刚柔相嵌液晶高分子的赝二级相变温度

讨论了刚柔相嵌液晶高分子的向列相－各向同性相转变与其分子结构的关系，给出了该一级相变的赝二级相变温度Ｔ与这类液晶高分子的液晶基元和间隔基的长度，柔顺性（相关长度）以及它们之间的相互作用的关系的解析表示式，分析了液晶基元与间隔基连接处的表观弯曲（接口效应）对Ｔ的影响，文中的结论与实验相符。     

刚柔相嵌液晶高分子的赝二级相变温度

讨论了刚柔相嵌液晶高分子的向列相一各向同性相转变与其分子结构的关系．给出了该一级相变的赝二级相变温度Ｔ＊与这类液晶高分子的液晶基元和间隔基的长度、柔顺性（相关长度）以及它们之间的相互作用的关系的解析表示式．分析了液晶基元与间隔基连接处的表观弯曲（接口效应）对Ｔ＊的影响．文中的结论与实验相符．     

Theoretical analysis of polydispersity in the nematic phase of self-assembled semiflexible chains

In recent simulations of semiflexible equilibrium polymers [X. Lu and J. T. Kindt, J. Chem. Phys. 120, 10328 (2004)] a roughly biexponential distribution of chain lengths was observed in the nematic phase. In this study, we show that a theory representing the nematic phase as an equilibrium mixture of randomly oriented chains below a critical length Lc and chains above Lc obeying a Gaussian orientational distribution reproduces this distribution qualitatively. The agreement between predicted and simulated phase boundaries is improved, with a narrower isotropic-nematic coexistence region, compared with a monoexponential chain distribution. We find, furthermore, that the critical length Lc scales as the inverse of monomer concentration, irrespective of the bond strength of the chains, but that at the phase boundary, the fraction of monomers found in disordered chains peaks at a certain bond strength.     

Role of chain stiffness on the conformation of single polyelectrolytes in salt solutions

Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a coarse-grained model, using Langevin dynamics simulations. The chain size, studied by the radius of gyration, shows three different variational behaviors with salt concentration, depending on the chain stiffness. According to the size variations, polyelectrolytes of fixed chain length are classified into three categories: (1) flexible chain, for which the variation shows a curve similar to a tilted L, (2) semiflexible chain, whose curve resembles U, and (3) rigid chain, for which the curve is a straight line. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. In a low salt region, a flexible polyelectrolyte extends more significantly than a semiflexible chain, in reference of the size of their uncharged counterparts, and in a high salt region, regardless of chain stiffness, a chain attains a dimension comparable to that of its neutral polymer. The chain stiffness influences both the local and the global chain structures. A flexible chain exhibits a zigzagged local structure in the presence of salt ions, and the condensed structure is a disordered, random globule. A semiflexible chain is locally smooth, and the condensed structure is orderly packed, taking a form such as hairpin or toroid. Moreover, the chain stiffness can also affect the nature of the coil-globule transition. The transition occurred in a discrete manner for semiflexible chain, whereas it occurred in a continuous way for flexible chain. This discrete feature happened not only at low salt concentration when a semiflexible chain collapsed but also at high salt concentration when the collapsed chain is reexpanded. At the end, the effects of chain stiffness and salt concentration on the conformation of single polyelectrolytes are summarized in a schematic state diagram.     

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined.     

Thermotropic homopolyesters. IV. Study of fiber formation

We report a melt spinning and viscosity study of two semiflexible homopolyesters containing both rigid and flexible segments in the repeating unit. Single filaments of the polyesters formed from 4,4′-diacetoxybiphenyl and azelaic acid (PB7) and sebacic acid (PB8), and from 4′-hydroxyphenyl-4-hydroxycinnamate and azelaic acid (C7), were spun at temperatures between 205 and 255°C. The temperature dependence of the Newtonian melt viscosity of PB7 and C7 was investigated, and a range of molecular weights was studied for PB7. The spinning parameters, fiber characteristics, and viscosity-temperature behavior are related to the type of mesophase formed. The mechanical properties of fibers spun from both the nematic and smectic phases of these semiflexible chain polymers were poor. Increasing the polymer molecular weight or extrusion rate only afforded a modest improvement in fiber properties. Most polymers could not be spun at temperatures corresponding to the existence of the single mesophase. Hence the low viscosity typical of the nematic mesophase is not necessarily an advantage in fiber formation from the melt. It appears from these results that this type of polyester does not possess adequate chain extension to develop ultrahigh-modulus properties. The director, which describes the local orientation of molecules within the mesophase, may undergo more frequent variations than is the case for rigid chain polyesters. Mechanisms relevant to flexible polymers may contribute to the development of orientation for this class of nematogenic melts.     

