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A model of the polymerization process during the formation of a pair of polymer brushes was designed and investigated. The obtained system consisted of two impenetrable parallel surfaces with the same number of chains grafted on both surfaces. Coarse-grained chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions were obtained by a ‘grafted from’ procedure. The structure of synthesized macromolecular systems was also studied. Monte Carlo simulations using the dynamic lattice liquid model were employed using dedicated parallel machine ARUZ in a large size and time scale. The parameters of the polymerization process were found to be crucial for the proper structure of the brush. It was found that for high grafting densities, chains were increasingly compressed, and there is surprisingly little interpenetration of chains from opposite surfaces. It was predicted and confirmed that in a polydisperse sample, the longer chains have unique configurations consisting of a stretched stem and a coiled crown.

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.

The dynamics of spatial hierarchical processes displays fascinating images of the evolution of attraction basins of towns. Assuming in the present paper a random character of such complex processes, gravitational modeling is employed to depict changes in the nature of fuzzy boundaries between attraction basins in a hexagonal world, i.e. the geographical pattern central in the renowned and influential Christaller–Lösch central place theory in geography. The paper presents various interesting stylized maps of such stochastic processes. Our findings demonstrate that the collective behavior of actors in geographic space shows a white noise pattern that mirrors a fuzzy gravitation towards large population concentrations. These results support the validity of the conventional central place theory.

This review addresses the impact of different nanoadditives on the glass transition temperature (Tg) of polyvinyl chloride (PVC), which is a widely used industrial polymer. The relatively high Tg limits its temperature-dependent applications. The objective of the review is to present the state-of-the-art knowledge on the influence of nanofillers of various origins and dimensions on the Tg of the PVC. The Tg variations induced by added nanofillers can be probed mostly by such experimental techniques as thermomechanical analysis (TMA), dynamic mechanical analysis (DMA), differential scanning calorimetry (DSC), and dielectric thermal analysis (DETA). The increase in Tg is commonly associated with the use of mineral and carbonaceous nanofillers. In this case, a rise in the concentration of nanoadditives leads to an increase in the Tg due to a restraint of the PVC macromolecular chain’s mobility. The lowering of Tg may be attributed to the well-known plasticizing effect, which is a consequence of the incorporation of oligomeric silsesquioxanes to the polymeric matrix. It has been well established that the variation in the Tg value depends also on the chemical modification of nanofillers and their incorporation into the PVC matrix. This review may be an inspiration for further investigation of nanofillers’ effect on the PVC glass transition temperature.

In the presence of a midblock-selective solvent, triblock copolymers not only self-organize but also form a molecular network. Thermoplastic elastomer gels constitute examples of such materials and serve as sealants and adhesives, as well as ballistic, microfluidic, and electroactive media. We perform Monte Carlo and dissipative particle dynamics simulations to investigate the phase behavior and network characteristics of these materials. Of particular interest is the existence of a truncated octahedral morphology that resembles the atomic arrangement of various inorganic species. Both simulation approaches quantify the midblock bridges responsible for network development and thus provide a detailed molecular picture of these composition-tunable soft materials.

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...

Systems kept out of equilibrium in stationary states by an external source of energy store an energy $\Delta U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $\Delta U$ for two model systems: ideal gas and Lennard-Jones fluid. $\Delta U$ depends not only on the total energy flux, $J_U$, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where: the energy flux per unit volume is (i) constant; (ii) proportional to the local temperature (iii) proportional to the local density. We show that $\Delta U /J_U=\tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $\tau$ is the characteristic time scale of energy outflow from the system immediately after the shutdown of energy flux. We prove that $\tau$ is minimized in stable states of the Rayleigh-Benard cell.

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.

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long “flights”. Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for “reprogramming” the Lévy walks into either diffusive or ballistic movements.

We investigate triblock-homopolymer blends of types A1BA2/A and A1BA2/B, using a lattice Monte Carlo method. While the simulated triblock chains are compositionally symmetric in terms of the A-to-B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt and the A1BA2 solutions in selective solvent the phase behavior is relatively well known, including existence and stability of the interstitial micelles which were discovered in previous Monte Carlo simulations. In this paper we study the stability of the interstitial micelles as a function of triblock volume fraction in selective homopolymers of either type A or type B, using two significantly different homopolymer chain lengths. We found that adding selective homopolymer of type A shifts the stability of the interstitial micelles into significantly higher temperatures. We also obtained, via self-assembly, intriguing new nanostructures which can be identified as ordered truncated octahedra. Finally, we established that the phase behavior of the triblock-homopolymer blends depends relatively weakly on the chain length of the added homopolymer.

