Atomistic calculations on the high-temperature condis phase of poly(trans-1,4-butadiene) (PTBD)

The structure of the low-temperature phase of poly(trans-1,4-butadiene) was calculated by means of semiempirical atomistic potentials. Without using any symmetry assumptions there is good agreement with experimental data. In order to understand the high-temperature phase, packing energy calculations were performed with different chain conformations. There are a great number of possible packing modes. They show an approximately linear relation between defect volume and defect energy. The results of these calculations are taken as a basis for a thermodynamic treatment (cooperative pair theory) of the phase transition. The experimental transition enthalpy can only partially be explained by intermolecular interactions, and the defect energy of the various intramolecular equilibrium conformations is not sufficient to explain the difference. A refined treatment with a simultaneous inter-and intramolecular minimization of the energy reveals that the chains are not in their intramolecular equilibrium state. This results in an additional intramolecular defect energy which seems to lead to an understanding of the experimental transition data.     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Intramolecular phase separation of a copolymer chain with mobile primary structure

The phenomenon of intramolecular phase separation of a single copolymer chain with mobile primary structure (i.e., a polymer chain with reversibly adsorbable ligands) in dilute solution is investigated on the basis of a Flory-type interpolation theory of the coil-globule phase transition. It is shown that under certain critical conditions the stability of the homogeneous primary structure is violated and intramolecular phase separation takes place. Phase diagrams for the cases of rigid and flexible chains are calculated. The main characteristics of a polymer chain in the two-phase state (such as fraction of monomeric units, swelling coefficient and fraction of units with ligands for coexisting intramolecular phases) are investigated.     

Structure of flexible and semiflexible polyelectrolyte chains in confined spaces of slit micro/nanochannels

Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.     

Phase transitions of a single polyelectrolyte in a poor solvent with explicit counterions

Conformational properties of a single flexible polyelectrolyte chain in a poor solvent are studied using constant temperature molecular dynamics simulation. The effects of counterions are explicitly taken in to account. Structural properties of various phases and the transition between these phases are studied by tracking the values of asphericity, radius of gyration, fraction of condensed counterions, number of non-bonded neighbours, and Coulomb interaction energies. From our simulations, we find strong evidence for a first-order phase transition from extended to collapsed phase consistent with earlier theoretical predictions. We also identify a continuous phase transition associated with the condensation of counterions and estimate the critical exponents associated with the transition. Finally, we argue that previous suggestions of existence of an independent intermediate phase between extended and collapsed phases is only a finite size effect.     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

Cascade of coil-globule conformational transitions of single flexible polyelectrolyte molecules in poor solvent

We show that hydrophobic flexible polyelectrolyte molecules of poly(2-vinylpyridine) and poly(methacryloyloxyethyl dimethylbenzylammonium chloride) are trapped and frozen due to adsorption on the mica surface, and the observed AFM single molecule structures reflect the molecular conformation in solution. An increase of the ionic strength of the solution induces the cascade of abrupt conformational transitions due to the intrachain segregation from elongated coil to compact globule conformations through intermediate pearl necklace-globule conformations with different amounts of beads per chain. The length of the necklaces and the number of beads decrease, while the diameter of beads increases with the increase of ionic strength. Coexistence at the same time of extended coils, necklaces with different amounts of beads, and compact globules indicates the cascade of the first-order-type phase transitions.     

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.     

PSS/PDDA自组装膜形成过程中的临界浓度效应

Decher等提出的阴阳聚电解质层层组装膜技术(LbL),方便快捷,结构有序,其纳米级可控,可用于生物传感器、杂多酸多层膜修饰电极及天然多糖类功能膜等领域．LbL膜的厚度直接影响其性能,而膜厚度与紫外吸光度(A)成正比．故A是通常用于评价膜厚度的一种简便方法．紫外吸光度与聚电解质溶液浓度(cp)往往呈递增关系,随着溶液中cp的增大,单位面积上吸附聚电解质的量也增加。     

Theory of the orientational ordering for dimers with conformational flexibility

In the self-consistent field approximation a theory of the orientational ordering is developed for the melt of dimers containing two mesogenic fragments capable of conformational reorganization. Discrete conformations of the dimers (rotational isomers) are characterized by the values of valence angles. Both three-dimensional and two-dimensional melts are considered. It is shown that the presence of bent isomers in the melt reduces the temperature of the phase transition to the anisotropic phase. For a three-dimensional system with first-order phase transition to the ordered state, the jump of the order parameter at the transition point for dimers with conformational flexibility appears to be greater than for rigid dimers. For dimers with two isomers (a linear and a bent one) the order parameter and the statistical weight of the linear isomer at the transition point depend nonmonotonously on the statistical weight of this isomer in the isotropic phase. The effect of “supercooling” of the isotropic phase for linear conformations of flexible dimers is discussed.     

