Electron mobility in disordered polymers

Theoretical and Experimental Chemistry -     

Charge‐carrier transport in disordered polymers

The general properties of charge‐carrier transport in disordered organic materials are discussed. The spatial correlation between energies of transport sites determined the form of drift‐mobility field dependence. The type of spatial correlation in a disordered material depends on its nature. Mobility field dependences must be different in polar and nonpolar materials. Different methods of mobility calculation from the shape of photocurrent transient were analyzed. A widely used method is very sensitive to the variation of the shape of the transient and sometimes produces results that effectively masquerade the true dependence of the mobility on the electric field or trap concentration. Arguments in favor of the better, more reliable method are suggested. Charge transport in materials containing charged traps was considered without using the isolated trap approximation, and this led to qualitatively different results. The results indicated that the effect of charged traps can hardly be responsible for the experimentally observed transport properties of disordered organic materials. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2584–2594, 2003     

Elastic constant anisotropy and disclination interaction in nematic polymers I. Apparent variation in anisotropy

This work presents the effect of elastic anisotropy and disclination interaction on wedge disclinations in the nematic phase of thermotropic polymers, by combining experimental measurements, (this paper part I), with numerical simulation (part II [1]). In part I, the decoration provided by spontaneous banded texture gives much information about the defect structure of polymeric nematics. Working with a semi-rigid polyester, the optical images of +1/2 disclinations revealed by banding enable the distortion to be determined as a function of polar coordinates from the cores. Continuum theory allows the apparent elastic anisotropy, ε_a, of bend and splay constants of the copolyester to be determined from the distortion measurement. The values of ε_a, are seen to vary greatly in the range -1 to +1 between different +1/2 disclinations in the same sample. The statistics of the measurement indicate that the distribution of the values of ε_a is random. The implication of these observations is that the curvature of wedge disclinations is affected not only by the elastic anisotropy of the material, but also by other factors. The possible reasons are discussed: the interaction of neighbouring disclinations has been numerically analysed to be the predominant factor in [1]. This work also implies that values of the intrinsic elastic anisotropy obtained by measuring the distortion of individual wedge disclinations must be viewed with some circumspection.     

Photoinduced optical anisotropy in films of photochromic liquid crystalline polymers

The light-induced modification of the optical properties of photochromic liquid crystalline (side-group) polymers (LCPs) containing azobenzene moieties was studied. Films of such polymers were irradiated with unpolarized and linearly polarized light. Unpolarized irradiation results in a modification of the order parameter, whereas the director orientation remains constant. The light-induced disturbance of the supramolecular order is strongly dependent on the structure of the polymer. A correlation with the enthalpic stability of the liquid crystalline phases is given. Linearly polarized irradiation causes a modification of the order parameter and a reorientation of the side-groups towards a direction perpendicular to the electric vector of the actinic light. This reorientation process is caused by an angular-dependent photoselection within the steady state of the photoisomerization of the azobenzene units. The amount and kinetic of the reorientation differ considerably as a function of certain structural features of the polymers, such as the content of photochromic moieties and the lengths of the spacer chains between the polymeric backbone and the rod-like moieties. It is shown that under certain circumstances the angular-dependent photoselection process may cause a reorientation of the non-photochromic moieties by a cooperative process. The result is a light-induced rotation of the optical axis of the LCP and thus an efficient modification of the birefringent and dichroic properties. This effect can be used in optical data storage.     

Effects of disordered interchain interactions on polaron dynamics in semiconducting polymers

Polaron dynamics in a system of two randomly coupled polymer chains is simulated using a nonadiabatic evolution method. The simulations are performed within the framework of the Su-Schrieffer-Heeger model modified to include disordered interchain interactions and an external electric field. By analysing the polaron velocity statistically, we find that the polaron motion is determined by the competition between the electric field and the disordered interchain interactions. Polaron dynamics are classified into two types, weak-coupling dynamics and strong-coupling dynamics. It is found that the strength of interchain interactions is the dominant factor controlling charge propagation in weak-coupling dynamics, whereas the effects of disorder are dominant in strong-coupling dynamics. The charge carriers tend to have higher mobility for stronger interchain coupling, and interchain coupling disorder can be favorable for charge transport depending on the coupling strength and the electric field.     

