Free‐energy model of asymmetry in side‐chain liquid‐crystalline diblock copolymers

Side‐chain liquid‐crystalline‐b‐amorphous copolymers combine the thermotropic ordering of liquid crystals (LCs) with the physics of block copolymer phase segregation. In our earlier experiments, we observed that block copolymer order–order and order–disorder transitions could be induced by LC transitions. Here we report the development of a free‐energy model to understand the interplay between LC ordering and block copolymer morphology in an incompressible melt. The model considers the interaction between LC moieties, the stretching of amorphous chains from curved interfaces, interfacial surface contributions, and elastic deformation of the nematic phase. The LC block is modeled with Wang and Warner's theory, in which nematogens interact through mean‐field potentials, and the LC backbone is modeled as a wormlike chain. Free energy is estimated for various morphologies: homogeneous, lamellar, cylinder micelle, and spherical micelle. Phase diagrams were constructed by iteration over temperature and composition ranges. The resulting composition diagrams are highly asymmetric, and a variety of first‐order transitions are predicted to occur at the LC clearing temperature. Qualitatively, nematic deformation energies destabilize curved morphologies, especially when the LC block is in the center of the block copolymer micelle. The thermodynamics of diblocks with laterally attached, side‐on mesogens are also explored. Discussion focuses on how well the model captures experimental phenomena and how the predicted phase boundaries are affected by changes in polymer architecture. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2671–2691, 2001     

Theoretical simulation of thermally induced phase separation in a main‐chain liquid‐crystalline polymer solution

Phase diagrams of main‐chain liquid‐crystalline polymer (MCLCP) solutions have been calculated self‐consistently on the basis of a simple addition of the Flory–Huggins free energy for isotropic mixing, the Maier–Saupe free energy for nematic ordering, and the Flory free energy for chain rigidity of the MCLCP backbone. The calculated phase diagram is an upper critical solution type overlapping with the nematic–isotropic transition. The phase diagram consists of liquid–liquid, liquid–nematic, and pure nematic regions. Subsequently, the dynamics of thermally induced phase separation and morphology development have been investigated by the incorporation of the combined free energy density into the coupled time‐dependent Ginzburg–Landau (model C) equations, which involve conserved compositional and nonconserved orientational order parameters. The numerical calculations reveal a variety of the morphological patterns arising from the competition between liquid–liquid phase separation and nematic ordering of the liquid‐crystalline polymer. Of particular interest is the observation of an inflection in the growth dynamic curve, which may be attributed to the nematic ordering of the MCLCP component, which leads to the breakdown of the interconnected domains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 913–926, 2003     

Characterization of annealed isotactic polypropylene in the solid state by 2D time‐domain 1H NMR

Two‐dimensional time‐domain ¹H NMR was used to investigate annealed isotactic polypropylene in the solid phase. The spin–lattice relaxation in the laboratory frame and in the rotating frame were correlated with the shape of the free induction decay to identify and characterize relaxation components over the temperature range −120 to 120 °C. Several phase transitions were observed, and three distinct solid phases, with different chain mobilities, were detected. Two of these phases were identified as regions with different mobilities within the crystalline phase. The third phase was characterized by a high degree of isotropy in molecular motion. This phase, identified as the amorphous phase, appeared as the polymer was heated above a low‐temperature (−45 °C) phase transition. All transitions observed at higher temperatures occurred exclusively in this phase. About one‐third of the polymer chains reside between crystalline lamellae, whereas the majority form amorphous regions outside fibrils of multilamellar structure. Furthermore, the glass‐to‐rubber transition, occurring above −15 °C, consists of three stages. During the first stage, between −15 °C and 15 °C, regions with an increased segment mobility (labeled intermediate phase) appear gradually within the amorphous phase. At 15 °C, the intermediate phase consists of ∼10% of the polymer units, or one‐third of the polymer units constituting the amorphous phase. Between 15 °C and 25 °C, the intermediate phase increases rapidly to 18%. This is associated with the appearance of semiliquid and liquid regions, likely within the intermediate phase. Polymer chain segments (and possibly entire chains) involved in the liquidlike phases exhibit heterogeneous molecular motion with a correlation frequency higher than 10⁶ Hz. These two stages of glass‐to‐rubber transition occur within amorphous regions outside multilamellar structures. The third stage of the glass transition, appearing above 70 °C, is associated with the upper glass transition and occurs within the interlamellar amorphous phase. Finally, on a timescale of 100 ms or less, spin diffusion does not couple the amorphous regions outside fibrils with crystalline and amorphous regions within multilamellar fibrils. However, on a timescale of hundreds of milliseconds to seconds, all different regions within isotactic polypropylene are partially coupled. It is proposed that the relative magnitude of the crystalline magnetization, as observed in the T_1ρ experiment, is a good measure of polymer crystallinity. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2487–2506, 2000     

