Microphase separation in a melt of graft copolymers formed by blocks with different grafting densities

The weak-segregation phase behavior of a monodisperse melt of a binary graft copolymer the macromolecules of which consist of two blocks with different densities of grafting of side chains is investigated. The length of the side chains in each block is assumed to be the same. Analysis of the structure factor of the system indicates the possibility of formation of two-scale structures in the melt. The realized scales differ significantly from each other and correspond to a phase separation between the blocks and between the monomeric units that form the repeating fragment of the graft copolymer. Classification diagrams are constructed, which describe the scale of the structures formed in the melt at different values of the parameters of the chemical structure of the macromolecules.     

Microphase separation in polydisperse miktoarm star copolymers

A two or more chemically different homopolymers attached to a single junction point form a macromolecule of miktoarm star copolymer. The model of such copolymer composed of an arbitrary number of types of homopolymer arms is considered. The lengths distributions of arms are assumed to be arbitrary, provided that average length of an each arm is long enough. The algorithm is suggested to find the contributions into the Landau free energy of this copolymer melt which are necessary to obtain a phase diagram in weak segregation regime. Using this algorithm the contributions are found up to the fourth order. The phase diagrams have been constructed for the simple model of AB₂ copolymer melt whose macromolecules consist of polydisperse A-block and two monodisperse B-blocks.     

A novel Monte Carlo scheme for the rapid equilibration of atomistic model polymer systems of precisely defined molecular architecture

Two novel connectivity-altering atomistic Monte Carlo moves are presented for the fast equilibration of condensed phases of long-chain systems with a variety of chain architectures. With the new moves, isotropic or oriented melts of linear or long-chain branched polymers, dense brushes of terminally grafted macromolecules, and cyclic peptides can be simulated. Results concerning the structural, conformational, and volumetric properties of linear, monodisperse polyethylene melts, simulated with a new united-atom molecular model, are in excellent agreement with experimental data.     

Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C₁₀₀₀H₂₀₀₂ polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory.     

On the self-organization of linear macromolecules

The new unified context for crystallization of linear macromolecules from the melt, established by recent work, is expounded. The morphology of spherulites shows that they form because of a short-range force operative at the branch points of dominant lamellae that causes them to diverge at noncrystallographic angles of about 20°. Work on monodisperse n-alkanes has confirmed the identification of this short-range force with the pressure from dynamic cilia during growth. Accordingly, spherulites, like chain folding, are a direct consequence of molecular length. It is suggested that the tendency to form coarse spherulites even for extended-chain growth at lower temperatures may result from the increasing difference between the lengths of nucleus and molecule. Crystallization on linear nuclei has been used to maximize the concentration of segregants at the growth front and to demonstrate cellulation in undoped polymers for the first time. The behavior of branched polyethylenes differs from the uniform growth of the linear polymer in coarsening and developing protuberances at the growth front, all the while slowing continuously toward an asymptotic steady state; differences of detail may be useful in distinguishing polymers of different catalytic origin and branch content. Spherulitie growth is also nonlinear for these polymers, but is always faster than for rows. When there is sufficient segregation, spherulites themselves cellulate, increasingly so for higher branch content. Cellulation is thus an uncommon and secondary process may be superposed on regular spherulitie growth beyond a certain distance. Cell dimensions do not scale with the diffusion length; in so doing, the phenomenon displays new physics.     

Bethe-Peierls approximation for linear monodisperse polymers re-examined

Bethe-Peierls approximation, as it applies to the thermodynamics of polymer melts, is reviewed. We compare the computed configurational entropy of monodisperse linear polymer melt with Monte Carlo data available in the literature. An estimation of the configurational contribution to the total liquid’s C _p is presented. We also discuss the relation between the Kauzmann paradox and polymer semiflexibility.     

Theoretical consideration of the phase behavior of polydisperse block copolymers

Qualitatively new types of the phase behavior of a binary polydisperse multiblock copolymer melt are revealed. For the first time, the amplitudes and periods of its mesophases are calculated.     

Flory theorem for structurally asymmetric mixtures

The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization (DP) of the surrounding linear chains, N(B), but also by the DP of the brush's side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N(2) < N (B) < N (A)/N, where N (A) is the degree of polymerization of the brush backbone. Experiment and theory demonstrated good agreement.     

