Finite- N effects for ideal polymer chains near a flat impenetrable wall

This paper addresses the statistical mechanics of ideal polymer chains next to a hard wall. The principal quantity of interest, from which all monomer densities can be calculated, is the partition function, G N(z) , for a chain of N discrete monomers with one end fixed a distance z from the wall. It is well accepted that in the limit of infinite N , G N(z) satisfies the diffusion equation with the Dirichlet boundary condition, G N(0) = 0 , unless the wall possesses a sufficient attraction, in which case the Robin boundary condition, G N(0) = - x G N ′(0) , applies with a positive coefficient, x . Here we investigate the leading N -1/2 correction, D G N(z) . Prior to the adsorption threshold, D G N(z) is found to involve two distinct parts: a Gaussian correction (for z <~Unknown control sequence '\lesssim' aN 1/2 with a model-dependent amplitude, A , and a proximal-layer correction (for z <~Unknown control sequence '\lesssim' a described by a model-dependent function, B(z).

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.

Effect of headgroup size, charge, and solvent structure on polymer−micelle interactions, studied by molecular dynamics simulations

We performed atomistic molecular dynamics simulations of anionic and cationic micelles in the presence of poly(ethylene oxide) (PEO) to understand why nonionic water-soluble polymers such as PEO interact strongly with anionic micelles but only weakly with cationic micelles. Our micelles include sodium n-dodecyl sulfate (SDS), n-dodecyl trimethylammonium chloride (DTAC), n-dodecyl ammonium chloride (DAC), and micelles in which we artificially reverse the sign of partial charges in SDS and DTAC. We observe that the polymer interacts hydrophobically with anionic SDS but only weakly with cationic DTAC and DAC, in agreement with experiment. However, the polymer also interacts with the artificial anionic DTAC but fails to interact hydrophobically with the artificial cationic SDS, illustrating that large headgroup size does not explain the weak polymer interaction with cationic micelles. In addition, we observe through simulation that this preference for interaction with anionic micelles still exists in a dipolar "dumbbell" solvent, indicating that water structure and hydrogen bonding alone cannot explain this preferential interaction. Our simulations suggest that direct electrostatic interactions between the micelle and polymer explain the preference for interaction with anionic micelles, even though the polymer overall carries no net charge. This is possible given the asymmetric distribution of negative charges on smaller atoms and positive charges oil larger units in the polymer chain.

Molecular dynamics simulation of interactions between a sodium dodecyl sulfate micelle and a poly(ethylene oxide) polymer

We have performed atomistic molecular dynamics simulations of an anionic sodium dodecyl sulfate (SDS) micelle and a nonionic poly(ethylene oxide) (PEO) polymer in aqueous solution. The micelle consisted of 60 surfactant molecules, and the polymer chain lengths varied from 20 to 40 monomers. The force field parameters for PEO were adjusted by using 1,2-dimethoxymethane (DME) as a model compound and matching its hydration enthalpy and conformational behavior to experiment. Excellent agreement with previous experimental and simulation work was obtained through these modifications. The simulated scaling behavior of the PEO radius of gyration was also in close agreement with experimental results. The SDS-PEO simulations show that the polymer resides on the micelle surface and at the hydrocarbon-water interface, leading to a selective reduction in the hydrophobic contribution to the solvent-accessible surface area of the micelle. The association is mainly driven by hydrophobic interactions between the polymer and surfactant tails, while the interaction between the polymer and sulfate headgroups on the micelle surface is weak. The 40-monomer chain is mostly wrapped around the micelle, and nearly 90% of the monomers are adsorbed at low PEO concentration. Simulations were also performed with multiple 20-monomer chains, and gradual addition of polymer indicates that about 120 monomers are required to saturate the micelle surface. The stoichiometry of the resulting complex is in close agreement with experimental results, and the commonly accepted "beaded necklace" structure of the SDS-PEO complex is recovered by our simulations.

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using latticebased Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.

Orientational behaviour of thermotropic and lyotropic liquid crystal polymer systems under shear flow

A comparison is made of the development of global orientation during shearing of lyotropic solutions of hydroxypropylcellulose with that observed for the thermotropic phase of hydroxypropylcellulose. At shear rates the behaviour of the two systems is similar, both during steady-state shear, and in terms of relaxation following cessation of shear flow. At low shear rates, the levels of orientation observed for the thermotropic system are substantially greater than observed for the lyotropic solutions. The relationship of these differences to variations in molecular parameters, viscous stress and to director tumbling is discussed.

