Exact effective force between star-polymers in a Theta-solvent

Critical microphase properties of crosslinked polymer blends with quenched random impurities

We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties.

Theory of microphase separation in charged crosslinked polymer blends with arbitrary charge distribution

In this paper, we are interested in the phase behavior and scattering properties of charged crosslinked polymer blends in solution. The system undergoes a microphase separation, below some critical temperature. To study such a transition, use is made of the standard de Gennes theory based on an analogy with a dielectric medium. This analogy is extended to include the effects of the initial composition fluctuations in order to improve its agreement with experimental data in the small wave vector range. The excluded-volume interactions are explicitly introduced through the blob model. The charge effects on the phase behavior are examined, for any charge distribution of polyions and for any salt concentration. This completes a previous study which was concerned with the situation where only one species is charged. The early kinetics of microphase separation is discussed, and the charges contribution to the growth rate is also evaluated.

Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time t, before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, S(q, t), which is a function of the wave vector q, temperature T, time t, and reticulation dose D. To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (model C) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, zeta. First, by averaging over zeta, we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of S(q, t), in space of relevant parameters. As result, S(q, t) depends on three kinds of lengths, which are the wavelength q(-1), a time length scale R(t) approximately t(1/z), and the mesh size xi*. The scale R(t) is interpreted as the size of growing microdomains at time t. When R(t) becomes of the order of xi*, the dynamics is stopped. The final time, t*, then scales as t* approximately xi*z, with the dynamic exponent z = 6-eta. Here, eta is the usual Ising critical exponent. Since the final size of microdomains xi* is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.

Exact effective force between star-polymers in a Theta-solvent

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f(1) and f(2), immersed in a common Theta-solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, F(r), decreases with the center-to-center distance r as F(r)/kappa BT congruent with Af1f2 x [r ln (R2/r2]-1 (r<R), with the exact universal amplitude Af1f2 = f1f2(f1 + f2 - 2)/22. Second, in dimension d = 2, we find that the force decays more slowly as F(r)/kappa BT congruent with Bf1f2 x r-1 (r<R), with the exact universal amplitude Bf1f2. For high distances compared to the gyration radius, R approximately a square root of N, of a single polymer chain at the Theta-point, an exponential decay of the force is expected.