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M Himmi

Publications and source records attributed to M Himmi.

2 recordsLinked to original sources
PubMed2004

Force between unlike star-polymers versus the solvent quality.

We re-examine here the computation of the effective force between two star-polymers A and B of different chemical nature, which are immersed in a common solvent. This force originates from the excluded-volume interactions and chemical segregation. We assume that the solvent quality may be different for the two unlike star-polymers, that is the solvent can be 1) a good solvent for A and B, 2) a good solvent for A and a Theta-solvent for B, or 3) a Theta-solvent for the two polymers. The purpose is a quantitative study of the effect of the solvent quality on the effective force, which is a function of the center-to-center distance. Calculations are achieved using the renormalization theory applied to the Edwards continuous model. We first show that, when the mutual interactions are present, the effective force decays as the inverse of distance, but with a universal amplitude depending on the solvent quality. Second, we demonstrate the existence of three kinds of forces related to situations 1), 2) and 3) described above, and give the third-order epsilon-expansions (epsilon = 4 - d, 4 is the critical dimension) of the corresponding amplitudes. These series can be resummed using the Borel-Leroy techniques to obtain the best three-dimensional values for the expected force amplitudes. Finally, this work must be regarded as a natural extension of a published one which dealt with the same problem, but where the solvent was assumed to be good for the two unlike star-polymers.

Journal Article↗
PubMed2004

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.

Journal Article↗