Nuclear magnetic relaxation without spin diffusion in polymers at interfaces

We consider theoretically the possibility of solid state NMR experiments with frozen linear polymer chains at interfaces. Three different cases are studied, namely, when the macromolecules are grafted on the surface, when they are adsorbed, and when they are very strongly adsorbed from a melt that is subsequently washed by a good solvent. The latter case is somewhat intermediate between the two former ones. For each case, we consider the relaxation when paramagnetic centers are located on the surface. We show that the shape of the relaxation curves depends critically on the monomer concentration profile, and exhibits characteristic power-law variations.     

On the rotational diffusion of rod-like macromolecules in lyotropic-mesomorphic phases

The rotational diffusion of rod-like macromolecules, idealized as monodisperse rods, in concentrated solution is considered. The Doi-Edwards model is modified to explain the experimentally observed increase of the rotational relaxation time with increasing concentration in the lyotropic-nematic phase of rigid rod-like molecules in solution. Our approach consists in (i) reconsidering the original Doi-Edwards model to eliminate unphysical behaviour of the rotational relaxation time at the limit of perfect order, and (ii) including concentration effects on the translational diffusivity of rods in the Doi-Edwards model. Predictions of the corrected model are compared with steady flow viscosity data for poly(n-alkylisocyanates). In the lyotropic-nematic phase a very good qualitative agreement between the theory and experiment is observed. Additionally, the model applied to a highly concentrated isotropic phase explains in a natural way the viscosity behaviour as the concentration is increased towards the critical value for formation of the lyotropic-nematic phase.     

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using lattice-based Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.     

Reptation and diffusive modes of motion of linear macromolecules

It is shown that the model of underlying stochastic motion of a macromolecule leads to two modes of motion: reptative and isotropically diffusive. There is a length of a macromolecule M* ≈ 10M _e , where M _e is “the macro-molecule length between adjacent entanglements,” above which macromolecules of a melt can be regarded as obstacles to motion of each other, and the macromolecules reptate. The transition to the reptation mode of motion is determined by both topological restrictions and local anisotropy of motion. The investigation confirm that the reptation motion determines the M ⁻² molecular-weight dependence of the self-diffusion coefficient of macromolecules in melts. The text was submitted by the author in English.     

Isotropic-to-nematic transition in melt of polydisperse semi-flexible homopolymers

The isotropic-to-nematic phase transition in a melt of semi-flexible homopolymers with length polydispersity have been considered within the Landau–de Gennes approach. The number of monomer units in chain is assumed to be a random variable distributed by the Schulz–Zimm distribution; the stiffness of macromolecules has been taken into account within discrete worm-like chain model. It was found that increase of polydispersity yields the increase of the temperature of the isotropic–nematic transition.     

Size and average density spectra of macromolecules obtained from hydrodynamic data

It is proposed to normalize the Mark-Kuhn-Houwink-Sakurada type of equation relating the hydrodynamic characteristics, such as intrinsic viscosity, velocity sedimentation coefficient and translational diffusion coefficient of linear macromolecules to their molecular masses for the values of linear density M_L and the statistical segment length A. When the set of data covering virtually all known experimental information is normalized for M_L, it is presented as a size spectrum of linear polymer molecules. Further normalization for the A value reduces all data to two regions: namely the region exhibiting volume interactions and that showing hydrodynamic draining. For chains without intachain excluded volume effects these results may be reproduced using the Yamakawa-Fujii theory of wormlike cylinders. Data analyzed here cover a range of contour lengths of linear chains varying by three orders of magnitude, with the range of statistical segment lengths varying approximately 500 times. The plot of the dependence of [η]M on M represents the spectrum of average specific volumes occupied by linear and branched macromolecules. Dendrimers and globular proteins for which the volume occupied by the molecule in solution is directly proportional to M have the lowest specific volume. The homologous series of macromolecules in these plots are arranged following their fractal dimensionality.     

Theory of microphase separation on side-chain liquid-crystalline polymers with flexible spacers

We model a melt of monodisperse side-chain liquid-crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded-volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free-energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases or phases with modulated wave vector but without nematic ordering. Such microphases are the result of the competition between the incompatibility among the blocks and the connectivity constraints imposed by the spacer and the backbone. Also the effects of the polymerization degree and structural conformation of the monomeric units on the phase behavior of the side-chain liquid-crystalline polymers are studied.     