Phase transitions in the crystals of L- and DL-cysteine on cooling: intermolecular hydrogen bonds distortions and the side-chain motions of thiol-groups. 1. L-cysteine

The role of the distortion of the hydrogen bond network and of the motions of the -CH 2SH side chains in the phase transition in the orthorhombic L-cysteine ( (+)NH 3-CH(CH 2SH)-COO (-)) on cooling and the reverse transformation on heating is discussed. The extended character of the phase transition, which was recently discovered by adiabatic calorimetry [ J. Phys. Chem. B 2007, 111, 9186 ], and its very high sensitivity to the thermal prehistory of the sample could be interpreted based on the changes in the polarized Raman spectra measured for the single-crystals in several orientations in the temperature range 3-300 K and precise diffraction data on the changes in intramolecular conformations and intermolecular hydrogen bonding. In the low-temperature phase the SH...S hydrogen bonds dominate as compared to the weaker SH...O contacts, and at ambient temperature the situation is inverse. The transition from one phase to another goes via a series of states differing in conformations of the cysteine zwitterions and the intermolecular contacts of the thiol-group. Motions of different molecular fragments (NH 3 (+), CH 2, CH, SH) are activated at different temperatures. Structural strain on cooling involves several dynamic processes, such as a rigid rotation of the molecule in the lattice, a rigid rotation of the NH 3 group with respect to NH 3-CH bond, and the rotation of the thiol side chain resulting in the switching of S-H hydrogen bonding from one type to another. Different NH...O hydrogen bonds forming the framework in the L-cysteine crystal structure are distorted to a different extent, and this provokes the rotation of the -CH 2SH side chains within the cavities of this framework resulting in a change in the coordination from SH...O to SH...S at low temperatures. The results are interesting for understanding the polymorphism of molecular crystals and the factors determining their dynamics and structural instability, and also for biophysical chemistry, since the properties of the hydrogen bonded thiole-groups in biomolecules can be mimicked using L-cysteine in the crystalline state, variations in temperature and pressure serving as powerful tools, to modify the intramolecular conformations and the intermolecular hydrogen bonding.     

Conformational properties of rigid-chain amphiphilic macromolecules: The phase diagram

The coil-globule transition in rigid-chain amphiphilic macromolecules was studied by means of computer simulation, and the phase diagrams for such molecules in the solvent quality-persistence length coordinates were constructed. It was shown that the type of phase diagram depends to a substantial extent on the degree of polymerization of a macromolecule. Relatively short amphiphilic macromolecules in the poor-solvent region always form a spherical globule, with the transition to this globule involving one or two intermediate conformations. These are the disk globule if the Kuhn segment is relatively large and the string of spherical micelles or the disk globule in the case of relative flexible chains. The phase diagram of a long rodlike amphiphilic chain turned out to be even more complex. Namely, three characteristic regions were distinguished in the region of a poor solvent, depending on the chain rigidity: the region of a cylindrical globule without certain order in the main chain, the region of the cylindrical globule with blobs having the collagen ordering of the chain, and the region of coexistence of collagen-like and toroidal globules. In the intermediate transitional region, not only conformations of strings of spherical micelle beads but also the necklace conformations in which the polymer chain in each bead has collagen ordering can occur in this case.     

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.     

Diagram of State of Stiff Amphiphilic Macromolecules

Summary: We studied coil-globule transitions in stiff-chain amphiphilic macromolecules via computer modeling and constructed phase diagrams for such molecules in terms of solvent quality and persistence length. We showed that the shape of the phase diagram essentially depends on the macromolecule degree of polymerization. Relatively short amphiphilic molecules always form a spherical globule in a poor solvent, and the coil-globule transition includes one or two intermediate conformations, depending on the chain's stiffness. These are a disk-like globule in case of high enough Kuhn segment length, and a pearl necklace-like structure of spherical micelles and a disk-like globule in case of relatively flexible chains. The phase diagram of a long stiff amphiphilic chain was found to be more complex still. Thus three specific regions can be distinguished in the poor solvent region, depending on the chain stiffness. These correspond to a cylindrical globule without any specific backbone ordering, a cylindrical globule containing blobs with collagen-like ordering of the chain, and co-existence of collagen-like and toroidal globules. In the intermediate transition region in this case, apart from the pearl necklace-like conformations with spherical micelles, necklace conformations can be also observed where the polymeric chain has collagen-like ordering within each bead.     

