  We apply extensive Molecular Dynamics simulations and analytical
considerations in order to study the conformations and the effective
interactions between weakly charged, flexible polyelectrolyte chains in
salt-free conditions. We focus on charging fractions lying below 20%, for which
case there is no Manning condensation of counterions and the latter can be thus
partitioned in two states: those that are trapped within the region of the
flexible chain and the ones that are free in the solution. We examine the
partition of counterions in these two states, the chain sizes and the monomer
distributions for various chain lengths, finding that the monomer density
follows a Gaussian shape. We calculate the effective interaction between the
centers of mass of two interacting chains, under the assumption that the chains
can be modeled as two overlapping Gaussian charge profiles. The analytical
calculations are compared with measurements from Molecular Dynamics
simulations. Good quantitative agreement is found for charging fractions below
10%, where the chains assume coil-like configurations, whereas deviations
develop for charge fraction of 20%, in which case a conformational transition
of the chain towards a rodlike configuration starts to take place.
