Effective Interaction Parameter Research Articles

Phase Behavior of Pyrene and Vinyl Polymers with Aromatic Side Groups

The phase behavior and thermodynamic properties of mixtures of pyrene and model vinyl polymers with and without aromatic side groups are investigated using differential scanning calorimetry (DSC) measurements. The melting temperature and associated heat of melting of the pyrene crystals in the mixtures are utilized to extract the effective interaction parameters χ and the composition of polymer-rich phases, respectively. The χ of pyrene mixed with polymers with aromatic side groups investigated in this study, polystyrene, poly(2-vinylpyridine), and poly(3-vinylanisole), is less than 0.5 at the melting point of the pyrene crystals, suggesting that pyrene and the polymers with aromatic sides groups are enthalpically compatible, likely due to aromatic π–π interactions. In contrast, the χ of pyrene mixed with poly(1,4-isoprene) or poly(ethylene-alt-propylene) is larger than 0.5. The DSC measurements also enable characterization of the composition of polymer-rich phases. Interestingly, the polymers with aromat...

Revisiting the Anionic Polymerization of Methyl Ethacrylate

AbstractSynthesis of poly(methyl ethacrylate), (PMEA), in tetrahydrofuran at −78 °C using anionic polymerization techniques results in high molar mass (>30 kg mol−1), low dispersity (1.3), and high conversion (>81%). The molar masses of a series of samples are consistent with values anticipated by the monomer‐to‐initiator ratio and conversion. These results represent a significant improvement to earlier reported attempts to prepare PMEA using anionic methods. Successful diblock polymerization of polystyrene‐block‐PMEA, (PS‐PMEA), and poly(4‐tert‐butylstyrene)‐block‐PMEA, (PtBS‐PMEA), is achieved through sequential anionic polymerization techniques with dispersities as low as 1.06 and segment molar fractions close to those targeted. Broad principal scattering peaks observed by small‐angle X‐ray scattering (SAXS) for symmetric PS‐PMEA at relatively high molar mass (39 kg mol−1) suggests an effective interaction parameter (χeff) that is smaller than for PS‐block‐poly(methyl methacrylate). On the other hand, PtBS‐PMEA block polymers form a well‐ordered morphology based on SAXS measurements and is attributable to the more hydrophobic PtBS segment. These results confirm the viability of PMEA as a new constituent in the expanding suite of polymers suitable for preparing nanostructured block polymers.

Pressure dependence of dynamically screened Coulomb interactions in NiO: Effective Hubbard, Hund, intershell, and intersite components

In this work, we report the pressure dependence of the effective Coulomb interaction parameters (Hubbard U) in paramagnetic NiO within the constrained random phase approximation (cRPA). We consider five different low energy models starting from the most expensive one that treats both Ni-d and O-p states as correlated orbitals (dp-dp model) to the smallest possible two-orbital model comprising the eg states only (eg-eg model). We find that in all the considered models, the bare interactions are not very sensitive to the compression. However the partially screened interaction parameters show an almost linear increment as a function of compression, resulting from the substantial weakening of screening effects upon compression. This counterintuitive trend is explained from the specific characteristic changes of the basic electronic structure of this system. We further calculate the nearest neighbor inter-site d-d interaction terms which also show substantial enhancement due to compression. Our results for both the experimental and highly compressed structures reveal that the frequency dependence of the partially screened interactions can not be ignored in a realistic modeling of NiO. We also find that the computed interaction parameters for the antiferromagnetic NiO are almost identical to their paramagnetic counter parts.

Investigations on the Phase Diagram and Interaction Parameter of Poly(styrene-b-1,3-cyclohexadiene) Copolymers

A series of linear diblock copolymers containing polystyrene (PS) and poly(1,3-cyclohexadiene) (PCHD) with high 1,4-microstructure (>87%) was synthesized by anionic polymerization and high vacuum techniques. Microphase separation in the bulk was examined by transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) and compared to computational analysis of the predicted morphological phase diagram for this system. Because of the high conformational asymmetry between PS and PCHD, these materials self-assemble into typical morphologies expected for linear diblock copolymer systems and atypical structures. Rheological measurements were conducted and revealed order–disorder transition temperatures (TODT), for the first time for PS-b-PCHD copolymers, resulting in a working expression for the effective interaction parameter χeff = 32/T – 0.016. Furthermore, we performed computational studies that coincide with the experimental results. These copolymers exhibit well-ordered structures even at...

Self-assembly of gradient copolymers synthesized in semi-batch mode by nitroxide mediated polymerization.