Self-consistent molecular theory of polymers in melts and solutions

We propose a self-consistent molecular theory of conformational properties of flexible polymers in melts and solutions. The method employs the polymer reference interaction site model for the intermolecular correlations and the Green function technique for the intramolecular correlations. We demonstrate this method on n-alkane molecules in different environments: water, hexane, and in melt, corresponding to poor, good, and theta condition, respectively. The numerical results of the intramolecular correlation function, the radius of gyration, and the characteristic ratio of a polymer chain are indicative of conformational changes from one environment to another and are in agreement with other findings in the literature. Scaling laws for the chain size with respect to the number of monomers are discussed. We show results for the intra- and intermolecular correlation functions and the medium-induced potential. We also extract the Kuhn length and the characteristic ratio for the infinite chain limit for melts. The latter is compared to the experimental results and computer simulation. The conformational free energy per monomer in different solvents is calculated. Our treatment can be generalized readily to other polymer-solvent systems, for example, those containing branched copolymers and polar solvents.     

MOLECULAR FIELD THEORY FOR NEMATIC LIQUID CRYSTAL POLYMER COMPRISING FLEXIBLE SPACER

Basea on the new model and concept of mtramolecular orientational order parameter, a molecular field theory was built up for main chain liquid crystalline polymer (MC-LCPs) with flexible spacers. The theory takes account of orientational correlation among all mesogens in a polymer chain and the relationship between the intramolecular orientation and spatial orientation of the mesogens. The free energy, temperature and entropy of the nematic-isotropic transition were determined with the theory and compared with experiments in current work. It was found that many unique transition properties of the MC-LCPs comprising flexible spacer are correctly predicted by the theory and the agreement of the theory with the experiments is impressive.     

Transition between collapsed state phases and the critical swelling of a hydrogen bonding gel: poly(methacrylic acid-co-dimethyl acrylamide)

Transition between collapsed state phases and discontinuous volume phase transition for a hydrogen bonding gel, poly(methacrylic acid-co-dimethyl acrylamide), were observed by using both the volume measurements and fluorescence intensity of the pyranine fluoroprobe (8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt) bonded to the gel by means of electrostatic interactions. In the collapsed state, while there is no appreciable change in the volume of the gel, a considerable variation in the fluorescence intensity occurred around 30 degrees C signaling a second order phase transition between collapsed state phases, from relatively frozen to a fluctuating phase. Our analysis of the data around 30 degrees C indicates that the critical point of gel volume transition belongs to the so-called mean-field universality class, as predicted in Onuki [Phys. Rev. A 38, 2192 (1988)] and by Golubovic and Lubensky [Phys. Rev. Lett. 63, 1082 (1989)]. The relaxation time for the equilibrium swelling critically depends on the temperature and diverges near 60 degrees C, where both fluorescence intensity and the volume of the gel change drastically and indicate the discontinuous volume phase transition. The swelling kinetics of the critical gel during the discontinuous volume phase transition can be modeled best with the first term in the expansion of the Li-Tanaka equation for a long initial period of the swelling time.     

Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.     

Molecular order and thermodynamics of the solid-liquid transition in triglycerides via Raman spectroscopy

The conformational and thermodynamic behavior of five monoacid saturated triglycerides (TGs) before, during, and above the beta polymorph --> liquid phase transition was studied using Raman spectroscopy. The Raman ratio I[upsilon(s)(CH(2))]/I[upsilon(as)(CH(2))], used to identify intramolecular order about TG hydrocarbon chains, demonstrated that a single conformation, geometry and symmetry existed in liquid-state TGs. The Raman ratio I(1080)/I(1130), used to determine the intermolecular order/disorder about the hydrocarbon chains and relative trans/gauche content, remained constant for TGs in the crystalline state, but steadily increased as a function of temperature in the liquid state. Use of the van't Hoff relation and the spectroscopically-determined trans/gauche content indicated the presence of distinctive pre- and post-transition enthalpies/entropies indicating that the beta --> liquid phase transition is "soft", with possible intermediate conformations. The liquid-state ester carbonyl stretching region, which gave rise to a broad peak between 1780-1700 cm(-1), was decomposed into multiple components. It demonstrated solid-like character 2-3 degrees C above the TG beta-polymorph melting point, above which no further change in spectral character was observed. These results indicate that the solid-liquid transition in TGs is of the "soft" type with non-lamellar conformations likely present in the melt.