含有烷基侧链的杂环芴基共聚物的光电性能

通过对9,9-二辛基芴(DOF)与4,7-二噻吩-2,1,3-萘并噻二唑(DNT)共聚物(PFDNT)和9,9-二辛基芴(DOF)与4,7-二(3-己基噻吩)-2,1,3-萘并噻二唑(HDNT)共聚物(PFHDNT)的光电特性进行比较研究,发现烷基侧链上引入杂环窄带隙单体能有效提高芴基共聚物的分子量和光荧光的量子产率。共聚物PFHDNT的光致发光和电致发光峰相对于共聚物PFDNT发生了蓝移,可能是由于长烷基侧链的空间位阻减小了π^*有效共轭长度导致其发射峰发生蓝移。此外共聚物PFHDNT器件的电荧光量子效率并未由于引入烷基侧链而降低。     

A Gibbs free energy formula for protein folding derived from quantum statistics

The fundamental law for protein folding is the thermodynamic principle. The amino acid sequence of a protein determines its native structure and the native structure has the minimum Gibbs free energy. Lacking of a Gibbs free energy formula is the reason that all ab initio protein structure prediction only empirical and various empirical energy surfaces or landscapes are introduced to fill the gap. We make a quantum mechanics derivation of the Gibbs free energy formula G(X) using quantum statistics for a single conformation X. For simplicity, only monomeric self folding globular proteins are considered.     

Thermodynamic behaviour of solid–liquid grain boundary grooves

ABSTRACT

Grain boundary grooves (GBGs) are local features that develop along polycrystalline solid–liquid interfaces. Interest in GBGs lies in their ability to form interface defects during crystallization that promote, in fact, dominate, morphological instability and affect microstructure formation in cast alloys. Recently, we reported on unobserved subtle aspects of the thermodynamic behaviour of GBG microstructures by combining sharp-interface field theory with diffuse-interface phase-field simulations. A surprising feature revealed about steady-state GBGs is that despite their stationarity they nonetheless support persistent capillary-mediated energy fluxes with divergences that continuously cool their interfaces and increase local curvatures. We now analyse the energetic behaviour of GBGs as ‘open’ thermodynamic systems, and report further details of their formation free energy that show how geometric constraints and capillary-mediated thermodynamic fields self-interact and influence the steady-state shapes of GBGs.     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Size effect on thermodynamic properties of free nanocrystals

We demonstrate that the discrete character of the vibrational spectrum of a small crystal accounts for size dependence of its thermodynamic properties and melting temperature. Using a self-consistent statistical method [Phys. Rev. B 66, 054302 (2002)] we derive the Gibbs free energy of free nanocrystalline plates and calculate the thermodynamic parameters as functions of plate thickness for Cu.     

Thermodynamic limit for classical systems with Coulomb interactions in a constant external field

We introduce a new method for studying the thermodynamic limit for systems of particles with Coulomb interactions. The method is based on calculating the potential energy of the Coulomb interactions from the electric or magnetic fields in the system rather than from the energy of the individual particle — particle interactions. We are able to include the effects of a constant external field being imposed at the boundary of the system. The difficulties associated with Coulomb potentials being not even weakly tempered are overcome by imposing the boundary condition that at the boundary of the region containing the particles, the electric or magnetic field has normal component equal to that of the applied field. We prove that the thermodynamic free energy density exists and is independent of the sequence of regions used to define the limit. We introduce sequences of regions all of the same shape and show that for these sequences of regions the thermodynamic free energy density is independent of shape. Finally, we prove that the thermodynamic free energy is a convex function of the density of particles and of the applied field.     

