vapour coexistence densities. In this work, we extend the applicability of the recipe and demonstrate that it is also valid for predicting the surface tension of two different chainlike molecular models, namely, linear tangent chains that interact through the Lennard-Jones intermolecular potential and fully flexible chains formed by spherical segments interacting through the square-well potential. Computer simulation data for vapour-liquid surface tension of fully flexible and rigid linear Lennard-Jones, and fluid flexible square-well chains is taken from our previous works. Our results indicate that the universal scaling relationship is able to correlate short- and long-chain molecules with different degrees of flexibility and interacting through different intermolecular potentials.     

Freezing of Lennard-Jones-type fluids

We put forward an approximate method to locate the fluid-solid (freezing) phase transition in systems of classical particles interacting via a wide range of Lennard-Jones-type potentials. This method is based on the constancy of the properly normalized second derivative of the interaction potential (freezing indicator) along the freezing curve. As demonstrated recently it yields remarkably good agreement with previous numerical simulation studies of the conventional 12-6 Lennard-Jones (LJ) fluid [S.A.Khrapak, M.Chaudhuri, G.E.Morfill, Phys. Rev. B 134, 052101 (2010)]. In this paper, we test this approach using a wide range of the LJ-type potentials, including LJ n-6 and exp-6 models, and find that it remains sufficiently accurate and reliable in reproducing the corresponding freezing curves, down to the triple-point temperatures. One of the possible application of the method--estimation of the freezing conditions in complex (dusty) plasmas with "tunable" interactions--is briefly discussed.     

Capillary condensation of short-chain molecules

A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.     

Compatibility of coils and rods bearing flexible side chains

We present a theoretical treatment of nematic-isotropic phase equilibria in mixtures which consist of random coils and comblike polymers, the latter components being composed of a rigid backbone and flexible side chains. The mixing partition function is evaluated by using the Flory lattice model. The comblike component is characterized by the axial ratio x_r of its rigid main chain and the number of flexible side chains z, each containing m segments. The coiled component is described by its number of segments x_c. The net exchange energy of mixing is assumed to be zero; i.e., we consider athermal solutions. It is shown that the flexible side chains attached to the rigid main chains markedly enhance the compatibility in the isotropic phase. If the ratio of the volume fraction of the side chains to the volume fraction of the main chains is high enough, there is even a finite range of concentration where the random coils mix homogeneously with the comblike component. This is in contrast to mixtures of rods and coils, which have been shown by Flory to be incompatible over nearly the full range of composition. These conclusions hold true only when ordered states are involved. For comblike polymers with flexible backbones mixed with random coils in isotropic melts, the resulting free energy of mixing is given by the familiar Flory-Huggins expression.     

Short chains at solid surfaces: wetting transition from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the wetting transition changes with the change of the chain length and with the relative strength of the fluid-solid interaction. End segments adsorb preferentially in the first adsorbed layer whereas the concentration of the middle segments is enhanced in the second layer. We observe that the wetting temperature rescaled by the bulk critical temperature decreases with an increase of the chain length. For longer chains this temperature reaches a plateau. For the surface critical temperature an inverse effect is observed, i.e., the surface critical temperature increases with the chain length and then attains a plateau. These findings may serve as a quick estimate of the wetting and surface critical temperatures for fluids of longer chain lengths.     

Influence of bond flexibility on the vapor-liquid phase equilibria of water

The authors performed Gibbs ensemble simulations on the vapor-liquid equilibrium of water to investigate the influence of incorporating intramolecular degrees of freedom in the simple point charge (SPC) water model. Results for vapor pressures, saturation densities, heats of vaporization, and the critical point for two different flexible models are compared with data for the corresponding rigid SPC and SPC/E models. They found that the introduction of internal vibrations, and also their parametrization, has an observable effect on the prediction of the vapor-liquid coexistence curve. The flexible SPC/Fw model, although optimized to describe bulk diffusion and dielectric constants at ambient conditions, gives the best prediction of saturation densities and the critical point of the examined models.     