The effect of diffuse compositional interfaces on copolymer self-assembly was studied via gradient copolymers (GCP). Poly(methyl methacrylate)-grad-(styrene) (PMMA-grad-PSt) copolymers were synthesized in semi-batch mode using nitroxide-mediated polymerization (NMP) with varied monomer injection protocols to produce varied diffuse interfaces (number average molecular weights (Mn) ranged from 62 000 g mol-1 to 94 000 g mol-1 with dispersities (Đ) between 1.35 and 1.59). The GCPs were spun into thin films on substrates made neutral by (St-ran-MMA-ran-hydroxyethyl methacrylate) terpolymers and annealed at elevated temperature to produce vertically oriented microphase-separated domains. The GCPs were found to have domain spacing larger than equivalent monodisperse BCPs, due to their polydisperse nature. This effect was partially offset by the decrease in χ due to the gradient. GCPs synthesized with a single-injection protocol (i.e. less diffuse interfaces) were found to self-assemble into ordered domains. However, GCPs synthesized with long injection times (i.e. more diffuse interfaces) exhibited poor self-assembly attributed to their predicted statistical-copolymer-like middle sequence, which caused a reduction of the effective enthalpic interaction parameter.

Thermodynamics and phase behavior of acid-tethered block copolymers with ionic liquids.

We investigate the phase behavior of acid-tethered block copolymers with and without ionic liquids. Two phosphonated block copolymers and their sulfonated analogs were synthesized by fine-tuning the degree of polymerization and the acid content. The block copolymers carrying acid groups with ionic liquids exhibited rich phase sequences, i.e., disorder-lamellae (LAM), gyroid-LAM, gyroid-hexagonal cylinder (HEX), and gyroid-A15 lattice, and the cation/anion ratio in the ionic liquid exerted profound effects on the segregation strength and topology of the self-assembled structures. Additionally, using ionic liquids with excessive cation content was found to enhance the effective Flory-Huggins interaction parameter, χeff, of the samples. However, as the anion content of the ionic liquids increased the segregation strength decreased. This is attributed to the packing frustration accompanied by the prevailing repulsive electrostatic interactions of the anions in the ionic liquid and the polymer matrix. As the hydrophobicity of the ionic liquids increased, well-defined ordered phases emerged in the phosphonated block copolymers with increased anion content, contrary to the disordered phases of the sulfonated samples. Thus, the balance between solvation energy of the anions and the electrostatic interactions is a key determinant of the thermodynamics of acid-tethered block copolymers containing ionic liquids.

Coupling quantum Monte Carlo and independent-particle calculations: Self-consistent constraint for the sign problem based on the density or the density matrix

Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem. The constraint involves an input trial wave function which restricts the random walks. We introduce a systematically improvable constraint which relies on the fundamental role of the density or one-body density matrix. An independent-particle calculation is coupled to an auxiliary-field QMC calculation. The independent-particle solution is used as the constraint in QMC, which then produces the input density or density matrix for the next iteration. The constraint is optimized by the self-consistency between the many-body and independent-particle calculations. The approach is demonstrated in the two-dimensional Hubbard model by accurately determining the ground state when collective modes separated by tiny energy scales are present in the magnetic and charge correlations. Our approach also provides an ab initio way to predict effective interaction parameters for independent-particle calculations.

α-particle elastic scattering from 12C, 16O, 24Mg, and 28Si

The elastic scattering of α-particle is analyzed in terms of the optical model over the energy 104–172.2 MeV for 12C, 48.7–146 MeV for 16O, 50–119 MeV for 24Mg, and 104, 166, 120 and 240 MeV for 28Si. We generate the real part of the optical model potential using the single folding model. In the single folding procedure, the ground state density of the target is folded with an effective density dependent α-nucleon interaction. For the imaginary part, the usual Woods–Saxon form is used. The parameters of the effective density dependent α-nucleon interaction are determined by fitting the experimental data of elastic scattering. The effective interaction's parameters are optimized using the χ2 criterion. We reasonably reproduce the elastic scattering cross sections for all studied systems. The obtained results reflect the success of our obtained α-nucleon effective interaction.

Ordered Mesoporous to Macroporous Oxides with Tunable Isomorphic Architectures: Solution Criteria for Persistent Micelle Templates

Porous and nanoscale architectures of inorganic materials have become crucial for a range of energy and catalysis applications, where the ability to control the morphology largely determines the transport characteristics and device performance. Despite the availability of a range of block copolymer self-assembly methods, the conditions for tuning the key architectural features such as the inorganic wall-thickness have remained elusive. Toward this end, we have developed solution processing guidelines that enable isomorphic nanostructures with tunable wall-thickness. A new poly(ethylene oxide-b-hexyl acrylate) (PEO-b-PHA) structure-directing agent (SDA) was used to demonstrate the key solution design criteria. Specifically, the use of a polymer with a high Flory–Huggins effective interaction parameter, χ, and appropriate solution conditions leads to the kinetic entrapment of persistent micelle templates (PMT) for tunable isomorphic architectures. Solubility parameters are used to predict conditions for mai...