Study of the nonlinear optical properties of a crosslinkable chromophore for use in guest host polymer films

A guest/host material system in which the guest molecule is a functionalized, optically nonlinear, chromophore is described. A verification of the crosslinking process, an assessment of the nonlinear properties of the chromophore, using Solvatochromic methods, and an investigation of the electric field induced molecular orientation using second-harmonic generation are included.

A comparison of photoinduced poling and thermal poling of azo‐dye‐doped polymer films for second order nonlinear optical applications

Photoinduced poling (PIP) is a new technique which allows the room‐temperature preparation of guest/host polymer films exhibiting significant polar order for nonlinear optical applications. We report a comparison of this novel technique with the conventional electrode poling procedure performed at the glass transition temperature of the polymer using disperse red 1/poly(methylmethacrylate) films. In particular, in situ second harmonic generation measurements show that levels of polar order achieved using these two techniques are similar. In contrast, the stability of the polar order is reduced by up to 20 times in terms of the decay time constant in films prepared using PIP although the stability is very dependent upon the temperature at which the poling was performed.

Evolution of network structure in polymer-stabilised liquid crystals

Experiments were performed to investigate the evolution of structure and morphology of the network in polymer-stabilised liquid crystals. In situ optical microscopy revealed that the morphology was significantly altered by extraction of the LC host, while scanning electron microscopy showed that the network morphology was also dependent on the polymerisation conditions and closely related to the depletion of monomer, as monitored by high performance liquid chromatography. Transmission electron microscopy allowed observation of internal structure, resolving microstructure on the order of 0. 1 μm.

A novel study of the polymerisation process involved in the formation of the network component of polymer-stabilised liquid crystals within electro-optic cells using high performance liquid chromatography

Polymer-stabilised liquid crystals are systems in which a small amount of monomer is dissolved within a liquid crystalline host, and then polymerised in situ to produce a network. The progress of the polymerisation, performed within electro-optic cells, was studied by establishing an analytical method novel to these systems. Samples were prepared by photopolymerisation of the monomer under well-defined reaction conditions; subsequent immersion in acetone caused the host and any unreacted monomer to dissolve. High performance liquid chromatography was used to separate and detect the various solutes in the resulting solutions, enabling the amount of unreacted monomer for a given set of conditions to be quantified. Longer irradiations cause a decrease in the proportion of unreacted monomer since more network is formed, while a more uniform LC director alignment (achieved by decreasing the sample thickness) or a higher level of order (achieved by decreasing the polymerisation temperature) promotes faster reactions.

A transmission electron microscopy study of polymer-stabilised liquid crystal structure

A method has been established for observing the internal structure of the network component of polymer-stabilised liquid crystals. In situ photopolymerisation of a mesogenic diacrylate monomer using ultraviolet light leads to a sparse network (∼1 wt%) within a nematic host. Following polymerisation, the host was removed through dissolution in heptane, revealing the network. In order to observe a cross-section through the network, it was embedded in a resin and then sectioned using an ultramicrotome. However, imaging of the network was not possible due to poor contrast. To improve this, several reagents were used for network staining, but only one was successful: bromine. The use of a Melinex-resin composite for sectioning was also found to be advantageous. Imaging of the network using transmission electron microscopy revealed solid “droplets” of width 0.07–0.20 μm, possessing an open, yet homogeneous structure, with no evidence for any large-scale internal structures.

Exploitation of a pulsed neutron source for the structural study of anisotropic polymer films

A novel but simple time-of-flight neutron scattering geometry which allows structural anisotropy to be probed directly, simultaneously and thus unambiguously in polymeric and other materials is described. A particular advantage of the simultaneous data collection when coupled to the large area of the beam is that it enables thin films (< 10 μm < 10 mg) to be studied with relative ease. The utility of the technique is illustrated by studies on both deformed poly(styrene) glasses and on thin films of electrical conducting polymers. In the latter case, the power of isotopic substitution is illustrated to great effect. The development of these procedures for use in other areas of materials science is briefly discussed.