Thermodynamic Parameters of Temperature‐Induced Phase Transition for Brushes onto Nanoparticles: Hydrophilic versus Hydrophobic End‐Groups Functionalization

Quantification of the stimuli‐responsive phase transition in polymers is topical and important for the understanding and development of novel stimuli‐responsive materials. The temperature‐induced phase transition of poly(N‐isopropylacrylamide) (PNIPAm) with one thiol end group depends on the confinement—free polymer or polymer brush—on the molecular weight and on the nature of the second end. This paper describes the synthesis of heterotelechelic PNIPAm of different molecular weights with a thiol end group—that specifically binds to gold nanorods and a hydrophilic NIPAm end group by reversible addition‐fragmentation chain‐transfer polymerization. Proton high‐resolution magic angle sample spinning NMR spectra are used as an indicator of the polymer chain conformations. The characteristics of phase transition given by the transition temperature, entropy, and width of transition are obtained by a two‐state model. The dependence of thermodynamic parameters on molecular weight is compared for hydrophilic and hydrophobic end functional‐free polymers and brushes.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 2. The Regime of Strong Adsorption

The transition from incomplete to complete wetting of the solid surface by a semidilute polymer solution coexisting at equilibrium with the very-dilute polymer solution was studied using the Canh–de Gennes theory under the conditions corresponding to the tricritical state of semidilute solution and strong adsorption of the chain units on a substrate. It was established that the wetting transition can occur as the first- or second-order phase transition or as the transition of tricritical wetting depending on the repulsion energy of segments that are on the substrate surface. Near the temperatures of these transitions, the character of the variations in the differences of surface concentrations that are established at the boundaries of the substrate with semidilute and dilute polymer solutions, as well as in the differences of interfacial tensions and the cosine of contact angle were determined. It was shown that the temperature of each of these phase transitions varies in proportion to the surface potential of the substrate and does not depend on the polymer molecular mass. The observed behavior differs essentially from that established near the critical point of a polymer–solvent system.     

Giant deuteron migration during the isosymmetric phase transition in deuterated 3,5-pyridinedicarboxylic acid

Deuterated 3,5‐pyridinedicarboxylic acid exhibits reversible temperature‐induced deuteron migration of a magnitude unprecedented in this class of compounds. We used a combination of variable‐temperature powder and single‐crystal neutron diffraction and density functional theory (DFT)‐based computational methods to elucidate the origin of this remarkable behaviour. Single‐crystal neutron diffraction shows that between 15 and 300 K, the deuteron moves by 0.32(1) Å and the structure changes from a low‐temperature N? D???O form to a high‐temperature N???D? O form. Variable‐temperature powder neutron‐diffraction data, which was fitted by using parametric Rietveld refinement, show that this deuteron migration is due to an isosymmetric, first‐order phase transition that occurs by growth of the daughter phase in the parent‐phase matrix. Similar phase transitions are observed in two selectively deuterated forms of the material. DFT calculations demonstrate the role of phonons and show that vibrational free‐energy stabilisation, which plays a key role in the observed structural phase transitions, is more pronounced in the fully deuterated material and proportional to the mass of the molecule, that is, the level of deuteration. This is consistent with our experimental work, for which distinct crystallographic phase transitions were clearly observed for the three deuterated systems, but not for the fully protonated material.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 3. The Regime of Weak Adsorption

The transition from incomplete to complete wetting occurring near the critical temperature of a two-phase polymer–solvent system at the substrate surface that weakly adsorbs macromolecules was studied using the Cahn–de Gennes model. It was shown that, depending on the force of attraction between the segments and the wall, the energy of interaction between the segments in the surface layer, as well as on the length of chain, the wetting transition can occur as the first- or second-order phase transitions, or as the tricritical wetting transition. Near the temperatures of these transitions, we determined the character of the variations in the difference of the surface concentrations that are established at the boundaries between the substrate and semidilute or dilute polymer solutions, as well as in the difference between the interfacial tensions and of the cosine of contact angles. It was shown that the temperature of each transition varies inversely to the square root of the molecular mass of polymer, and its deviation from the critical temperature is determined by the type of transition. At the first-order transitions at the SP-regime, the deviation is proportional to the energy of attraction between the chain units and the wall and is independent of polymer chain length, whereas at the critical wetting it is proportional to the squared energy of attraction between the segments and the substrate and increases with polymer chain length according to the N ^1/2law. At the considered asymptotic regime, which corresponds to the substrates that weakly attract polymer chain units, the type of the wetting transition can be regulated by varying only the length of polymer chain at the same energy characteristics of a substrate. The possibility of observing the critical wetting transitions using the solutions of high-molecular-mass compounds is discussed.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Theory of the cooperative transition between two ordered conformations of poly(L-proline). II. Molecular theory in the absence of solvent.

