Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

Modified conformation and physical properties in conducting polymers due to varying conjugation and solvent interactions

Small angle X-ray scattering (SAXS) studies of poly2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) with varying conjugation, and polyethylene dioxythiophene complexed with polystyrene sulfonate (PEDOT-PSS) in different solvents have shown the importance of the role of pi-electron conjugation and solvent-chain interactions in controlling the chain conformation and assembly. In MEH-PPV, by increasing the extent of conjugation from 30 to 100%, the persistence length (l(p)) increases from 20 to 66 angstrom. Moreover, a pronounced second peak in the pair distribution function has been observed in the fully conjugated chain, at larger length scales. This feature indicates that the chain segments tend to self-assemble as the conjugation along the chain increases. In the case of PEDOT-PSS, the chains undergo solvent induced expansion and enhanced chain organization. The clusters formed by chains are better correlated in dimethyl sulfoxide (DMSO) solution than water, as observed in the scattered intensity profiles. The values of radius of gyration and the exponent (water: 2.6, DMSO: 2.31) of power-law decay, obtained from the unified scattering function (Beaucage) analysis, give evidence for chain expansion from compact (in water) to an extended coil in DMSO solutions, which is consistent with the Kratky plot analysis. The mechanism of this transition and the increase in dc conductivity of PEDOT-PSS in DMSO solution are discussed. The onset frequency for the increase in ac conduction, as well as its temperature dependence, probes the extent of the connectivity in the PEDOT-PSS system. The enhanced charge transport in PEDOT-PSS in DMSO is attributed to the extended chain conformation, as observed in the SAXS results.

Synthesis, characterization, and thermal degradation studies on group VIA derived weak-link polymers

Polymers containing group VIA derived weak links, viz. poly(styrene disulfide) (PSD), poly- (styrene tetrasulfide) (PST), and poly(styrene diselenide) (PSDSE), have been synthesized. The polymers PSD and PST were characterized by NMR, IR, UV, TGA, and fast atom bombardment m w spectrometric (FABMS) techniques. The presence of different configurational sequences in PSD and PST were identified by *3C NMR spectroscopy. PSDSE, being insoluble in common organic solvents, was characterized using solid-state lac NMR (CP-MAS) spectroscopy. Thermal degradation of polymers under direct pyrolysis-mass spectrometric (DP-MS) conditions revealed that all the polymers undergo degradation through the weaklink scission. A comparative study of the pyrolysis products of these polymers with that of poly(styrene peroxide) (PSP) revealed a smooth transformation down the group with no monomer (styrene or oxygen) formation in PSP to only styrene and selenium metal in PSDSE. This trend of group VIA is explained from the energetics of the C-X bond (X = 0, S, and Se) which also seems to be important in addition to the weak X-X bond cleavage. In PSP and PSD, the behavior is also explained from the energetics of the alkoxy and thiyl radicals. The unique exothermic degradation in PSP compared to endothermic degradation in PSD and PSDSE is explained from the nature of the producta of degradation.

Interfacial shear rheology of highly confined glassy polymers

We present results on interfacial shear rheology measurements on Langmuir monolayers of two different polymers, poly(vinyl acetate) and poly(methyl methacrylate) as a function of surface concentration and temperature. While for the high glass transition poly(methyl methacrylate) polymer we find a systematic transition from a viscous dominated regime to an elastic dominated regime as surface concentration is increased, monolayers of the low glass transition polymer, poly(vinyl acetate), remain viscous even at very high surface concentrations. We further interpret the results in terms of the soft glassy rheology model of Sollich et al. P. Sollich, F. C. Lequeux, P. Hebraud and M. E. Cates, Phys. Rev. Lett., 1997, 78, 2020-2023] and provide evidence of possible reduction in glass transition temperatures in both poly(methyl methacrylate) and poly(vinyl acetate) monolayers due to finite size effects.

