  We study asymptotically AdS Brans-Dicke (BD) backgrounds, where the Ricci
tensor R is coupled to a scalar in the radial dimension, as effective models of
metals with a varying coupling constant. We show that, for translational
invariant backgrounds, the regular part of the dc conductivity $\sigma_Q$
deviates from the universal result of Einstein-Maxwell-Dilaton (EMD) models.
However, the shear viscosity to entropy ratio saturates the
Kovtun-Son-Starinets (KSS) bound. Similar results apply to more general f(R)
gravity models. In four bulk dimensions we study momentum relaxation induced by
gravitational and electromagnetic axion-dependent couplings. For sufficiently
strong momentum dissipation induced by the former, a recently proposed bound on
the dc conductivity $\sigma$ is violated for any finite electromagnetic axion
coupling. Interestingly, in more than four bulk dimensions, the dc conductivity
for strong momentum relaxation decreases with temperature in the low
temperature limit. In line with other gravity backgrounds with momentum
relaxation, the shear viscosity to entropy ratio is always lower than the KSS
bound. The numerical computation of the optical conductivity reveals a linear
growth with the frequency in the limit of low temperature, low frequency and
large momentum relaxation. We have also shown that the module and argument of
the optical conductivity for intermediate frequencies are not consistent with
cuprates experimental results, even assuming several channel of momentum
relaxation.
