Flexible Tangent Research Articles

Multiscale Approaches for Confined Ring Polymer Solutions.

We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.

A Simple Method for Determining the Critical Point of the Soil Water Retention Curve

Core Ideas A fixed tangent line method was developed to estimate the critical point of the soil water retention curve as an alternative to the commonly used flexible tangent line method. The critical points of the soil water retention curve from the proposed method and the flexible tangent line method were compared. Particle‐size distribution and specific surface area had significant effects on the critical point of the soil water retention curve. The transition point between capillary water and adsorbed water, which is the critical point Pc [defined by the critical matric potential (ψc) and the critical water content (θc)] of the soil water retention curve (SWRC), demarcates the energy and water content region where flow is dominated by capillarity or liquid film flow. Accurate estimation of Pc is crucial for modeling water movement in the vadose zone. By modeling the dry‐end (matric potential < –104.2 cm H2O) and wet‐end (matric potential > –104.2 cm H2O) sections of the SWRC using the models of Campbell and Shiozawa, and of van Genuchten, a fixed tangent line method was developed to estimate Pc as an alternative to the commonly used flexible tangent line method. The relationships between Pc, and particle‐size distribution and specific surface area (SSA) were analyzed. For 27 soils with various textures, the mean RMSE of water content from the fixed tangent line method was 0.007 g g–1, which was slightly better than that of the flexible tangent line method. With increasing clay content or SSA, ψc was more negative initially but became less negative at clay contents above ∼30%. Increasing the silt contents resulted in more negative ψc values, whereas soils with higher sand content had less negative ψc values. The magnitude of θc increased linearly with SSA and clay content. Our findings suggest that Pc estimated from the fixed tangent line method could represent the actual values and clarify the effect of particle‐size distribution and SSA on Pc.

大口径望远镜主镜支撑系统装调

According to 1.2 m large aperture telescope primary mirror support system, an effective assembly method was advanced to insure the root-mean-square (RMS) of the surface accuracy. The primary mirror support system was designed following kinematic principle. To achieve excellent performance of the RMS of primary mirror surface accuracy at different ambient temperature (from -20℃ to 60℃) and different elevation(from vertical to horizontal), whiffletree structure were used for axial support,while lateral support mechanisms based on flexible tangent link structure were adopted. Resulting from machining error and installation error of the flexible structures, assembly stress was presented certainly, that could increase primary mirror distortion range evidently. By the finite element analysis(FEA) simulation, the effects of various errors were calculated. According to simulation results, assembly processes were established. After assembly of primary mirror support system, the RMS of primary mirror surface accuracy was measured by compensator and laser interferometer. In measurement, the RMS of surface accuracy was /42 and /31(=632.8 nm), when optical axis of primary mirror was vertical and horizontal.

Chemical potentials and phase equilibria of Lennard-Jones chain fluids

Computer simulations (molecular dynamics) were performed for ensembles of flexible tangent Lennard-Jones chains consisting of n sites (n = 1, 2, 4, 8, and 16). From these simulations, the orthobaric liquid and vapour densities were calculated not only with the traditional method of simulating a liquid film in coexistence with vapour, but also using the rigorous thermodynamic condition of satisfying the chemical potential equality between the phases in equilibrium. The agreement with literature data, as far as such exist, is excellent.

The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: an analytical equation of state.

An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation.

An equation of state for the isotropic phase of linear, partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.

Effect of flexibility on liquid-vapor coexistence and surface properties of tangent linear vibrating square well chains in two and three dimensions

The effect of flexibility on liquid-vapor and interfacial properties of tangent linear vibrating square well chains is studied. Surface tension, orthobaric densities, vapor pressures, and interfacial thicknesses are reported and analyzed using corresponding states principles. Discontinuous molecular dynamics simulations in two and three dimensions are performed on rigid tangent linear vibrating square well chains of different lengths. In the case of two dimensions, simulation results of completely flexible tangent linear vibrating square well chains are also reported. Properties are calculated for chains of 2-12 monomers. Rigidity is controlled by trapping the first and last monomer in the chain in a vibrating well at half of the distance of the whole chain. Critical property values are reported as obtained from orthobaric densities, surface tensions, and vapor pressures. For the fully flexible chains, the critical temperatures increase with chain length but the effect saturates. In contrast, the critical temperatures increase for the rigid chains until no more critical point is found.

Minimal energy packings of nearly flexible polymers

We extend recent studies of the minimal energy packings of short flexible polymers with hard-core-like repulsions and short-range attractions to include bond-angle interactions with the aim of describing the collapsed conformations of "colloidal" polymers. We find that flexible tangent sticky-hard-sphere (t-SHS) packings provide a useful perturbative basis for analyzing polymer packings with nonzero bending stiffness only for small ratios of the stiffnesses for the bond-angle (k(b)) and pair (k(c)) interactions, i.e., k(b) (crit)/k(c)</~0.01 for N < 10 monomers, and the critical ratio decreases with N. Below k(b) (crit), angular interactions give rise to an exponential (in N) increase in the number of distinct angular energies arising from the diversity of covalent backbone paths through t-SHS packings. As k(b) increases above k(b) (crit), the low-lying energy landscape changes dramatically as finite bending stiffness alters the structure of the polymer packings. This study lays the groundwork for exact-enumeration studies of the collapsed states of t-SHS-like models with larger bending stiffness.

An investigation of the shape and crossover scaling of flexible tangent hard-sphere polymer chains by Monte Carlo simulation

Results are presented from our simulation study of flexible, tangent hard-sphere polymer chains, using a Monte Carlo technique with a reptation algorithm. We examine the crossover region from the swollen (dilute) region to the semidilute regime using chains of degree up to N=2000. The (average) chain end-to-end distance is analyzed as a function of the number of chain links, as is a correlation function for the internal separation of segments, expressed in terms of their connectivity. We study the structure of the polymer chains using scattering functions, which are presented in addition to the segment–segment distribution functions from which they are calculated. Not surprisingly, the Flory exponent ν changes gradually from the dilute value of ν≈0.59 to ≈12 at high density. We find that for chains of 2000 segments, this transition begins at the very low molecular volume fraction of about 0.1%. An analysis of the correlation function for internal segments provides a similar but more detailed picture, in that the role of the screening length ξ becomes explicit. The pair distribution and scattering functions in the swollen, crossover, and melt regions are determined and the scaling behavior is reexamined in the context of these functions. The system considered will form a reference system for subsequent studies in which the model will be broadened to include a network and/or attractive interactions. In this paper we seek first of all to establish that reference, and to relate our work to previous studies in this area of interest. As an important technical point, we also note that the use of an inappropriate random number generator can cause the complete failure of simulations of this type.