Effective electrostatic interactions among charged thermo-responsive microgels immersed in a simple electrolyte.

This work explores the nature and thermodynamic behavior of the effective electrostatic interactions among charged microgels immersed in a simple electrolyte, taking special interest in the effects due to the thermally induced variation of the microgel size while the remaining parameters (microgel charge and concentration, plus the amount of added salt) are kept constant. To this end, the rigorous approach obtained from applying the precise methodology of the dressed ion theory to the proper definition of the effective direct correlation functions, which emerge from tracing-out the degrees of freedom of the microscopic ions, is employed to provide an exact description of the parameters characterizing such interactions: screening length, effective permittivity, and renormalized charges. A model solution with three components is assumed: large permeable anionic spheres for the microgels, plus small charged hard spheres of equal size for the monovalent cations and anions. The two-body correlations among the components of this model suspension, used as the input for the determination of the effective interaction parameters, are here calculated by using the hyper-netted chain approximation. It is then found that at finite microgel concentrations the values of these parameters change as the microgel size increases, even though the ionic strength of the supporting electrolyte and the bare charge of the microgels remain fixed during this process. The variation of the screening length, as well as that of the effective permittivity, is rather small, but still interesting in view of the fact that the corresponding Debye length stays constant. The renormalized charges, in contrast, increase markedly as the microgels swell. The ratio of the renormalized charge to the corresponding analytic result obtained in the context of an extended linear response theory allows us to introduce an effective charge that accounts for the non-linear effects induced by the short-ranged association of microions to the microgels. The behavior of these effective charges as a function of the amount of added salt and the macroion charge, size, and concentration reveals the interplay among all these system parameters.

Influence of Skyrme-type interaction on HICs observables

A new version of the improved quantum molecular dynamics model has been developed by including Skyrme type momentum dependent interaction. 12 Skyrme like parameter sets {K0, S0, L, m ∗, m ∗} are adopted in the transport model code to calculate the isospin diffusion, single and double ratios of transverse emitted nucleons, neutron proton isoscaling ratios. The calculations and correlation analysis evidence that isospin diffusion observable at lower beam energy is sensitive to the slope of symmetry energy and m ∗. The high energy neutrons and protons yield ratios from reactions at different incident energies provide a sensitive observable to study the nucleon effective mass splitting, at higher beam energy. The properties of isospin asymmetric nuclear equation of state is of fundamental importance in our understanding of nature’s asymmetric objects including neutron stars as well as heavy nuclei with very different number of neutrons and protons. Currently, there exist, lot of effective interaction parameter sets [1, 2], for fitting the ground-state properties of stable nuclei, symmetric and asymmetric nuclear matter. It also leads very different neutron Equation of state which may have different nuclear matter (NM) parameters, such as incompressibility K0, isoscalar effective mass m ∗ ,s ymmetry energy coef fi cientS0, slope of symmetry energy L and isovector effec

Fabrication of ultra-dense sub-10 nm in-plane Si nanowire arrays by using a novel block copolymer method: optical properties.

The use of a low-χ, symmetric block copolymer as an alternative to the high-χ systems currently being translated towards industrial silicon chip manufacture has been demonstrated. Here, the methodology for generating on-chip, etch resistant masks and subsequent pattern transfer to the substrate using ultra-small dimension, lamellar, microphase separated polystyrene-b-poly(ethylene oxide) (PS-b-PEO) block copolymer (BCP) is described. Well-controlled films of a perpendicularly oriented lamellar pattern with a domain size of ∼8 nm were achieved through amplification of an effective interaction parameter (χeff) of the BCP system. The self-assembled films were used as 'templates' for the generation of inorganic oxides nanowire arrays through selective metal ion inclusion and subsequent processing. Inclusion is a significant challenge because the lamellar systems have less chemical and mechanical robustness than the cylinder forming materials. The oxide nanowires of uniform diameter (∼8 nm) were isolated and their structure mimics the original BCP nanopatterns. We demonstrate that these lamellar phase iron oxide nanowire arrays could be used as a resist mask to fabricate densely packed, identical ordered, good fidelity silicon nanowire arrays on the substrate. Possible applications of the materials prepared are discussed, in particular, in the area of photonics and photoluminescence where the properties are found to be similar to those of surface-oxidized silicon nanocrystals and porous silicon.

