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Opposing polymer brush systems were synthesized and investigated by molecular modeling. Chains were restricted to a face-centered cubic lattice with the excluded volume interactions only. The system was confined between two parallel impenetrable walls, with the same number of chains grafted to each surface. The dynamic properties of such systems were studied by Monte Carlo simulations based on the dynamic lattice liquid model and using a highly efficient parallel machine ARUZ, which enabled the study of large systems and long timescales. The influence of the surface density and mean polymer length on the system dynamic was discussed. The self-diffusion coefficient of the solvent depended strongly on the degree of polymerization and on the polymer concentration. It was also shown that it is possible to capture changes in solvent mobility that can be attributed to the regions of different polymer densities.

We summarize our knowledge of the phase behavior of polymer solutions and blends using a unified approach. We begin with a derivation of the Flory–Huggins expression for the Gibbs free energy of mixing two chemically dissimilar polymers. The Gibbs free energy of mixing of polymer solutions is obtained as a special case. These expressions are used to interpret observed phase behavior of polymer solutions and blends. Temperature- and pressure-dependent phase diagrams are used to determine the Flory–Huggins interaction parameter, χ. We also discuss an alternative approach for measuring χ due to de Gennes, who showed that neutron scattering from concentration fluctuations in one-phase systems was a sensitive function of χ. In most cases, the agreement between experimental data and the standard Flory–Huggins–de Gennes approach is qualitative. We conclude by summarizing advanced theories that have been proposed to address the limitations of the standard approach. In spite of considerable effort, there is no con...

Incipient microphase separation is observed by wide angle X-ray scattering (WAXS) in short chain multiblock copolymers consisting of perfluoropolyether (PFPE) and poly(ethylene oxide) (PEO) segments. Two PFPE-PEO block copolymers were studied; one with dihydroxyl end groups and one with dimethyl carbonate end groups. Despite having a low degree of polymerization (N ∼ 10), these materials exhibited significant scattering intensity, due to disordered concentration fluctuations between their PFPE-rich and PEO-rich domains. The disordered scattering intensity was fit to a model based on a multicomponent random phase approximation to determine the value of the interaction parameter, χ, and the radius of gyration, Rg. Over the temperature range 30-90 °C, the values of χ were determined to be very large (∼2-2.5), indicating a high degree of immiscibility between the PFPE and PEO blocks. In PFPE-PEO, due to the large electron density contrast between the fluorinated and non-fluorinated block and the high value of χ, disordered scattering was detected at intermediate scattering angles, (q ∼ 2 nm-1) for relatively small polymer chains. Our ability to detect concentration fluctuations was enabled by both a relatively large value of χ and significant scattering contrast.

We performed Monte Carlo simulations using a minimal lattice model with short-range interactions modeled using Flory–Huggins interactions parameters, χ, to investigate morphology of ion-containing A–B diblock copolymers. A fraction of the segments in the A block, p, were ionic (labeled S) while the B block segments were nonionic (p was held fixed at 0.588). The dielectric constants of the polymers is assumed to be low, and thus charge dissociation effects are negligible. The magnitude of the χ between ion and nonionic species, determined in previous experiments on poly(styrenesulfonate)-b-poly(methyl butylene), PSS–PMB, is an order of magnitude larger than that between the nonionic segments. Simulations indicate that complex morphologies such as gyroid and perforated lamellae are obtained in symmetric block copolymers wherein the volume fraction of the B block, ϕB, is about 0.5, while simple unperforated lamellae are obtained in asymmetric block copolymers wherein ϕB is about 0.25. This result is very dif...

The underpinnings of microphase separation in symmetric poly(styrenesulfonate-block-methylbutylene) (PSS−PMB) copolymer melts were examined by Monte Carlo lattice simulations. The main challenge is understanding the effect of ion pairs in the PSS block on thermodynamics. We assume that experimentally determined Flory−Huggins interaction parameters are adequate for describing intermonomer interactions. Our model does not account for either electrostatic or dipolar interactions. This enables comparisons between simulated and experimentally observed microphases reported by Park and Balsara [Macromolecules 2008, 41, 3678] without resorting to any adjustable parameters. The PSS block in both experiments and theory is partially sulfonated. We quantified the effect of sequence distribution on phase behavior by using alternating and blocky PSS chains in the simulations. Depending on temperature and sequence distribution, simulations show perforated lamellae, gyroid, and hexagonally packed cylinders in addition to...