Structural features of melts in the In-Bi system

A testing device for the resistivity of high-temperature melt was adopted to measure the resistivity of In-Bi system melts at different temperatures. The resistivity of In_xBi_100−x(x=0-100) melt is in linear relationship with temperature, which is within the temperature measuring range. The resistivity of melt lowers with the increase of the In content. Based on Nordheim law and combined with the experimental resistivity of In-Bi melts, we verified the existence of InBi atom clusters and estimated the mole fraction of the InBi atom clusters in the melt, and the estimated value shows fine consistency with the result in literature [1]. The study reveals that the structural feature of In-Bi melts can be briefly divided into two intervals: in the interval of 0-50 at% In, the structural feature of the melt is that InBi atom clusters distribute in matrices, which have similar properties of Bi; in the interval of 50 at%-100 at% In, the structural feature of the melt is that InBi atom clusters distribute in matrices, which have similar properties of In. The content of InBi atom clusters in In₅₀Bi₅₀ melts reaches a higher value when the temperature is cooled down to a point, which is 152 K above the melting point. At the same time, the melts have an obvious fluctuation of concentration, which leads to that the resistivity of the melts deviates from the linear relationship at high temperature.     

Controlling Necking in Extrusion Film Casting Using Polymer Nanocomposites

The research described was concerned with the effect of layered-silicate-based organically modified nanoclay fillers on controlling the extent of necking in a polymer melt extrusion film casting (EFC) process. We show that a linear polythylene resin (such as a linear low-density polyethylene—LLDPE) filled with a very low percentage of well-dispersed (or intercalated) nanoclay displays an enhanced resistance to the necking phenomenon. In general, melt-compounded nanoclay-filled LLDPE resin formulations displayed a higher final film width (less necking), thus a lower final film thickness (greater draw down for the same draw ratio), and cooled down faster when compared to the base LLDPE resin. Incorporation of nanoclay filler in the mainly linear chain LLDPE resin led to significant modification of the melt rheological properties that, in turn, affected the melt processability of these formulations. Primarily, the intercalated nanoclay-filled LLDPE formulations displayed the presence of strain-hardening in unaxial extensional rheology. Additionally, the presence of well-dispersed nanoclay in the LLDPE resin led to a display of prominent extrudate swell indicating the presence of melt elasticity in such formulations. The presence of melt elasticity, as shown by shear rheology and strain-hardening, observed by uniaxial extensional rheology, contributed to the LLDPE nanoclay formulations displaying an enhanced resistance to necking for these films. It can be concluded that linear chain polymers susceptible to necking in an EFC process can be made more resistant to such necking by using nanoclay fillers at very low levels of loading.     

AFM, SEM and GIXRD studies of thin films of red polycarbazolyldiacetylenes

In this paper we report the results of a morphological and structural investigation on film properties of a soluble polydiacetylene, the poly[1,6-bis(3,6-dihexadecyl-N-carbazolyl)-2,4-hexadiyne] (polyDCHD-HS). The red films of this polymer, prepared by standard spin-coating techniques, revealed absence of linear dichroism and birefringence in contrast with the ordered mesophases detected by powder X-ray studies. In order to interpret the optical behavior of this polymer, we performed AFM and SEM studies of polyDCHD-HS films spun on hydrophylic and hydrophobic glass substrates. We found the presence of surfaces organized in rod-like particles, more regularly oriented on the hydrophylic substrate. GIXRD studies, carried out on films sufficiently thick to allow the observation of the diffraction pattern, reveled the presence of a lamellar structure with a spacing of 3.22 nm. The low intensity of the diffraction peaks and the isotropic linear optical properties of the films show that the lamellar mesophases are not extended over large areas. These findings were compared with the data obtained from AFM and SEM studies on films of two other polydiacetylenes, the poly[1-(3,6-dihexadexyl-N-carbazolyl)-6-(N-carbazolyl)-2,4-hexadyine] (polya-DCHD) and the poly[1,6-bis(3,6-dipalmitoyl-N-carbazolyl)-2,4-hexadyine] (polyDPCHD), spun on hydrophylic glass substrate. The results confirmed the presence of nodular morphologies which seem to be a general characteristic of this class of materials. The particles organization appears instead related to the chemical nature of the substituents on the carbazolyl rings.