Phenomenological theories of the transition between helical form I (cis peptide bond) and helical form II (trans peptide bond) of poly(-L-proline), which is a typical order in equilibrium order transition, have been presented by Schwarz (using the parameters s, sigma, beta', and beta' in a 2 X 2 matrix formulation) and by the present authors (using the parameters s, sigma betaC, and betaN in a 4 X 4 matrix formulation). A molecular theory of the same transition has been formulated to account for the phenomenological parameters. The statistical weights of regular helical sequences with and without junctions between the two forms were computed from empirical potential energy functions. Two puckering conformations of the pyrrolidine ring, i.e., with the Cgamma atom down and up, were allowed, and the free energy was computed for chains with four types of puckering, viz., regular down, regular up, random A, and random B, in the latter two of which the up and down puckerings were randomly distributed. The random A and random B chains have higher energy than those with regular down or up puckering, in both forms I and II. From both an energetical and a free energetical point of view, form I is more stable than form II under vacuum at room temperature. The dependence of the relative stabilities of form I and form II under vacuum on chain length was examined from both an energy and free energy point of view. The four parameters, s, sigma, beta', and beta', which describe the transitions in Schwarz's theory, were calculated from the statistical weights of various types of sequences. It was found that the thermally induced transition between form I and II under vacuum occurs with the pyrrolidine rings remaining in the down conformation. The calculated values of s suggest that form I is more stable than form II in the regular down chain, while form II is more stable than form I in the regular up chain under vacuum at room temperature. The calculated values of sigma for regular down and regular up pyrrolidine ring puckering are in good agreement with experimental observations, whereas those for random A and random B puckering are much smaller than the experimental values. A theory for the effect of solvent on the parameters s, sigma, beta', and beta' (at constant temperature) is developed, and the computations involving solvent effects are described in the next paper.     

半刚性高分子链塌缩相变的蒙特卡洛模拟

本文主要研究半刚性高分子链在不同温度下的形态变化,特别是在低温下的塌缩相变。我们对半刚性高分子链在三维简立方点阵上进行蒙特卡洛数值模拟。计算模型中考虑了链段间的排斥势、近邻间的吸引势和局域刚性势。链的刚性程度由刚性势与吸引势的比值确定。计算证明在温度逐步下降时,柔性链的形态由高温下的无规线团逐渐收缩为低温下的无规紧缩线团;但刚性程度较高的链则首先扩展,然后再收缩为具有一定有序度的紧缩态。同时我们也证明半刚性高分子链的塌缩相变是与柔性链的形态转变相同,它们的热力学行为都符合二级相变的特征。     

Tailoring the liquid crystalline property via controlling the generation of dendronized polymers containing azobenzene mesogen

The first‐ and second‐generation dendronized polymers containing azobenzene mesogen were designed and successfully synthesized via free radical polymerization. The chemical structures of the monomers were confirmed by elemental analysis, ¹H NMR, and ¹³C NMR. The molecular characterizations of the polymers were performed with ¹H NMR and gel permeation chromatography. The phase structures and transition behaviors were studied using differential scanning calorimetry, polarized light microscopy, and small‐angle X‐ray scatter experiments. The experiment results revealed that the first‐generation dendronized polymer exhibited liquid crystalline behavior of the conventional side‐chain liquid crystalline polymer with azobenzene mesogen, that is, the polymer exhibited smectic phase structure at lower temperature and nematic phase structure at higher temperature. However, the second‐generation dendronized polymers exhibited more versatile intriguing liquid crystalline structures, namely smectic phase structure at lower temperature and columnar nematic phase structure at higher temperature, and moreover, the phase structure still remained before the decomposition temperature. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1149–1159, 2010     

Cooperative movements associated with the Curie transition in P(VDF-TrFE) copolymers

The thermal and dielectric behavior of β-PVDF and a series of random P(VDF-TrFE) copolymers with various chemical composition has been investigated in the temperature range of their Curie transition. Dielectric relaxations and phase transitions were characterized by means of differential scanning calorimetry and thermostimulated current spectroscopy. The thermal hysteresis associated with the first order character of the Curie transition decreases as the TrFE content increases, and vanishes for P(VDF-TrFE) 50/50. For the latter, the distribution in lamellar thickness and the dependence of the conformational order in the ferroelectric phase upon thermal history yield an intricate thermal behavior. For the overall investigated polymers, the TSC mode associated with the ferro/para-electric transition is described by a distribution in relaxation times obeying a compensation law. This behavior has been interpreted based on cooperative movements in the ferroelectric phase in the vicinity of the transition temperature. These molecular movements are precursors of the transition. It is valid for β-PVDF, as well as for P(VDF-TrFE) copolymers which for the compensation temperature corresponds to the transition temperature. So, the Curie temperature of PVDF has been found at 170°C, i.e. the melting point. ©1995 John Wiley & Sons, Inc.     