Fluorescence and topological gap of conjugated phenylene polymers

We propose that strong fluorescence in conjugated polymers requires a dipole-allowed state to be the lowest singlet. Hückel theory for para-conjugated phenyl rings yields an extended, topologically one-dimensional ?-system with increased alternation, states localized on each ring, and charge-transfer excitations between them. Exact Pariser�Parr�Pople results and molecular spectra for oligomers support a topological contribution and a lowest dipole-allowed singlet in phenylene polymers.

Model Hamiltonians for nonlinear optical properties of conjugated polymers

Quantum cell models for delocalized electrons provide a unified approach to the large NLO responses of conjugated polymers and pi-pi* spectra of conjugated molecules. We discuss exact NLO coefficients of infinite chains with noninteracting pi-electrons and finite chains with molecular Coulomb interactions V(R) in order to compare exact and self-consistent-field results, to follow the evolution from molecular to polymeric responses, and to model vibronic contributions in third-harmonic-generation spectra. We relate polymer fluorescence to the alternation delta of transfer integrals t(1+/-delta) along the chain and discuss correlated excited states and energy thresholds of conjugated polymers.

Synthesis of epoxy-terminated polymers by radical polymerization using alpha-(t-butylperoxymethyl)styrene as chain transfer agent

Epoxy-terminated polystyrene has been synthesized by radical polymerization using alpha-(t-butylperoxymethyl) styrene (TPMS) as the chain transfer agent. The chain transfer constants were found to be 0.66 and 0.80 at 60 and 70 degrees C, respectively. The presence of epoxy end groups was confirmed by functional group modification of epoxide to aldehyde by treatment with BF3.Et(2)O. Thermal stability of TPMS was followed by differential scanning calorimetry and iodimetry. Thermal decomposition of TPMS in toluene follows first order kinetics with an activation energy of 23 kcal/mol. (C) 1996 John Wiley & Sons, Inc.

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Polymers containing disulfide, tetrasulfide, diselenide and ditelluride linkages in the main chain

The present review articulates the syntheses and properties of industrially important disulfide and tetrasulfide polymers. The diselenide and ditelluride polymers have also been reviewed, for the first time, so that a comprehensive view on the polymers containing group VIA elements can be obtained. The latter two polymers are gaining considerable current attention due to their semi-conducting properties. The emphasis has been made to sift through the developments in the last ten years or so to get the latest flavour in these rapidly developing polymers. We have also attempted to bring to the fore several contradicting results, like, for example, the crystallinity of ditelluride polymers, to clear the mist in such reports. We hope that this review will help those working in the field to assess the progress achieved in this area and that it may also provide useful orientation for those who wish to become involved.

Synthesis and characterization of photo-crosslinkable main-chain liquid-crystalline polymers containing bis(benzylidene)cycloalkanone units

A series of new photo-crosslinkable main-chain liquid-crystalline polymers containing bis(benzylidene)cycloalkanone units have been studied. These units in the polymers function as mesogens as well as photoactive centres. Polyesters with three different bis(4-hydroxybenzylidene)cycloalkanones corresponding to three cycloalkanones, namely cyclopentanone, cyclohexanone and cycloheptanone, have been prepared. Three dicarboxylic acids with ether linkages, which were derived from oligoethylene oxides, namely triethylene glycol, tetraethylene glycol and pentaethylene glycol, have been used as spacers in these polymers. Polymerization was carried out by both solution and interfacial polycondensation; the latter method gave high-molecular-weight polymers. Structural characterizations were done by ultra-violet, infra-red and H-1 nuclear magnetic resonance spectroscopy. Liquid-crystalline properties were studied by differential scanning calorimetry and polarized-light optical microscopy. These polymers show a nematic mesophase. Liquid-crystalline transition temperatures were correlated with polymer structure. The decrease in transition temperature with increase in cycloalkanone ring size was explained in terms of the change in geometrical anisotropy of bis(benzylidene)cycloalkanone units. MNDO (modified neglect of differential overlap) calculations were performed on the model compounds, bis(4-acetyloxybenzylidene)cycloalkanone to elucidate the geometrical variation of the mesogenic units with cycloalkanone ring size. Studies of photolysis reveal the two kinds of photoreactions that proceed in these polymer systems, namely photoisomerization and photo-crosslinking. The former reaction disrupts the parallel stacking of the chromophores and is reflected as an increase in the ultra-violet spectral intensity. The favourability of these two reactions depends on the mobility of the polymer chains. When the photolysis was done below T-g, photo-crosslinking dominates over photoisomerization. Above T-g, photoisomerization is followed by photo-crosslinking. The photosensitivity of the polymers decreases with increase in size of the cycloalkanone ring.

