Tethered polymer chains refers to macromolecular chains that are attached into microstructures by their ends. Highly branched polymers, polymer micelles and end-grafted chains on surfaces are a few examples. This review brings out the common features of these seemingly widely disparate microstructures. Tethering can be reversible or irreversible and is frequently sufficiently dense that the chains are crowded. Densely tethered chains stretch to alleviate the interactions caused by crowding. They thus exhibit deformed configurations at equilibrium. These effects of tethering on the structure of the polymer chains are reflected in distinctive behavior and properties of microstructures containing tethered chains.

Tethered chains in polymer microstructures

The formation of dispersed phase in blends of incompatible polymers during melt extrusion with a co-rotating twin screw extruder was studied, using nylon and polyester as the matrix and ethylene-propylene rubbers as the dispersed phase. A master curve is obtained, i.e., Gηmα/γ = 4p±0.84, where G is the shear rate, γ the particle diameter, η the interfacial tension, ηm the matrix viscosity, ηd the dispersed-drop viscosity, and p = ηd/ηm. The plus (+) sign applies for p > 1, and the minus (−) sign for p < 1. Thus, the dispersed-drop size is directly proportional to the interfacial tension and the ±0.84 power of viscosity ratio. The dispersed drops are the smaller, when the interfacial tension is the lower and the viscosity ratio is the closer to unity. The interfacial tension is largely controlled by the polarities of the two phases, and can be varied over several orders of magnitude by using appropriate dispersants.

Formation of dispersed phase in incompatible polymer blends: Interfacial and rheological effects

Functional nanomaterials based on block copolymer self-assembly

We introduce the Cohesive Energy Density (CED) method, a multiple sampling Molecular Dynamics computer simulation procedure that may offer higher consistency in the estimation of Hildebrand and Hansen solubility parameters. The use of a multiple sampling technique, combined with a simple but consistent molecular force field and quantum mechanically determined atomic charges, allows for the precise determination of solubility parameters in a systematic way (sigma = 0.4 hildebrands). The CED method yields first-principles Hildebrand parameter predictions in good agreement with experiment [root-mean-square (rms) = 1.1 hildebrands]. We apply the CED method to model the Caltech electronic nose, an array of 20 polymer sensors. Sensors are built with conducting leads connected through thin-film polymers loaded with carbon black. Odorant detection relies on a change in electric resistivity of the polymer film as function of the amount of swelling caused by the odorant compound. The amount of swelling depends upon the chemical composition of the polymer and the odorant molecule. The pattern is unique, and unambiguously identifies the compound. Experimentally determined changes in relative resistivity of seven polymer sensors upon exposure to 24 solvent vapors were modeled with the CED estimated Hansen solubility components. Predictions of polymer sensor responses result in Pearson R2 coefficients between 0.82 and 0.99.

http://wag.caltech.edu/publications/sup/pdf/587.pdf

Hildebrand and Hansen solubility parameters from Molecular Dynamics with applications to electronic nose polymer sensors

A simple microscopic model for micellar formation in mixtures of block copolymers and homopolymers is presented. The size, number of chains, and energy of formation of micelle are calculated. The fraction of copolymer chains aggregating into micelles is computed as a function of the overall copolymer content. A critical micelle concentration behavior is found for low copolymer contents even for weak incompatibilities of species. The similarity with an aborted phase transition is underlined.

Theory of critical micelle concentration for solutions of block copolymers

: The light scattering technique was utilized to measure the phase separation temperatures (cloud points) of mixtures containing a polystyrene and a polybutadiene of various molecular weights and also of mixtures containing a polystyrene and a random or block copolymer of styrene and butadiene. The data was analyzed to obtain the polymer-polymer interaction parameter for the styrene-butadiene pair as a function of temperature and concentration. The value of the parameter deduced from the homopolymer mixtures agrees well with that obtained from the mixtures containing a copolymer. The polymer-polymer interaction parameter thus evaluated was compared with a theoretical expression derived on the basis of the Flory equation-of-state theory. The effect of the free volume disparity between the two components was found to play a relatively minor role in determining the interaction parameter when the two polymers lack any specific interactions which would make them mutually miscible. (Author)

Determination of the Polymer-Polymer Interaction Parameter for the Polystyrene-Polybutadiene Pair

: The small-angle X-ray scattering (SAXS) technique is used to study the transition in styrene-butadiene block copolymers from a microdomain structure to a disordered homogeneous phase. The transition, occurring on raising the temperature, is reproducible and thermally reversible. The SAXS intensity pattern, exhibiting a main interdomain peak and a few secondary peaks at room temperature, shows a gradual decrease in intensity over a temperature range of more than 100 deg, but the position and the overall shape of the main peak remain unchanged. Analysis of the SAXS data shows that, with increasing temperature, the invariant and the length of inhomogeneity decrease, but the domain boundary thickness remains approximately constant. It is concluded that the disappearance of the microdomains proceeds by gradual intermixing of components into the opposite phases, with accompanying changes in the size of the microdomains, much in the same manner as would occur with coexisting phases of a binary liquid system. Even when the microdomains have finally disappeared and the mixture has become thermodynamically homogeneous, the SAXS pattern of diminished intensity persists, reflecting the presence of dynamic density inhomogeneity, as suggested in the theories be de Gennes and by Leibler. The similarity of our SAXS results with those obtainable with a supercooled mixture undergoing a spinodal decomposition is pointed out and its thermodynamic basis discussed.

Small-Angle X-Ray Diffraction Study of Thermal Transition in Styrene-Butadiene Block Copolymers.

A molecular dynamics simulation of bulk atactic polystyrene was performed. A united atom model and an all atom model were developed, in both of which the bond lengths were held fixed and the phenyl group was represented by a rigid, planar hexagon. The degree of success of the simulation was examined by comparing the calculated X-ray scattering intensity curve with experiment. The united atom model reproduces the so-called «polymerization peak», and the calculated curve agrees well with one of the most recently published experimental data. The degree of agreement achieved is in fact comparable to the degree to which two published experimental curves agree with each other

Molecular dynamics simulation of atactic polystyrene. 2. Comparison with neutron scattering data

Blends containing styrene-butadiene diblock copolymer (50 wt % styrene content) and polystyrene of various molecular weights are studied by light scattering, transmission electron microscopy, and small-angle X-ray scattering. The solubility of polystyrene in the styrene domain of the block copolymer is governed by the ratio of the homopolymer molecular weight to the block molecular weight. A finite solubility limit exists when this ratio exceeds [approximately]1. The lamellar repeat period increases linearly as more polystyrene is added, but the butadiene layer thickness remains constant, signifying that the average interfacial area occupied by a copolymer junction point does not change with added polystyrene. This contrasts to the case found by the others that the average area per junction point increases when the added homopolymer is smaller than the block size. Small-angle X-ray scattering patterns obtained from samples having lamellar morphology are described by an idealized model in which layers of styrene and butadiene of randomly varying thicknesses with a diffuse interface between them are stacked parallel.

Ryong-Joon Roe

Papers

Determination of the Polymer-Polymer Interaction Parameter for the Polystyrene-Polybutadiene Pair

Small-Angle X-Ray Diffraction Study of Thermal Transition in Styrene-Butadiene Block Copolymers.

Molecular dynamics simulation of atactic polystyrene. 2. Comparison with neutron scattering data

Solubilization of a Homopolymer in a Block Copolymer

Contribution of the Conformational Specific Heat of Polymer Chains to the Specific Heat Difference between Liquid and Glass