We perform off-lattice Monte Carlo simulations for multiblock chains, ( 5 A - 5 B ) n , with n = 10 , 20 , 30 , 40 , 50 , and 60 , in an implicit selective solvent, using a discontinuous square-well potential. We present selected thermodynamic and structural properties as a function of the reduced temperature, such as the reduced energy per segment, the reduced heat capacity, and the mean-squared radius of gyration. We observe that the collapse-driven self-assembled structure is not spherical above certain value of chain length, N, and develops a non-spherical globular structure with multiple cores.

We present both lattice and off-lattice Monte Carlo simulations for multiblock copolymer chains of two lengths, N = 64 and N=128, with microarchitectures (8-8)4 and (16-16) 4 , respectively. The simulations demonstrate that a variety of lattice and off-lattice Monte Carlo methods gives the same protein-like behavior, showing that the multiblock chains undergo a two-step transition, first from a swollen state to a secondary "pearl-necklace" state, and then to a tertiary super-globular state as the solvent quality decreases, that is upon cooling.

We present a lattice Monte Carlo study of a series of block copolymer chains in selective solvents of varying quality, first using a diblock chain of the length of N = 32 with a 16–16 microarchitecture, and then – two multiblock chains of N = 64 and N = 128 , with ( 8 – 8 ) 4 and ( 16 – 16 ) 4 microarchitectures, respectively. We report a variety of thermodynamic and structural properties, such as energy, specific heat, end-to-end distance and radius of gyration both for the whole chain and for individual blocks. The simulations have demonstrated that a multiblock copolymer in a selective solvent exhibits protein-like behavior undergoing a two-step transition, first from a swollen state to a secondary ‘pearl-necklace’ state and then to a tertiary super-globular state as the solvent quality decreases, i.e. upon cooling. We have found that mean-squared end-to-end distances of multiblock chains decrease as the temperature is reduced, as expected.

With a lattice Monte Carlo method, we investigate 16−16 symmetric diblock in selective solvent, A-b-B/A, at 10 volume fractions from 1.0 to 0.1, and for each volume fraction, we perform simulations at up to 54 temperatures, using simulation boxes of different sizes. We report temperature dependencies for a number of quantities such as energy, specific heat, and mean-squared end-to-end distances and construct a phase diagram using the thermodynamic and structural quantities as well as snapshots of the selected configurations. The simulated phase diagram is compared with the experimental data of Lodge and co-workers for nearly symmetric poly(styrene-b-isoprene) mixed with dimethyl phthalate.

A prototype equation of state, developed on the basis of thermodynamic perturbation theory of the first order (TPT1), using the Lennard-Jones potential for the reference fluid, is found to represent pure-fluid and binary phase equilibria in the systems of small chain molecules, such as normal alkanes.

Thermodynamic perturbation theory of the first order (TPT1) is extended to heterobonded chains, such as heteronuclear and branched copolymers. The TPT1 formalism provides the basis for a copolymer equation of state. This new copolymer equation of state, referred to as Copolymer SAFT (Statistical Associating Fluid Theory), explicitly accounts for the effects of chain heterogeneity and microstructure. In order to illustrate potential future applications, Copolymer SAFT is used to calculate high-pressure cloud points in real polymer solutions of supercritical propane + poly(ethylene-co-butene).

The compressibility factors for freely‐jointed Lennard‐Jones chains are determined in the context of Wertheim’s first‐order thermodynamic perturbation theory (TPT1). In the TPT1 treatment, nonbonded Lennard‐Jones spheres are used as the reference system. The compressibility factors of the chain system, at temperature T*, segment density ρ*, and chain length m, are obtained based on the compressibility factors of the Lennard‐Jones spheres, and the density derivative of the radial distribution function, ∂ ln gLJS(σ;ρ*,T*)/∂ρ*, evaluated at the same temperature T* and segment density ρ*. The exact values for these two quantities, obtained from Monte Carlo simulations, are used in our calculations. The TPT1 predictions are found in agreement with Monte Carlo simulation results for the 8‐mer, 16‐mer, and 32‐mer Lennard‐Jones chains over a wide range of densities and temperatures. When values of the density derivative of the reference Lennard‐Jones sphere system are estimated from the approximate Weeks–Chandler...