Mean-field theory for polymer adsorption on curved surfaces

We discuss the influence of polymer adsorption on the curvature energy of an interface. Following an article by Clement and Joanny (J. Phys. II 7, 973 (1997)), a mean-field theory is used to calculate the surface tension, rigidity constants and spontaneous curvature associated with both reversible and irreversible polymer adsorption. In the case of irreversible polymer adsorption it is assumed that the amount of adsorbed polymer remains constant upon curving the interface. Unfortunately, constraining the amount of polymer by adding a Lagrange multiplier affects the thermodynamic state of the (free) polymer far away from the interface. Clement and Joanny solve this problem by removing the polymers in the bulk. We allow for the presence of free polymers, but to achieve this we have to apply a local external field to keep the adsorbed amount fixed. The results of the two approaches are compared and a physical interpretation is given. Received 25 July 2001 and Received in final form 5 December 2001     

Structures and energetics of carbon bridged C 60 clusters

The structures and energetics of carbon bridged C₆₀ clusters (C ₆₀ ) _n C_m have been studied by simulated annealing technique within the tight-binding molecular-dynamics. The “sp² addition” ball-and-chain dimers exhibit odd-even alternations over the number of chain atoms, with the dimers containing even chain atoms more stable against dissociation than their immediate neighbors containing odd chain atoms. In addition to the usual “sp² addition” dimers, a pentagon-linked C₁₂₁ isomer and a hexagon-linked C₁₂₂ isomer are also found to be stable. Based on our tight-binding calculations, trimers and larger clusters can be simply regarded as being made up of independent or weakly interacting dimers, if the C-C₆₀ joints on a single cage are not too close to each other. Large C₆₀ clusters connected by chains each containing only one or two carbon atoms have similar stability to that of constituent dimers, indicating the possibility to form stable C₆₀-carbon polymers. Received 17 January 2001 and Received in final form 26 February 2001     

Modelling nucleation from solution with the string method in the osmotic ensemble

ABSTRACT

Direct molecular simulation of nucleation from solution is a challenging task, requiring a combination of ‘rare events’ techniques and methods to control the chemical potential. Rare event methods usually keep the total number of molecules fixed, resulting in artificial free energy profiles due to the depletion of solute from the solution phase. In order to address this issue, we present a new approach that uses the string method in collective variables in the osmotic ensemble to obtain minimum free energy pathways for nucleation at constant supersaturation. Our method does not require using an explicit reservoir of solute molecules, or making additional assumptions about the activity coefficients in the solution. We apply the new method to the crystallisation of sulfamerazine from acetonitrile and methanol solutions, and compare the resulting potential of mean force profiles to those obtained using analytical corrections previously employed in the literature.     

The Great Myths of Polymer Melt Rheology,Part I: Comparison of Experiment and Current Theory

Abstract

Star polymers consisting of poly(?‐caprolactone), (PCL), grafted onto third generation dendrimer, which had hyperbranched and dendron cores, were studied by polarized light microscopy together with reference linear PCL. The degree of polymerization of the PCL arms in the star polymers ranged between 14 and 81. The star polymers exhibited a greater tendency than the linear polymers to form spherulites. It is suggested that the preference of the star polymers for forming spherulites is due to the presence of amorphous material—dendritic cores and PCL cilia—between crystal lamellae that generates the necessary pressure to force the lamellae to diverge at lamellar branch points. The linear growth rate data followed a single crystallization regime. The fold surface free energy was higher for the star polymers than for their linear analogs. It is proposed that the presence of the large and rigid dendritic cores on the fold surfaces of the star polymer crystals increases the fold surface energy.     

Perturbative Analysis of Disordered Ising Models Close to Criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion is compatible with the infinite differentiability of the free energy but does not imply its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder. MSC2000. Primary 82B44, 60K35.     

Free energy reaction root mapping of alanine tripeptide in water

ABSTRACT

We have investigated the free energy surface of alanine tripeptide in water. To elucidate the secondary structure of the amide chain, information on the free energy surface with explicit water at room temperature, and the multidimensional reaction coordinates are required. We studied the minimum free energy paths (MFEPs) connecting reactants, transition structures (TS) and products. To solve this problem, we used the free energy reaction root mapping (FERRMap) method. This is an automated search method to find MFEPs by using umbrella integration and the scaled hypersphere search method. We calculated the four-dimensional free energy surface for alanine tripeptide in water using FERRMap and found 61 equilibrium structures (EQ) connected by 133 TS points. After elucidating the MFEP network, we analysed the structures of the EQ points and the MFEPs connecting beta-sheet structures and beta-turn structures or left-handed helix structures.     

