Interaction and percolation in the L64 triblock copolymer micellar system

Temperature-dependent micellar structures in poly(styrene-b-isoprene) diblock copolymer solutions near the critical micelle temperature

The temperature dependence of the micelle structures formed by poly(styrene-b-isoprene) (SI) diblock copolymers in the selective solvents diethyl phthalate (DEP) and tetradecane (C14), which are selective for the PS and PI blocks, respectively, have been investigated by small angle neutron scattering (SANS). Two nearly symmetric SI diblock copolymers, one with a perdeuterated PS block and the other with a perdeuterated PI block, were examined in both DEP and C14. The SANS scattering length density of the solvent was matched closely to either the core or the corona block. The resulting core and corona contrast data were fitted with a detailed model developed by Pedersen and co-workers. The fits provide quantitative information on micellar characteristics such as aggregation number, core size, overall size, solvent fraction in the core, and corona thickness. As temperature increases, the solvent selectivity decreases, leading to substantial solvent swelling of the core and a decrease in the aggregation number and core size. Both core and corona chains are able to relax their conformations near the critical micelle temperature due to a decrease in the interfacial tension, even though the corona chains are always under good solvent conditions.

Neutron- and light-scattering studies of the liquid-to-glass and glass-to-glass transitions in dense copolymer micellar solutions

Recent mode coupling theory (MCT) calculations show that if a short-range attractive interaction is added to the pure hard sphere system, one may observe a new type of glass originating from the clustering effect (the attractive glass) as a result of the attractive interaction. This is in addition to the known glass-forming mechanism due to the cage effect in the hard sphere system (the repulsive glass). The calculations also indicate that if the range of attraction is sufficiently short compared to the diameter of the particle, within a certain interval of volume fractions where the two glass-forming mechanisms nearly balance each other, varying the external control parameter, the effective temperature, makes the glass-to-liquid-to-glass reentrance and the glass-to-glass transitions possible. Here we present experimental evidence of both transitions, obtained from small-angle neutron-scattering and photon correlation measurements taken from dense L64 copolymer micellar solutions in heavy water. Varying the temperature in certain predicted volume fraction range triggers a sharp transition between these two different types of glass. In particular, according to MCT, there is an end point (called A3 singularity) of this glass-to-glass transition line, beyond which the long-time dynamics of the two glasses become identical. Our findings confirm this theoretical prediction. Surprisingly, although the Debye-Waller factors, the long-time limit of the coherent intermediate scattering functions, of these two glasses obtained from photon correlation measurements indeed become identical at the predicted volume fraction, they exhibit distinctly different intermediate time relaxation. Furthermore, our experimental results obtained from volume fractions beyond the end point are characterized by the same features as the repulsive glass obtained before the end point. A complete phase diagram giving the boundaries of the structural arrest transitions for L64 micellar system is given.

The glass-to-glass transition and its end point in a copolymer micellar system

We present experimental evidence, obtained from small-angle neutron scattering and photon correlation measurements, indicating the existence of two types of structurally arrested (glassy) states in a copolymer micellar system with a short-range interparticle attractive interaction. Within a certain range of micellar volume fractions, a sharp transition between these two types of glass is observed by varying the temperature. Furthermore, we found an end point of this transition line beyond which the two glasses become identical in their local structure and their long-time dynamics. These findings confirm the recent mode-coupling theory predictions regarding the phase behavior of the structurally arrested states for this type of system.

Graft polymer solutions as sticky hard-sphere colloids

We show that a solution of a graft (comb) polymer can exhibit an adhesive hard-sphere pair potential. In the present paper, static and dynamic light scattering measurements on a comb polymer at low molecular weight are performed and the results discussed in the framework of the colloidal theory for adhesive spheres. Renormalization group calculations are directly compared with experimental data on the cooperative diffusion coefficient using the scaled concentration parameter.

Relation between aggregation and phase separation: three-dimensional Monte Carlo simulations

We study phase separation of particles in solution using Monte Carlo simulations of reversible aggregation on a cubic lattice. Two stages of the phase separation can be clearly distinguished: initial random aggregation and subsequent densification. Step one leads to a distribution of fractal aggregates close to the binodal and to a temporary gel for large attractive interaction. Step two leads to isolated spherical dense domains close to the binodal and branched wormlike strands for large attractive interactions. The transition between the two types of structure is gradual and there is no clear feature that shows the existence of a spinodal. The first stage of the phase separation is metastable very close to the binodal or at very large interaction energy. In the latter case, the second step can be viewed as an aging process of the gel formed in the first step.

Theories and theoretical models for percolation and permeability in multiphase systems: comparative analysis

The terminology and the physical sense of percolation and permeability were analyzed. Existing theories of percolation and permeability were analytically compared with respect to their applicability and effectiveness. It is concluded that the main tendency in the development of the concept of percolation/permeability consists in the fundamental investigation of the relationship between the preparation conditions of the solid, its structural characteristics and measured properties - not only percolation/permeability but also adsorption, Hg-intrusion, etc.

Small-angle neutron scattering study of the temperature-dependent attractive interaction in dense L64 copolymer micellar solutions and its relation to kinetic glass transition

We made small-angle neutron scattering (SANS) study of a Pluronic L64 micellar system in aqueous solution at high polymer concentrations (wt %), 35%<c<53%, in a temperature range where a kinetic glass transition has been observed by photon correlation spectroscopy and zero shear viscosity measurements. We analyze SANS intensity distributions assuming that the micelles are spherical and interact among themselves by an effective pair potential, consisting of a hard core plus a narrow attractive square well, the depth of which is temperature dependent. The theory is able to account for the intensity distribution quantitatively when the micellar system is in the liquid phase (but qualitatively when the micellar system is in the glass state), giving values of four parameters: the aggregation number of the micelle N, the volume fraction occupied by the micelles phi, the fractional width of the square well epsilon, and the effective temperature T*=k(B)T/u, where -u is the depth of the square well. Thus, we are able to assign a point in the phase diagram (the T*-phi plane) for each measured micellar liquid and glass state. Comparison with a phase diagram predicted recently by mode coupling theory calculation allows us to identify the existence of the so-called liquid-to-attractive-glass transition line. We also found the evidence of glass-to-glass transition at volume fraction of 0.54 predicted by the mode coupling theory.

Liquid-solid transition in a model hard sphere system of block copolymer micelles

The transition between micellar liquid and face-centered-cubic crystalline solid in a solution of an amphiphilic diblock copolymer is investigated by small-angle x-ray scattering and rheology. The system is well described by the hard sphere model and there is no evidence for percolation driven by attractive interactions, in contrast to previous reports. Instead, a coexistence region separates liquid and crystal phases.

Higher-order glass-transition singularities in colloidal systems with attractive interactions

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third-order bifurcation point, i.e., in a A3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth-order A4 (swallow-tail) singularity at a critical well width. Close to the A3 and A4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.

Kinetic glass transition in a micellar system with short-range attractive interaction

We show that percolation and structural arrest transitions coexist in different regions of the phase diagram of a copolymer-micellar system and relate them to short-range intermicellar attraction. The intermediate scattering function shows a nonergodic transition along a temperature and concentration dependent line. Analyses show a logarithmic time dependence, attributed to a higher-order glass transition singularity predicted by mode-coupling theory, followed by a power law.