Semiflexible polymers in a random environment

We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degrees of flexibility and allows us to propose a phase diagram for the highly folded (localized) states of semiflexible polymers as a function of the disorder strength and chain rigidity.     

Molecular motion and anisotropy in polymers investigated by fluorescence techniques

Fluorescence polarization has been used to investigate the correlation between the orientation distribution function odf^G of quasi rigid rod fluorescent guest molecules and the odf^H of anisotropic host polymer in which the guests are imbedded, e.g. fluorescent molecules incorporated in the non-crystalline regions of uniaxially stretched polyethylene (LDPE). The orientation correlation between odf^G and odf^H is discussed with respect to the thickness to length ratio t/1 and the length of the probe molecules. For a rigid rod length around 2 nm there is a linear dependence between the factorizable orientation parameter P₂^G of odf^G and the length of rigid rods at given orientation of LDPE. This behaviour is obtained after correcting the different ratios t/1 of the probes. The variation of probe geometry, i.e. reference length and ratio t/1, gives information not only about the mechanism of orientation but also about the change of rotational mobility depending on size and fluorescence lifetime of the probes. Selecting probes of various length in the lifetime region of 1–6 ns, it results that microregions with reference length larger then 2 nm are rotationally immobile in the non-crystalline regions of LDPE at ambient temperature.     

Observations on the dielectric anisotropy of solutions of flexible polymers in flow

Measurements of the increase in the relative permittivity for solutions of polystyrenes, poly(p-ethoxystyrene), poly(methyl methacrylate), and poly(N-vinyl carbazole) when subjected to shear gradients are reported. The influences of such factors as shear rate, concentration, viscosity, solvent permittivity, polymer dipole moment, and polymer molecular weight on the phenomenon are described. An empirical correlation for the diverse data obtained with polystyrenes and poly(p-ethoxystyrene) has been established, but this relation does not entirely match the theoretically predicted effects. We discuss the various physical processes which may have an influence on the observed phenomenon.     

Structurally perfect ladder polymers: Shape and conversion

The influence of the symmetry and rigidity of Diels-Alder (DA) ladder polymers on their shape in solution is discussed. Theoretical evidence is presented, which shows that certain representatives of this class of polymers attain the unprecedented shape of two-dimensional coils. The second half of this article describes how one can unfold these polymers with chemical transformations and possibly even obtain fully aromatic ribbons.     

On the angular dependence of the optical polarization anisotropy in ladder-type polymers

Two ladder-type polymers have been examined using polarized optical absorption and fluorescence spectroscopy in solution and solid state. The fluorescence anisotropy excitation spectra of ladder-type methyl-substituted poly(para-phenylene) and poly(naphthylene-phenylene) follow their absorption profiles, contrary to the typical behavior in other conjugated polymers, which show excitation wavelength dependent anisotropy until the onset of the typical red edge effect. Using Raman microscopy and linear dichroism of aligned stretched polyethylene films containing the ladder polymer, it has been found that the orientation of the absorption transition dipole moment is dependent on the conjugation length. The transition dipole of the shorter conjugation lengths of the distribution is localized approximately 7 degrees off axis, and that of the longer conjugation lengths is delocalized along the chain.     

Shape variation of cross-linked liquid-crystalline polymers by electric fields

Abstract

First experiments show that cross-linked liquid-crystalline polymers, which are swollen with nematic low molar mass liquid crystals and freely dispersed in this liquid crystal, change their shape if an electic field is applied. This shape variation depends on the degree of swelling.     

Shape selectivity versus functional group pre-organization in molecularly imprinted polymers

A systematic survey of related molecular probes differing in shape or functional group orientation was used to compare the effects of shape selectivity versus pre-organization of functional monomers on imprinting and rebinding performance of molecularly imprinted polymers (MIPs). These studies revealed that templates with two functional group interactions with the MIPs are influenced to a larger degree by shape selective interactions than templates with three functional group interactions. For example, with two functional group interactions, increasing side chain size of compounds 1-5 increased selectivity 5-fold; while the same size change for compounds with three functional group interactions leads to a maximum 2-fold increase. Thus, the effects of shape selectivity and pre-organization of functional groups do not appear to work in concert with each other during the imprinting process or in the rebinding behavior. Furthermore, greater selectivity is generally found for templates with two functional groups, where the dominant mode of molecular recognition is shape selectivity. For example, the α value for the MIP elicited toward template compound 5 with two hydrogen bonding groups was 5-12-fold higher than equivalently shaped compounds 6-8 that have three non-covalent binding interactions (Table 3). On the other hand, pre-organization of functional groups dominated the performance of MIPs elicited toward templates with three template-functional group interactions. This is observed in Tables 6-8, where compounds with identical positioning of three functional groups all show less than an order of magnitude change in α values despite changes in shape.     