Polyimides Containing Azobenzene Side Units: Properties and Correlation with Conformational Parameters

Two series of aromatic polyimides differing by the bridging group between imide rings, polymers a, b, and c, having C?O linkages and polymers d, e, and f, having C(CF₃)₂ groups, have been obtained by polycondensation reaction of aromatic dianhydrides with aromatic diamines containing substituted azobenzene groups. These polymers with good solubility in polar amidic solvents, were able to form transparent flexible films and showed high thermal stability. Conformational parameters of the polymers were calculated by the Monte Carlo method with allowance for hindered rotation. Several physical properties of these polymers, such as solubility, glass transition temperature (T_g), and initial decomposition temperature (T_onset) were measured and discussed in relation to the volume factor of the macromolecular chains. The volume factor is equal to ratio of the Van der Waals volume of the pendent group to the Van der Waals volume of the repeating unit of the main chain.     

The effect of hydrogen-fluorine defects on the conformational energy of polytrifluoroethylene chains

Conformational energy calculations were employed to determine the effect of hydrogen-fluorine defects on the conformation of the polytrifluoroethylene chain. It was determined that the 3₁ helix was energetically favored for all but the highly syndiotactic polymers, which favored the all-trans conformation. The incorporation of head-to-head linkages into the polymer chain increased the Conformational energy of the 3₁ helix while the Conformational energy of the all-trans form decreased. The energies of these two conformations did not equalize until the head-to-head concentration reached 20 to 30%, depending on the tacticity of the polymer. The trans, gauche, trans, gauche' conformation was also determined to be energetically favorable for the syndiotactic polymer, but both tacticity defects and head-to-head linkages caused a rapid increase in the Conformational energy. This was, therefore, concluded to be unlikely structure when chemical defects are incorporated into the polymer chain.     

Stability of dense hydrophobic-polar copolymer globules: Regular,random and designed sequences

Stability of dense globular structures formed by amphiphilic copolymers consisting of hydrophobic (insoluble) units and a small fraction of single polar (soluble) monomer units is considered in the mean-field approximation for different types of unit distributions along the chain. Polar (P) units are located in a relatively thin surface layer due to their strong repulsion from hydrophobic (H) monomer units. We compared globules formed by different copolymer sequences with the same gross numbers of P- and H-units: regular HP-sequences (P-units separated by equal H-blocks), random copolymers (uncorrelated positions of P-units, i.e. Flory distribution of H-block lengths), proteinlike (PL) sequences (designed sequences involving both long H-blocks dominating by total mass, and short blocks dominating by number). We showed that PL-globules are more stable (lower free energy) and are characterized by a higher temperature of the coil-to-globule transition when compared with the other sequences mentioned above. We also considered HP-H-copolymers consisting of one long and many short hydrophobic blocks; we showed that it is these sequences that yield the dense globules corresponding to the lowest free energy.Received: 3 July 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Modelling in relation to cation ordering

We review the methodology of using computer models to obtain quantitative information about cation ordering. Empirical interatomic potentials or ab initio electronic structure calculations are used to generate the energies for many configurations containing disordered arrangements of cations, and the parameters in model Hamiltonians can be determined from these energies. Monte Carlo simulations are then used to generate ensemble averages as functions of temperature or chemical composition. Analysis of the Monte Carlo ensembles directly yields the temperature dependence of long-range and short-range order, and thermodynamic quantities such as energy and heat capacity. Use of thermodynamic integration allows for the calculation of entropy and free energy. The methods are illustrated by examples showing long-range order/disorder phase transitions (feldspars), short-range order in solid solutions (pyrope-grossular), and non-convergent ordering (magnesium aluminate spinel); where comparisons with experimental data are possible, the model calculations are seen to give results that are reasonably accurate. The example in which ab initio electronic structure calculations are used show that it is now possible to extract accurate thermodynamic data for ordering processes using models that require no prior experimental data.     