Internal orientations in externally deformed nematic polymer liquid crystals

The system of linear polymer liquid crystal (PLC) macromolecules, each modeled by semiflexible chain of alternate connected flexible and stiff rodlike sequences, is externally deformed. As a result, two orientation phases for hard rods are generated. One of them is nematic N+ with orientation parameter s>0; this has the place in monomer liquid crystal (MLC) systems and in PLCs. The nematic N- phase with s>0 appears in deformed PLCs only. This causes the fact that orientation of PLC chains, as a whole, is generated also by the system deformation. A discussion of that effect is the main goal of this article. The change of orientation is also discussed dependent on changes of the system temperature and parameters of the chain structure, such as the liquid crystal component concentration, contour lengths of stiff and flexible parts, and internal interactions parameters. Average shape of PLC chain and the shape anisotropy are calculated and discussed.     

Ejection dynamics of semiflexible polymers out of a nanochannel

Using theoretical analysis and three-dimensional Langevin dynamics simulations, we investigate the influence of chain rigidity on the ejection dynamics of polymers from a nanochannel. We find that there exist two distinct dynamical regimes divided by a critical chain length for both flexible and semiflexible chains. At the short chain regime, semiflexible chains eject faster than flexible chains of the same chain length due to the longer occupying length. In contrast, at the long chain regime, semiflexible chains eject slower than flexible ones as the effective entropic driving force decreases. Based on these results, we propose that the nanochannels could be used to separate flexible and semiflexible chains effectively.     

Viscoelastic properties of an isolated polymer chain with arbitrary flexibility,chain length and hydrodynamic interactions from 4‐dimensional Dirac propagator

Kholodenko's theory of semiflexible polymer chains, the conformation and properties of which are obtained from the Dirac propagator, shows applicability to dilute solutions of semiflexible polymers of arbitrary persistence and contour lengths by calculating the static scattering function and the squared end‐to‐end distance of the polymer chain. In the present work, the theory is extended and applied to obtain the intrinsic viscosity with consideration of hydrodynamic interactions. The intrinsic viscosity formula is derived as function of chain length and persistence length. The hydrodynamic interactions are also taken into account following the Kirkwood and Riseman scheme. From this calculation, we obtain the general expression for the intrinsic viscosity and diffusion coefficients covering the whole range of chain flexibilities without confusion with the excluded volume effects. Calculated limiting values of hydrodynamical observables are in complete agreement with those known for random coils and rigid rods.     

Statistical mechanics of worm-like polymers from a new generating function

We present a mathematical approach to the worm-like chain model of semiflexible polymers. Our method is built on a novel generating function from which all the properties of the model can be derived. Moreover, this approach satisfies the local inextensibility constraint exactly. In this paper, we focus on the lowest order contribution to the generating function and derive explicit analytical expressions for the characteristic function, polymer propagator, single chain structure factor, and mean square end-to-end distance. These analytical expressions are valid for polymers with any degree of stiffness and contour length. We find that our calculations are able to capture the fully flexible and infinitely stiff limits of the aforementioned quantities exactly while providing a smooth and approximate crossover behavior for intermediate values of the stiffness of the polymer backbone. In addition, our results are in very good quantitative agreement with the exact and approximate results of five other treatments of semiflexible polymers.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Thermodynamics of nematic phases formed from semiflexible chain polymers