The development and fabrication of mechanical devices powered by artificial molecular machines is one of the contemporary goals of nanoscience. Before this goal can be realized, however, we must learn how to control the coupling/uncoupling to the environment of individual switchable molecules, and also how to integrate these bistable molecules into organized, hierarchical assemblies that can perform significant work on their immediate environment at nano-, micro- and macroscopic levels. In this tutorial review, we seek to draw an all-important distinction between artificial molecular switches which are now ten a penny—or a dime a dozen—in the chemical literature and artificial molecular machines which are few and far between despite the ubiquitous presence of their naturally occurring counterparts in living systems. At the single molecule level, a prevailing perspective as to how machine-like characteristics may be achieved focuses on harnessing, rather than competing with, the ineluctable effects of thermal noise. At the macroscopic level, one of the major challenges inherent to the construction of machine-like assemblies lies in our ability to control the spatial ordering of switchable molecules—e.g., into linear chains and then into muscle-like bundles—and to influence the cross-talk between their switching kinetics. In this regard, situations where all the bistable molecules switch synchronously appear desirable for maximizing mechanical power generated. On the other hand, when the bistable molecules switch “out of phase,” the assemblies could develop intricate spatial or spatiotemporal patterns. Assembling and controlling synergistically artificial molecular machines housed in highly interactive and robust architectural domains heralds a game-changer for chemical synthesis and a defining moment for nanofabrication.

A theoretical study of the lamellar microphase of block copolymer/selective solvent blends in which the solvent is good for one block and either good or near-θ for the other is presented. The calculations used numerical solutions to the equations of the self-consistent mean-field theory of polymer blends. Two types of systems were studied. In the first, all pure-component densities were taken to be equal, as were the two Kuhn statistical lengths, and the solvent was idealized as being athermal for one of the blocks. In the other type, realistic values for these parameters were used.

Te lamellar structure of binary A-b-B/A and ternary A-b-B/A/B copolymer/homopolymer blends near the microphase separation transition was investigated. The approach combines perturbative solutions to the modified diffusion equation with a model for the total A and B polymer density profiles. The equilibrium domain and subdomain thicknesses, swelling of the copolymers by the homopolymers, individual polymer density profiles, and their dependence on the copolymer and homopolymer degrees of polymerization, composition, and Flory interaction parameter were calculated.

The theory of polymer blends developed by Hong and Noolandi was extended and applied to the calculation of phase diagrams of ternary A-b-B/A/B copolymer/homopolymer blends which can undergo microphase and macrophase separation. The main results are phase diagrams for a variety of modelsystems containing symmetric or asymmetric copolymersmixed with homopolymers of varying molecular weights and for a polystyrene (PS)/polyisoprene (PI)/PS-b-PI mixture. Induced microphase formation in ternary and binary blends were compared.

We report the experimental and simulation studies for the system of nitrobenzene-cyclododecane, showing an apparent critical point, which lies in their metastable, experimentally inaccessible state, below their melting point, affecting physical and chemical properties of this system in the stable liquid phase. The nonlinear dielectric effect (NDE) was measured in the mixture of nitrobenzene with cyclododecane. The mixture has been found to show an apparent critical point which lies below the melting point, manifested as anomalous NDE behavior in the vicinity of the critical concentrations in the stable liquid phase. The melting temperature of this system was estimated using the differential scanning calorimetry method. For such a system, we also performed Monte Carlo (MC) simulations that aimed to analyze the kinds of phase transitions observed and the conditions of their occurrence in Lennard-Jones mixture. The enthalpy, configurational energy, and radial distribution function have been estimated by the MC simulation method in the N-P-T system. Immiscibility conditions according to the approach by Schoen and Hoheisel [Mol. Phys. 57, 65 (1986)] are also discussed.

The formation of lamella microphases in symmetric neutral-ionic block copolymers has been investigated by constant volume--constant temperature (NVT) molecular-dynamics computer simulations using a generic coarse-grain model. Computations of counterion diffusion, pressure tensor, and the anisotropy of the structure factor are used to characterize the order-disorder transition (ODT). There is strong counterion condensation on the ionic blocks at temperatures well above the ODT; this creates a slight imbalance in the volume composition of the two blocks and results in a perforated lamella structure in the microphase. Below the ODT counterion diffusion is decoupled from the chain motions but is strongly anisotropic due to the microphase morphology. The high counterion diffusional mobility is discussed in terms of the relatively low value of the glass transition for the ionic blocks.

On the basis of experimental batch-cell data, increasing short-chain branch density is found to reduce the cloud-point pressure of poly(ethylene-1-butene) solutions in propane, by as much as a factor of 3. This trend is captured by a SAFT approximation via an effective. segment energy that depends on the branch density. Increasing branch density is found to decrease the effective segment energy and, hence, to make it closer to that of propane, which is consistent with the enhanced miscibility of branchy poly(ethylene-1-butenes) in propane