Using two complementary numerical methods, the lattice Monte Carlo simulations with parallel tempering and self-consistent field theory, we investigate the distribution of A1, B, and A2 segments in the lamellar nanostructure of A1BA2 triblock copolymer melts. While the lattice Monte Carlo method is in principle exact, it is limited by a variety of factors, such as finite size effects, long relaxation times required to reach the thermal equilibrium and geometry of the underlying lattice. It is also limited to chains consisting of relatively few segments. The self-consistent field theory, on the other hand, is free of the above limitations, but it is a mean-field approach which does not take into account the thermal fluctuations. Therefore we confront the results obtained from the two above methods and draw conclusions concerning both the comparison of the two methods and the localization of the A1 segments in the B domain with increasing length of the A1 block. For Monte Carlo simulations we employ two types of chains, 2-32-30 and 1-16-15, and for the self-consistent field theory we use the corresponding values of the thermodynamic incompatibility parameter, N.

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...

We present the results of Monte Carlo lattice simulations of a model symmetric diblock copolymer wherein a fraction of segments of one block, p, corresponds to ionic species, and the other block do...

We simulate selective $A1BA2\text{\ensuremath{-}}A$ and $A1BA2\text{\ensuremath{-}}B$ triblock solutions (that is, mixtures of the $A1BA2$ triblock with a solvent of either type $A$ or type $B$) using a lattice Monte Carlo method. Although the simulated triblock chains are compositionally symmetric in terms of the $A$ to $B$ volume ratio, the $A1$ block is significantly shorter than the $A2$ block. For the pure $A1BA2$ melt the phase behavior is relatively well known, including the existence and stability of the recently discovered interstitial micelles which were found at the very strong segregation limit. In this paper, we investigate the stability of the interstitial micelles as a function of triblock volume fraction in a selective solvent of either type $A$ or type $B$. The main finding of this paper is that adding a selective solvent of type $A$ shifts the stability of the interstitial micelles into significantly higher temperatures which may provide a pathway towards experimental studies of interstitial micelles in real triblock solutions. We also find that adding selective solvents to the $A1BA2$ melt gives rise to a variety of nonlamellar nanostructures for temperatures and compositions at which the interstitial micelles are stable.

Although most ABA triblock copolymers are molecularly symmetric (i.e., the terminal blocks possess the same mass), molecularly asymmetric A1BA2 triblock copolymers are of greater fundamental interest in that they can be used to explore the transition from diblock to triblock copolymer in systematic fashion. In this study, we use a lattice Monte Carlo method known as the cooperative motion algorithm to simulate molten ABA triblock copolymers possessing a short terminal block to explore the effect of molecular asymmetry on the copolymer order–disorder transition (ODT). Reduced ODT temperatures, discerned by simultaneously analyzing several features of the simulation results, are found to compare favorably with experimental data. Of particular interest here is the initial depression in the ODT temperature for A1BA2 copolymers possessing a relatively short terminal (A2) block. This signature feature is successfully captured by the simulations and is found to be strongly dependent on composition, but weakly dependent on copolymer chain length. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013

Using self-consistent eld theory in spherical unit cells of various dimensionality, D = 1, 2, 3, and 4, we calculate phase diagram of a diblock, A-b-B, copolymer melt in 4-dimensional space, d = 4. The phase diagram is parameterized by the chain composition, f , and incompatibility between A and B, quanti ed by the product χN . We predict 4 stable nanophases: layers, cylinders, 3D spherical cells, and 4D spherical cells. We also calculate order disorder and order order transition lines. In the strong segregation limit, that is for large χN , the order order transition compositions are determined by the strong segregation theory in its simplest form, for D = 1, 2, 3, and 4.

We simulate ABA triblock copolymer melts using a lattice Monte Carlo method, known as cooperative motion algorithm, probing various degrees of compositional asymmetry. Selected order-disorder transition lines are determined in terms of the segment incompatibility, quantified by product $ \chi$ N , and the triblock asymmetry parameters, $ \alpha$ and $ \beta$ . We correlate the results of the simulation with the self-consistent field theory and an experimental study of polyisoprene-polystyrene-polyisoprene triblock melt by Hamersky and coworkers. In particular, we confirm the mean-field prediction that for highly asymmetric triblocks the short A -block is localized in the middle of the B -domain due to an entropic advantage. This results in the middle block relaxation and is consistent with the experimental data indicating that as the relatively short A -blocks are grown into AB diblock, from the B -block side, the order-disorder transition temperature is considerably depressed.

Network characteristics in physical gels composed of solvated block copolymers varying in molecular design are examined here by dynamic rheology and computer simulations. In two triblock copolymer series, one with chain length (N) varied at constant copolymer composition (f) and the other with f varied at constant N, we discern the dependence of equilibrium network metrics on both N and f. Increasing the block number in a linear multiblock series at constant N and f escalates conformational complexity, which dominates network connectivity classified according to a midblock conformation index.

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.

Physical-chemical reasoning is used to demonstrate that the sizes of both prokaryotic and eukaryotic cells are such that they minimize the times needed for the macromolecules to migrate throughout the cells and interact/react with one another. This conclusion does not depend on a particular form of the crowded-medium diffusion model, as thus points toward a potential optimization principle of cellular organisms. In eukaryotes, size optimality renders the diffusive transport as efficient as active transport - in this way, the cells can conserve energetic resources that would otherwise be expended in active transport.