The phase behavior of polyethylene ring chains

The equilibrium properties of an isolated polyethylene ring chain are studied by using molecular dynamics (MD) simulations. The results of an 80-bond linear chain are also presented, which are in agreement with previous studies of square-well chains and Lennard-Jones (LJ) homopolymers. Mainly, we focus on the collapse of polyethylene ring chains. At high temperatures, a fully oblate structure is observed for the ring chains with different chain lengths. For such an oblate structure, a shape factor of delta(*)=0.25 and a rodlike scaling relation between the radius of gyration and chain lengths could be deduced easily in theory, and the same results are obtained by our MD simulations. Such an oblate structure can be obtained by Monte Carlo simulation only for sufficient stiff ring chains. When the temperature decreases, an internal energy barrier is observed. This induces a strong peak in the heat capacity, denoting a gas-liquid-like transition. This energy barrier comes mainly from the local monomer-monomer interactions, i.e., the bond-stretching, the bond-bending, and the torsion potentials. A low temperature peak is also observed in the same heat capacity curve, representing a liquid-solid-like transition. These numerical simulation results support a two-stage collapse of polyethylene ring chains; however, the nature should be different from the square-well and LJ ring chains.     

Vapor-liquid interfacial properties of rigid-linear Lennard-Jones chains

We have obtained the interfacial properties of short rigid-linear chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapour-liquid interface. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janec?ek [J. Phys. Chem. B 110, 6264-6269 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 4, and 5 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtain density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The surface tension has been scaled by critical properties and represented as a function of the difference between coexistence densities relative to the critical density.     

Coarse grained models for flexible liquid crystals: parameterization of the bond fluctuation model

We extend the bond fluctuation model, originally devised to investigate polymer systems, to contain anisotropic interactions suitable for the simulation of large flexible molecules such as liquid crystalline polymers and dendrimers. This extended model coarse grains the interaction between the flexible chains at a similar level of detail to the mesogenic units. Suitable interaction parameters are obtained by performing trial simulations on a low molar mass liquid crystalline system. The phase diagram of this system is determined as a function of the molecular stiffness. The nematic to isotropic transition temperature is found to increase with increasing stiffness.     

Liquid-vapor interfacial properties of vibrating square well chains

Liquid-vapor interfacial properties of square well chains are calculated. Surface tension, orthobaric densities, and vapor pressures are reported. Spinodal decomposition with a discontinuous molecular dynamics simulation program is used to obtain the results which are compared to previously published data for orthobaric densities and vapor pressures. In order to analyze the effect of the chain stiffness results for near tangent and overlapping linear chains as well as angled chains are obtained. Properties are calculated for linear chains of 2, 4, and 8 spheres for intramolecular distances of 0.97, 0.6, and 0.4 as well as for angled chains of 4 and 8 spheres and intramolecular distances of 0.4. The complete series of fully flexible near tangent square well chains is also studied (chains of 2, 4, 8, 12, and 16 particles with intramolecular distances of 0.97). The corresponding states principle applies to most of the systems considered. Critical properties values are reported as obtained from orthobaric densities, surface tensions, and vapor pressures. For the near tangent chains the critical temperatures increase with chain length but the rate of increment tends to zero for the longest chains considered. When the stiffness of the chain increases (intramolecular distance from 1 , 0.6, and 0.4) this saturation effect is either not present or reverses itself. The surface tension increases with the length of the chain while the width of the interface decreases.     

The influence of flexible segments on liquid crystalline properties in terms of solubility parameters. An attempt at quantitative interpretation

The phase behavior of some rodlike block molecules has been reviewed with reference to the polarity of constituent segments. It was found that the ability of the mesophase formation is connected with differences in polar character between the flexible chains and rigid cores. Thus the polar poly(oxyethylene) group connected with the polar rigid core reduces mesophase stability but is advantageous when put together with some apolar building blocks. An attempt at quantitative estimation of the incompatibilities of different parts of molecules by means of Hansen solubility parameters delta and Flory interaction parameters chi has also been made. On the basis of chi parameters the Gibbs free energies of mixing of these segments were calculated. The changes of Gibbs free energy reflecting the compatibility of segments and their tendency to the phase separation and the volume fraction of mesogenic rigid core reflecting their ability to arrangement in one direction appear to be crucial in terms of type of the mesophase formation.     