Thermodynamics of activated phase transitions of 8CB: DSC and MC calorimetry

The present paper reports the heating rate effect on the phase transitions of a pure liquid crystal octylcyanobiphenyl (8CB) with use of Differential Scanning Calorimetry (DSC) and Modulation Calorimetry (MC) techniques. The DSC runs were taken at various temperature ramp rates from 20 to 0.5 K/min for heating and cooling scans. Well-defined endothermic/exothermic peaks were found at the melting/crystallization, smectic-A to nematic (SmA-N), and nematic to isotropic (N-I) transitions on heating/cooling scans, respectively. All transitions shift in temperature significantly with different ramp rates. The temperature shift of C(p) peaks between heating and cooling scans indicates the order of the transitions. In addition, all transitions follow an Arrhenius behavior. The activation energy of a transition increases as the total energy involved in the transition decreases. The respective enthalpy and entropy change of each transition provides information on the Gibbs free energy. The significance of the results is discussed in terms of the order of transitions. A comparative analysis of MC and DSC techniques highlights the significance of the two techniques. MC is a practicable tool for observing the phase dynamics whereas DSC is a good tool for studying the rate kinematics of the transitions.     

Monte carlo study of star-branched polymers on the tetrahedral lattice. II. Statistical thermodynamics of single macromolecules

The thermodynamical properties of the star-branched polymers on the tetrahedral lattice are studied taking into account nearest-neighbor interactions. The excess free energy and energy and heat capacities are computed for wide ranges of chain lengths, reduced potential ?/kT, and number of branches. A significant influence of the degree of branching on long-range interactions in the polymer random coil is observed. The possibilities of phase transitions in both linear and branched systems are discussed on the basis of the Monte Carlo data.     

Thermodynamics of polymeric fluids – effect of volume on the configurational entropy of chain molecules

Various conformation‐dependent properties of chain molecules have been successfully treated within the rotational isomeric state approximation. The conformation entropy is one of such properties which can be readily defined by the partition function, the sum of all possible configurations of the chain. Flexible polymers often exhibit crystallization and in some cases liquid‐crystallization as well. In these first‐order transitions, changes in the spatial arrangement of polymer chains are considered to be a major factor involved. In order to explicitly determine the conformational contribution to the melting entropy, the latent entropy observed under the isobaric condition must be corrected for the volume change. The entropy separation involves a hypothetical assumption that the volume of the isotropic fluid may be compressed to that of the solid state without affecting the configurational part of the entropy of molecules. Finally thermodynamic significance of the conformation entropy in these transitions is emphasized on the basis of the critical studies of the entropy‐volume relation of chain molecules in the liquid state.     

侧链型丙烯酸酯共聚物相变的正电子湮没谱研究

利用正电子湮没技术对侧链型热致高分子液晶丙烯酸酯共聚物进行了变温相变研究．除实验标识出样品的相变温度点外，根据试样中自由体积随温度的变化关系，对高分子液晶材料内部立链、侧链以及介晶基元的相变行为特点进行了探讨，并就与小分子液晶变化特点的一些不同做了解释．     

Continuous self-avoiding walk with application to the description of polymer chains

We develop the continuous self-avoiding walk (CSAW) methodology for investigating temperature dependent thermodynamic properties of finite polymer chains without imposing a lattice. This leads to a new concept: the free energy theta temperature, T(theta)(F), at which the free energy is proportional to chain length. Above T(theta)(F), the polymer chain-solvent mixture leads to a single phase, whereas below T(theta)(F) the polymer solvent system has a positive surface tension with a tendency to phase separation to form a globular phase. For finite chains this coil-globule transition lies above the geometric theta temperature at which the distribution describes a Gaussian coil. CSAW provides the basis for a new approach to predict globular properties of real polymers.     

Branchings of the fully symmetrical solution of the molecular field equation in liquid crystals

A general scheme has been constructed to study the branching of the fully symmetrical solution of the molecular field equation in the case when the molecular coordinates parametrise a certain group Q. A relationship is established between these branchings and the phase transitions. Branchings corresponding to the formation of orientationally ordered and spatially modulated structures are studied explicitly. Special attention is paid to phase transitions from the isotropic liquid to nematic and cholesteric phases. Characteristics of these transitions (for example Curie temperature, order of transition, and symmetry of the phase formed) have been related to the intermolecular potential energy and the pair correlation function.