Analysis of solution properties of polystyrene in 2-butanone in the framework of the hard-sphere model

Role of Branching on the Structure of Polymer Brushes Formed from Comb Copolymers

“…To coalesce the force profiles displayed in Figure to a single profile, we reduce the measured forces of interaction, F/R , and surface separation distances, d , by the scalings for the equilibrium free energy (per unit area) and height, respectively, of a brush comprised of the same PS molecular weight and tethering density: 2,3 In these equations, the factor 2 L PI removes the thickness of the anchoring PI block from the height of the brush, b is the statistical segment size, σ is the tethering density based on the equivalent diblock copolymer (the miktoarm subunit of the comb), and ν is the parameter that scales radius of gyration with degree of polymerization, N . Previous light scattering measurements on PS homopolymers in MEK yielded values of b = 1.88 Å and ν = 0.571 . As seen in Figure , scaling the SFA results in this fashion gathers the force profiles for the brushes formed from the combs into a single master curve, which demonstrates that the well-known scaling relationships for linear brushes embodied in eqs 1 and 2 are valid for the brushes produced by preferential adsorption of the comb copolymers.…”

“…7 As seen in Figure 2, scaling the SFA results in this fashion gathers the force profiles for the brushes formed from the combs into a single master curve, which demonstrates that the well-known scaling relationships for linear brushes embodied in eqs 1 and 2 are valid for the brushes produced by preferential adsorption of the comb copolymers. This is reasonable given that the Alexander-de Gennes model describes a global balance of the elastic and stretching energies for tethered linear chains, which depends on N, b, and σ but not local elements, such as how the tethering is achieved.…”

“…2 Given the analyses of the effect of architecture and confinement on the osmotic free energy of the brush, it is straightforward to determine a numerical value for β from eq A6. This yields a value of β ) 0.259, which along with values of ν and K π 7,11 and the experimentally determined reduced force and distance data (F and d), leaves no adjustable parameters in the model expressed by eq 4. The data for the brushes produced from the combs recast according to eq 4 are plotted in Figure 4, along with a pair of representative results from a PS brush in toluene and near-theta cyclohexane formed from a preferentially adsorbed PVP-PS diblock copolymer.…”

“…This reduction of the PI “length” between grafts causes local crowding within the layer, causing the chains to extend further from the tethering plane. If we take one-half of the onsets of repulsion as the height of one brush layer and divide this value by the radius of gyration (in free solution) of the PS grafts, we can obtain a measure of the degree of stretching of the brush. These results, along with the surface density based on the constituting miktoarm subunit of the comb, which is calculated from the dry layer thickness, , are reported in Table .…”

Structure and Dynamics of Interacting Nanoparticles in Semidilute Polymer Solutions

“…29 We verify this prediction by measuring the intrinsic viscosity of our polymer in dilute solutions using a capillary viscometer to be 104 ± 12 mL/g (Supporting Information, Figure S1), in agreement with predictions. Using standard relations, 30 we calculate the overlap concentration c* = 1/[η] and approximate the radius of gyration 31 in dilute solution R g,0 ≈ [M w /(4/3πN av c*)] 1/3 to be 10.7 g/L and 29 nm, respectively.…”