Shape variation of cross-linked liquid-crystalline polymers by electric fields

First experiments show that cross-linked liquid-crystalline polymers, which are swollen with nematic low molar mass liquid crystals and freely dispersed in this liquid crystal, change their shape if an electic field is applied. This shape variation depends on the degree of swelling.     

Effect of the elastic constant anisotropy on disclination interaction in the nematic polymers

In this work, disclination interaction behavior in relation to Frank elastic constant anisotropy in nematics has been studied. A large number of (+(1/2), -(1/2)) disclination pairs are revealed by spontaneous band texture in a semiflexible copolyester. The pairs show no preferential relative orientation, with the intervening fields showing intermediate patterns. A two-dimensional tensor lattice model considering unequal elastic constants is applied to simulate the interaction behavior and patterns of disclination pairs in the presence of elastic anisotropy. Scaling laws for disclination density rho(t) as a function of time step t with different elastic anisotropy are obtained as t(-nu). The value of the exponent nu decreases as elastic anisotropy is increased. Obviously, elastic anisotropy slows the texture coarsening. The simulations also show that angular forces arise in the presence of elastic anisotropy and change the patterns of pairs during the texture coarsening. When disclination density is considerably decreased, some +(1/2) disclinations start to rotate to the energetically favored patterns depending on the sign of the elastic anisotropy. As a result of the disclination rotation, the distribution of patterns of pairs continues to change during the annihilation. However, disclination pairs are influenced not only by elastic anisotropy but also by disclination interaction during the whole annihilation. Therefore, in a real system, the dependence of pairs on elastic anisotropy is not as strong as the theoretical prediction for an isolated pair, and the full pattern range of disclination pairs can be observed.     

Shape optimization of a cruciform geometry for biaxial testing of polymers

The presented literature review of cruciform shapes used for biaxial characterization of materials indicates that the majority of shapes can be divided into two large groups when the following selection criteria are taken into consideration: (i) the shape of the outer boundaries and (ii) the load capacity needed to achieve failure in the biaxial region. Manipulation of the outer shape boundaries appears to be essential to bundle the applied loads to the central zone where failure is intended to be built up. For each group, one particular cruciform design is reported whereby the outer boundaries are based on a single curved shape. Although the use of discontinuous double radii edges should be avoided according to earlier reports [1,2], it is shown here through the construction of an optimization algorithm, that the use of a single curve for the outer boundaries leads to strains in the arms that are strongly dependent on these single curved edges. Numerical simulations based on the finite element method as well as experiments performed on polymeric test pieces in combination with DIC measurements, show good agreement on this matter and demonstrate this sensitivity very clearly.     

Shape memory polymers with interconnected nanopores and high mechanical strength

The fabrication of shape memory polymers with both interconnected nanopores and high mechanical strength is challenging. In this work, porous shape memory polymers (PSMPs) were prepared based on the combination of crystallization and phase separation in a ternary blend of poly(l ‐lactic acid)/polyvinyl acetate/poly(ethylene oxide) (i.e., PLLA/PVAc/PEO). The phase separation between the PLLA and PVAc/PEO resulted in bicontinuous structures in microscale including a PLLA‐rich phase and a mixed PVAc/PEO phase. On one hand, the continuous PLLA‐rich phase contributed to the high mechanical strength and shape memory performance, in which tiny crystals and amorphous matrix of PLLA act as the shape fixed phase and reversible phase, respectively. On the other hand, the crystallization of PEO in the miscible PVAc/PEO blend produced submicrometer bicontinuous structures. The interconnected nanopores have been obtained by selective etching of the PEO. Our strategy opens a new avenue for fabricating PSMPs with both interpenetrated channels and high strength. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 125–130