A lattice computer simulation of a symmetric A–B–A triblock copolymer melt is reported. This melt is quenched, in simulation, from an athermal state to 39 different temperatures using cooperative motion algorithm. Energy, specific heat, copolymer end-to-end distance, bridging fraction, lamellar spacing, concentration profiles, and microstructure visualizations are reported. The quenching simulation results are compared with those obtained by alternative thermal treatments, that is by slow heating and slow cooling. Quenches yield data consistent with theory and experiment, whereas slow cooling and slow heating results do not capture the expected behavior for the lamellar spacing and the bridging fraction. Finally, at very low temperatures, below the conventional order–disorder transition temperature, an additional ordering is recorded, from a conventional lamellar phase to a lamellar structure showing copolymer junction points condensed into a two-dimensional plane.

While $ABC$ triblock copolymers are known to form a plethora of dual-mode (i.e., order-on-order) nanostructures, bicomponent $ABA$ triblock copolymers normally self-assemble into single morphologies at thermodynamic incompatibility levels up to the strong-segregation regime. In this study, we employ on-lattice Monte Carlo simulations to examine the phase behavior of molecularly asymmetric ${A}_{1}B{A}_{2}$ copolymers possessing chemically identical endblocks differing significantly in length. In the limit of superstrong segregation, interstitial micelles composed of the minority ${A}_{2}$ endblock are observed to arrange into two-dimensional hexagonal arrays along the midplane of $B$-rich lamellae in compositionally symmetric $(50:50 A:B)$ copolymers. Simulations performed here establish the coupled molecular-asymmetry and incompatibility conditions under which such micelles form, as well as the temperature dependence of their aggregation number. Beyond an optimal length of the ${A}_{2}$ endblock, the propensity for interstitial micelles to develop decreases, and the likelihood for colocation of both endblocks in the ${A}_{1}$-rich lamellae increases. Interestingly, the strong-segregation theory of Semenov developed to explain the formation of free micelles by diblock copolymers accurately predicts the onset of interstitial micelles confined at nanoscale dimensions between parallel lamellae.

Self-assembly of symmetric A/S-B copolymer melt to gyroid nanostructure, partitioning space into interpenetrating nano-labyrinths (channels), in thin films, is investigated using a minimal lattice model with short-range interactions. This model is relevant to poly(styrenesulfonate)-b -polymethylbutylene melt consisting of three types of segments, A, B and S, corresponding to styrene, methylbutylene and styrenesulfonate, respectively. A single sequence of A, B, and S is used in simulations and the fraction of S segments is fixed at p = 0.647 which corresponds to experimental data. The film thickness, L z , is restricted to nine values (L z = 17 , 22, 26, 30, 34, 42, 51, 60, and 68 in units of the underlying lattice constant). The gyroid nanostructure is found to be stable if the film thickness is equal to or greater than the bulk period of the nanophase. The observed gyroid is referred to as swollen since the volume fraction of two continuous networks made of the B segments is anomalous with respect to that of conventional diblock copolymers. In contrast to bulk state, we do not directly observe the order-disorder transition to the gyroid nanophase for thin films. In this case, however, simulations indicate a direct order-disorder transition to a lamellar phase and the order-disorder transition temperature is higher than that in the bulk state, varying strongly with the film thickness.

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.

Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of $120 A$ and $120 B$ monomers, arranged in three distinct microarchitectures: $(10\ensuremath{-}10){}_{12}, (6\ensuremath{-}6){}_{20}$, and $(3\ensuremath{-}3){}_{40}$, collapse to globular states upon cooling, as expected. By varying both the reduced temperature ${T}^{*}$ and the compatibility between monomers $\ensuremath{\omega}$, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and $n$ clusters with $ng3$ (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the (${T}^{*},\ensuremath{\omega}$) space are mapped. The structure factor $S(k)$, for a selected microarchitecture and $\ensuremath{\omega}$, is calculated. Since $S(k)$ can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.

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.

A lattice simulation of a model diblock copolymer melt is presented. In a series of simulation experiments an 8-8 diblock melt is quenched from an athermal state to 47 lower temperatures. A set of simulation boxes, 30 x 32 x 30, 40 x 32 x 60, 50 x 32 x 30, and 60 x 32 x 30, is used in order to explore the size effects. Energy, specific heat, copolymer end-to-end distance, lamellar spacing, and the degree of interfacial ordering are reported. For all sizes considered, the low-temperature interfacial ordering is noticeable.

A set of computer simulations for three symmetric $A\ensuremath{-}B\ensuremath{-}A$ triblock copolymer microarchitectures at varying temperatures is reported. By using the cooperative motion algorithm we obtain energy, specific heat, end-to-end distance, and bridging fraction as a function of the reduced temperature. The order-disorder transition temperatures are determined, an outline of a symmetric $A\ensuremath{-}B\ensuremath{-}A$ triblock copolymer phase diagram is presented, and the visualization of different microstructures is given. A bicontinuous microstructure is reported at 67% fraction of A component.