Self-diffusion coefficient equation for polyatomic fluid

An equation for the self-diffusion coefficient in a polyatomic fluid is presented as a sum of three friction coefficient terms: the temperature-dependent hard-sphere contribution, the chain contribution and the soft contribution. This equation has been developed by using the molecular dynamics simulation data for the HS chain fluid and the expression for the Lennard–Jones (LJ) fluid proposed by Ruckenstein and Liu. The real nonspherical compounds are modeled as chains of tangent LJ segments. The segment diameter σ_LJ, segment–segment interaction energy ε_LJ and chain length N (the number of segments) are obtained from the experimental diffusion data. The equation reproduces the experimental self-diffusion coefficients with an average absolute deviation (AAD) of 3.72% for 22 polyatomic compounds (1081 data points) over wide ranges of temperature and pressure. The results have been compared with that of the rough LJ (RLJ) equation. To minimize the number of the fitting parameters, the energy parameter ε_LJ is estimated using a correlation obtained from viscosity data. The equation with two parameters gives an AAD of 4.72%.     

Thermodynamic properties and aggregate formation of surfactant-like molecules from theory and simulation

The goal of this work is twofold: to predict the phase equilibria behavior of simplified surfactant models and to predict the population of aggregates as a function of pressure. We compare Monte Carlo simulation results of these systems with predictions from a modified version of the statistical associating fluid theory (soft-SAFT). Surfactant-like molecules are modeled as Lennard-Jones chains of tangent segments with one or two association sites. We study the influence of the number and location of the association sites on the thermodynamic properties and fraction of nonbonded molecules in all cases. The influence of the chain length is also investigated for a particular location of the sites. Results are compared with NPT Monte Carlo simulations to test the accuracy of the theory, and to study the molecular configurations of the system. Soft-SAFT is able to quantitatively predict the MC PVT results, independently of the location of the association sites. The theory is also able to capture the qualitative trend of the population of aggregates with pressure. Quantitative agreement is only obtained for specific locations of the sites.     

Molecular dynamics study on homonuclear and heteronuclear chains of Lennard–Jones segments

We report molecular dynamics (MD) simulation data for three simulated fluids: a homopolymer with 16 tangent Lennard–Jones (LJ) segments at the reduced temperature of 1.25, an equimolar binary homopolymer fluid with eight tangent LJ segments at 15 state points, and three corresponding copolymers with equimolar segment fraction and varying segment distribution at 15 state points. We find that the compressibility factors and energies do not change as the segment distribution varies in the copolymer example. The simulation data are compared with thermodynamic perturbation theory (TPT1) calculations. The TPT1 compressibility factors compare favorably with the MD data at high reduced temperatures but differ significantly at lower temperatures.     

Silsesquioxane Films on Water Surface

The properties of films formed on the water surface by rigid molecules of organosilicon compounds, oligomeric silsesquioxanes containing phenyl and ethyl side groups, are studied. These compounds are shown to form insoluble stable layers. The properties of the monomolecular films of rigid macromolecules are similar to those of the monolayers of flexible-chain molecules, and the former can be considered as two-dimensional solutions. In contrast to flexible chains, the collapse of the monolayers of rigid molecules, which is formally considered as the first-order phase transition, is accompanied by the formation of an anisotropic lamellar structure, which can be referred to as the mesomorphic state of the substance.     

Evaporation of Lennard-Jones fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature T/T(c), where T(c) is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.     

Phase transition of short linear molecules adsorbed on solid surfaces from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on strongly attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the layering transitions change with the change of the chain length and with relative strength of the fluid-solid interaction. The critical temperature of the first layering transition, rescaled by the bulk critical temperature, increases slightly with an increase of the chain length. We have found that for longer chains the layering transitions within consecutive layers are shifted toward very low temperatures and that their sequence is finally replaced by a single transition.