Growth kinetics of polymer crystals in bulk

Temperature-dependent measurements of spherulite growth rates carried out for i-polystyrene, poly(ε -caprolactone) and linear polyethylene show that the controlling activation barrier diverges at a temperature which is 14K, 22K and 12K, respectively, below the equilibrium melting points. We discuss the existence of such a “zero growth temperature” T _zg in the framework of a recently introduced thermodynamic multiphase scheme and identify T _zg with the temperature of a (hidden) transition between the melt and a mesomorphic phase which mediates the crystal growth. The rate-determining step in our model of crystal growth is the attachment of chain sequences from the melt onto the lateral face of a mesomorphic layer at the growth front. The necessary straightening of the sequence prior to an attachment is the cause of the activation barrier. A theory based on this view describes correctly the observations. With a knowledge of T _zg it is possible to fully establish the nanophase diagram describing the stability ranges of crystalline and mesomorphic layers in a melt. An evaluation of data from small-angle X-ray scattering, calorimetry and optical growth rate measurements yields heats of transition and surface free energies of crystals and mesophase layers, as well as the activation barrier per monomer associated with the chain stretching. According to the theory, the temperature dependence of the crystallization rate is determined by both the activation energy per monomer and the surface free energy of the preceding mesomorphic layer. Data indicate that the easiness of crystallization in polyethylene is first of all due to a particularly low surface free energy of the mesomorphic layer.     

Conformation-dependent sequence design: evolutionary approach

A new modification of evolutionary approach to sequence design of copolymers has been proposed. A model of step-by-step evolution of a two-letter (HP) copolymer sequence has been studied by means of a coarse-grained Monte Carlo algorithm. The conditions for accepting a change in the primary sequence depend on the spatial conformation of HP-copolymer chain. This leads to a coupling between sequence and conformation and to formation of protein-like conformations and primary sequences (for some values of parameters of the model) independently of initial sequence and/or conformation. Simple theory describing these computer simulation observations is developed.Received: 3 September 2003, Published online: 2 March 2004PACS: 87.15.Aa Theory and modeling; computer simulation - 87.15.Cc Folding and sequence analysis - 82.35.Jk Copolymers, phase transitions, structure - 82.35.Lr Physical properties of polymers     

Ethylene-co-vinyl alcohol blends

The presence of the aliphatic hydroxyl group in poly(ethylene-co-vinyl alcohol) (EVOH) suggests that these copolymers have the potential for forming miscible blends with a variety of polymers containing complementary functional groups such as esters, (meth)acrylates, acetoxys, pyridines, etc. There is a paucity of examples of miscible EVOH blends in the literature, however. Hydrogen bonding, which is very complicated in EVOH copolymers and involves an extraordinary variety of nter- and intramolecular species, plays an important role in the phase behavior of EVOH blends. We have applied an association model to this problem and arrived at the following important conclusion. Miscibie EVOH blends with polymers containing ester or acetoxy groups do exist, but they have lower critical solution temperatures below normal processing temperatures (< 200 °C). This is primarily a consequence of the fact that EVOH copolymers are strongly self-associated, while the interassociation of the hydroxyl groups of EVOH with the carbonyl groups of the complementary polymers is comparatively weak.     

Dielectric and anelastic relaxation of crystals containing point defects

A theory is developed which describes the linear, reversible, time-dependent response of a crystal containing point defects to stress or electric fields, respectively known as anelastic and dielectric relaxation. Such relaxation occurs because of the redistribution of the defects among sites which are initially equivalent, but which becomes inequivalent in the presence of the external field. The macroscopic behaviour of such a crystal is found to be describable in terms of the symmetry which can be assigned to the defect. This defect symmetry determines whether or not the crystal will undergo dielectric or anelastic relaxation and, if relaxation can occur, which specific coefficients of elastic compliance or electric susceptibility show the relaxation effect. The latter information, called the ‘selection rules’ tells, in effect, which combination of stress or electric field components is capable of redistributing the defects. Tables are given for these selection rules for all possible defect symmetries in each of the 32 crystal classes. It is also shown that a hitherto unobserved phenomenon of piezoelectric relaxation may occur; the selection rules for this effect are also given.

Aside from its symmetry, the defect can be described as an electric dipole in terms of a suitable dipole moment vector μ, and as an ‘elastic dipole’ in terms of a tensor λ. It is shown that the defect symmetry determines the number of independent components of μ and λ. Finally, a thermodynamic theory is developed which permits calculation of the relaxation strengths for those compliance, susceptibility, and piezoelectric coefficients which undergo relaxation, in terms of the independent components of μ and λ. Applications of the theory to specific cases are then reviewed.