SANS study on the solvated structure and molecular interactions of a thermo-responsive polymer in a room temperature ionic liquid.

We have utilized small-angle neutron scattering (SANS) to quantitatively characterize the LCST-type phase behavior of the poly(benzyl methacrylate) (PBnMA) derivative poly(2-phenylethyl methacrylate) (PPhEtMA) in the deuterated ionic liquid (IL) d8-1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide (d8-[C2mIm(+)][TFSA(-)]). The SANS curves showed a discontinuous change from those characteristics of dispersed polymer chains to those of large aggregates of PPhEtMA chains suspended in the IL solution, indicating that phase separation occurs discontinuously at Tc. Furthermore, we evaluated the enthalpic and entropic contributions to the effective interaction parameter χeff of PPhEtMA in [C2mIm(+)][TFSA(-)] and compared them with those of PBnMA. The absolute value of the enthalpic contribution observed for PPhEtMA was smaller than that for PBnMA. This difference in the enthalpic term can be attributed to the unfavorable interaction between the IL and the alkyl group in the side chain of PPhEtMA. In addition, the temperature dependence of χeff was smaller than the previously reported value for a thermo-responsive polymer in an aqueous system. It was found out that the strong dependence of Tc on the chemical structure in IL systems originated from the relatively smaller temperature dependence of χeff.

Phase behavior and second osmotic virial coefficient for competitive polymer solvation in mixed solvent solutions

We apply our recently developed generalized Flory-Huggins (FH) type theory for the competitive solvation of polymers by two mixed solvents to explain general trends in the variation of phase boundaries and solvent quality (quantified by the second osmotic virial coefficient B2) with solvent composition. The complexity of the theoretically predicted miscibility patterns for these ternary mixtures arises from the competitive association between the polymer and the solvents and from the interplay of these associative interactions with the weak van der Waals interactions between all components of the mixture. The main focus here lies in determining the influence of the free energy parameters for polymer-solvent association (solvation) and the effective FH interaction parameters {χαβ} (driving phase separation) on the phase boundaries (specifically the spinodals), the second osmotic virial coefficient B2, and the relation between the positions of the spinodal curves and the theta temperatures at which B2 vanishes. Our classification of the predicted miscibility patterns is relevant to numerous applications of ternary polymer solutions in industrial formulations and the use of mixed solvent systems for polymer characterization, such as chromatographic separation where mixed solvents are commonly employed. A favorable comparison of B2 with experimental data for poly(methyl methacrylate)/acetonitrile/methanol (or 1-propanol) solutions only partially supports the validity of our theoretical predictions due to the lack of enough experimental data and the neglect of the self and mutual association of the solvents.

Effect of magnetism and atomic order on static atomic displacements in the Invar alloy Fe-27 at.% Pt

Fe-27 at.% Pt was aged at 1123 K and quenched to room temperature (RT) to set up a state of thermal equilibrium. The local atomic arrangement was studied by diffuse x-ray scattering above (at 427 K) and below (at RT) the Curie temperature as well as at RT under a saturating magnetic field. The separated short-range order scattering remained unchanged for all three states, with maxima at 100 positions. Effective pair interaction parameters determined by the inverse Monte Carlo method gave an order-disorder transition temperature of about 1088 K, close to direct experimental findings. The species-dependent static atomic displacements for the first two shells show large differences, with a strong increase in magnitude from the state at 427 K over RT to the state under saturating magnetic field. This outcome is in agreement with an increase in atomic volume of Fe with increasing local magnetic moment. Electronic-structure calculations closely reproduce the values for the static atomic displacements in the ferromagnetic state, and predict their dependence on the atomic configuration. They also reveal a strong dependence of the magnetic exchange interactions in Fe-Pt on the atomic configuration state and lattice parameter. In particular, the increase of the Curie temperature in a random state relative to that in the ordered one is demonstrated to be related to the corresponding change of the magnetic exchange interactions due to the different local atomic chemical environment. There exists a similar strong concentration dependence of the chemical interactions as in the case of magnetic exchange interactions. Theoretical effective interactions for Fe-27 at.% Pt alloy are in good agreement with experimental results, and they also reproduce well the ${\mathrm{L}1}_{2}$-A1 transition temperature.

Lithium-Salt-Containing High-Molecular-Weight Polystyrene-block-Polyethylene Oxide Block Copolymer Films.