In co[poly(ethylene terephthalate)-p-oxybenzoate] containing 30 mole % oxybenzoate units, the ethylene terephthate units crystallize. The copolymer melts in the temperature range 180–210°C to form a nematic phase which, at a higher temperature, transforms to an isotropic liquid. The latent heat of the first transition is 5 cal/g, and the thermodynamic melting temperature, 247°C, is essentially that expected for a random copolymer of this composition. The nematic → isotropic transition occurs at 244°C, with an enthalpy change of 3.2 cal/g (10% of the heat of fusion of poly(ethylene terephthalate)). We conclude that semiflexible polymers form a nematic phase which is rather highly disordered. The model of the nematic phase treated by Flory is modified to increase its entropy through incorporation of chain bends (which must be correlated in position and direction with those in neighboring molecules). This increases the chain extension, as measured by the fraction (1–f) of collinear chain bonds, required to form the nematic phase. For binary polymer-solvent systems, an appropriate scaling of f values leaves the phase diagram as predicted by Flory's treatment essentially unchanged.     

Statics and dynamics of polymer-wrapped colloids

We study the complex between a colloidal particle and a semiflexible polymer chain that "wraps" around it. Via molecular dynamics simulation we investigate statistical and dynamical properties of this system. First we establish the dependence of wrapped chain length on absorption energy and chain persistence length and obtain the distribution of wrapped-sphere positions. Then we study the length and position distributions of thermally excited loop defects. Finally we consider the repositioning dynamics of the colloid, focusing on the case where the chain stays wrapped onto the complex. Specifically we determine the mean square displacement of the central monomer of the wrapped chain and the resulting diffusion coefficient of the chain as a function of its persistence length, absorption energy, chain length, and size of the sphere. We argue that both statics and dynamics of these complexes can be mainly understood by energetic arguments, whereas entropic contributions from the chain configurations play only a minor role.     

Synthesis and characterization of a semiflexible liquid crystalline polyester with a broad nematic region

In this paper, we report on the synthesis and detailed characterization of a new semiflexible nematic liquid crystalline polyester which could serve as a 'model' polyester for a variety of physical and physico-chemical investigations. The polymer is a nematic liquid over a wide temperature range-from the glass transition temperature at ∼95°C to the isotropic transition at ∼240°C. We expect this polyester to be particularly useful for studying the effect of flow on the orientation of liquid crystalline polymers, as well as the production and removal of disclinations.     

Molecular orientation in liquid fibers of nematic polymers

The degree of macroscopic orientation of molten fibrous samples of nematic semiflexible polymers has been investigated by x-ray diffraction. Melting of highly oriented fibers is followed by a partial loss of macroscopic orientation but does not produce collapse of the fiber. The residual orientational order remains unaltered for a considerable time. The degree of orientational order depends on the temperature and undergoes odd-even fluctuations according to the parity of the number of carbon atoms contained in the flexible part of the monomer unit. Extrapolation of the order parameter to the isotropization temperature leads to a value of about 0.63 for even-type polymers and to about 0.47 for odd-type polymers. An intermediate value is found for a copolymer containing equal amounts of even and odd monomer units along the polymer chain.     

Consequences of the 'jacketed' effect on mesomorphic and orientational properties of 'side-on fixed' liquid crystalline polymers

The mesomorphic properties have been studied as a function of the degree of polymerization for certain 'side-on fixed' polyacrylates. A peculiar evolution of the clearing temperature, T_IN, as well as of the glass transition temperatures, T_g, revealed that beyond a certain backbone length, T_IN and T_g decrease as the main chain length increases. The nematic 'jacketed' structure of these polymers induces a more or less high anisotropy of the polymer backbone conformation in the nematic phase and this can counterbalance the usual effect of an increase in the degree of polymerization on the thermodynamical properties of these systems. This evolution allows us to explain the unusual diamagnetic anisotropy anomaly observed as a function of temperature for this type of polymer.     

Polymer escape from a metastable Kramers potential: path integral hyperdynamics study

We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers' radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymers, the crossing rate (R) monotonically decreases with chain contour length (L), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with L but becomes nearly constant for large L. For a fixed L, the crossing rate becomes maximum at an intermediate bending stiffness. For the self-avoiding chain, the rate is a nonmonotonic function of L, first decreasing with L, and then, above a certain length, increasing with L. These findings can be instrumental for efficient separation of biopolymers.     

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.