Highly Efficient and Thermally Stable Second-Order Nonlinear Optical Chromophores and Electrooptic Polymers

Organic polymeric electro-optic (E-O) materials have attracted significant attention because of their potential use as fast and efficient components of integrated photonic devices (1,2). However, the practical application of these materials in optical devices is somewhat limited by the stringent material requirements imposed by the device design, fabrication processes and operating environments. Among the various material requirements, the most notable ones are large electro-optic coefficients (r(33)) and high thermal stability (3). The design of poled polymeric materials with high electro-optic activity (r(33)) involves the optimization of the percent incorporation of efficient (large beta mu) second order nonlinear optical (NLO) chromophores into the polymer matrices and the effective creation of poling-induced non-centrosymmetric structures. The factors that affect the material stability are a) the inherent thermal stability of the NLO chromophores, b) the chemical stability of the NLO chromophores during the polymer processing conditions, and c) the long-term dipolar alignment stability at high temperatures. Although considerable progress has been made in achieving these properties (4), organic polymeric materials suitable for practical E-O device applications are yet to be developed. This chapter highlights some of our approaches in the optimization of molecular and material nonlinear optical and thermal properties.

Synthesis, Structures, and Magnetic Behavior of a Series of Copper(II) Azide Polymers of Cu-4 Building Clusters and Isolation of a New Hemiaminal Ether as the Metal Complex

Four new neutral copper azido polymers, Cu-4(N-3)(8)(L-1)(2)](n) (1), Cu-4(N-3)(8)(L-2)(2)](n) (2), Cu-4(N-3)(8)(L-3)(2)](n) (3), and Cu-9(N-3)(18)(L-4)(4)](n) (4) L1-4 are formed in situ by reacting pyridine-2-carboxaldehyde with 22-(methylamino)ethyl]pyridine (mapy, L-1), N,N-dimethylethylenediamine (N,N-dmen, L-2), N,N-diethylethylenediamine (N,N-deen, L-3), and N,N,2,2-tetramethylpropanediamine (N,N,2,2-tmpn, L-4)], have been synthesized by using 0.5 mol equiv of the chelating tridentate ligands with Cu-(NO3)(2)center dot 3H(2)O and an excess of NaN3. Single-crystal X-ray structures show that the basic unit of these complexes, especially 1-3, contains very similar Cu-4(II) building blocks. The overall structure of 3 is two-dimensional, while the other three complexes are one-dimensional in nature. Complex 1 represents a unique example containing hemiaminal ether arrested by copper(R). Complexes 1 and 2 have a rare bridging azido pathway: both end-on and end-to-end bridging azides between a pair of Cu-II centers. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit dominant ferromagnetic behavior in all four complexes. Density functional theory calculations (B3LYP functional) have been performed on complexes 1-3 to provide a qualitative theoretical interpretation of their overall ferromagnetic behavior.

Stabilization of thermal degradation of poly(methyl methacrylate) by polysulfide polymers

The thermal degradation of poly(methyl methacrylate) (PMMA) in the presence of polysulfide polymers, namely, poly( styrene disulfide) (PSD) and poly(styrene tetrasulfide) (PST) was studied using thermogravimetry (TG) and direct pyrolysis-mass spectrometric (DP-MS) analysis. Both PSD and PST were found to stabilizethe PMMA degradation, which was explained by both radical recombination and a chain-transfer mechanism. (C) 1997 John Wiley & Sons, Inc.