Ionic conductivity in relation to the morphology of lithium-doped high-molecular-weight polystyrene-block-polyethylene oxide (PS-b-PEO) diblock copolymer films was investigated as solid-state membranes for lithium-ion batteries. The tendency of the polyethylene (PEO) block to crystallize was highly suppressed by increasing both the salt-doping level and the temperature. The PEO crystallites completely vanished at a salt-doping ratio of Li/EO>0.08, at which the PEO segments were hindered from entering the crystalline unit of the PEO chain. A kinetically trapped lamella morphology of PS-b-PEO was observed, due to PEO crystallization. The increase in the lamella spacing with increasing salt concentration was attributed to the conformation of the PEO chain rather than the volume contribution of the salt or the previously reported increase in the effective interaction parameter. Upon loading the salt, the PEO chains changed from a compact/highly folded conformation to an amorphous/expanded-like conformation. The ionic conductivity was enhanced by amorphization of PEO and thereby the mobility of the PEO blocks increased upon increasing the salt-doping level.

Low-energy effective interactions beyond the constrained random-phase approximation by the functional renormalization group

In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random-phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered constrained functional renormalization group (cfRG) generalizes the cRPA approach by including all interaction channels in an unbiased way. Here we present applications of the cfRG to two simple multiband systems and compare the resulting effective interactions to the cRPA. First, we consider a multiband model for monolayer graphene, where we integrate out the $\ensuremath{\sigma}$ bands to get an effective theory for $\ensuremath{\pi}$ bands. It turns out that terms beyond cRPA are strongly suppressed by the different $xy$-plane reflection symmetry of the bands. In our model the cfRG corrections to cRPA become visible when one disturbs this symmetry difference slightly, however, without qualitative changes. This study shows that the embedding or layering of two-dimensional electronic systems can alter the effective interaction parameters beyond what is expected from screening considerations. The second example is a one-dimensional model for a diatomic system reminiscent of a CuO chain, where we consider an effective theory for Cu $3d$-like orbitals. Here the fRG data shows relevant and qualitative corrections compared to the cRPA results. We argue that the new interaction terms affect the magnetic properties of the low-energy model.

Using tapered interfaces to manipulate nanoscale morphologies in ion-doped block polymers

Abstract

Fluctuations, Phase Transitions, and Latent Heat in Short Diblock Copolymers: Comparison of Experiment, Simulation, and Theory

We present a detailed quantitative comparison of experimental results and theoretical predictions for the structure and thermodynamics of low molecular weight symmetric (fL ≈ 1/2) poly(1,4-isoprene-b-dl-lactide) (IL) diblock copolymers near the order–disorder transition (ODT). Small-angle neutron and X-ray scattering (SANS and SAXS) measurements obtained in the disordered phase with IL degree of polymerization N = 39 were fit to the renormalized one-loop (ROL) theory in order to estimate the effective interaction parameter χe(T). Calorimetric measurements of the latent heat of the ODT for the same copolymer compare well with that obtained from corresponding coarse-grained simulations, when the comparison is based on this estimate of χe(T). The corresponding estimate of (χeN)ODT at the experimental ODT of this polymer is much closer to the value obtained from simulations than to any theoretical prediction but differs from the simulation result by somewhat more than the bounds implied by experimental uncertainties. A larger discrepancy between simulation and experimental results for (χeN)ODT is obtained for longer chains, with N ≥ 50, when also calculated using χe(T, N = 39). We discuss possible reasons for this discrepancy, including the possibility of a significant end-group effect for these polymers. These results confirm the overwhelming importance of fluctuation effects in short diblock copolymers, and the usefulness of coarse-grained simulations as a starting point for quantitative modeling, but also indicate the need for attention to nonuniversal features of specific polymers that can also become more important with decreasing chain length.

A general theory of flattened dipolar condensates

We develop theory for a flattened dipolar Bose–Einstein condensate produced by harmonic confinement along one direction. The role of both short-ranged contact interactions and long-ranged dipole–dipole interactions is considered, and the dipoles are allowed to be polarized along an arbitrary direction. We discuss the symmetry properties of the condensate and the part of the excitation spectrum determining stability, and introduce two effective interaction parameters that allow us to provide a general description of the condensate properties, rotons, and stability. We diagonalize the full theory to obtain benchmark results for the condensate and quasiparticle excitations, and characterize the exact mean field stability of the system. We provide a unified formulation for a number of approximate schemes to describe the condensate and quasiparticles, including the standard quasi-two-dimensional approximation, two kinds of variational ansatz, and a Thomas–Fermi approximation. Some of these schemes have been widely used in the literature despite not being substantiated against the exact theory. We provide this validation and establish the regimes where the various theories perform well.