  The origin of the diffuse astrophysical neutrino flux observed by the IceCube
experiment is still under debate. In recent years there have been associations
of neutrino events with individual blazars, which are active galaxies with
relativistic jets pointing toward Earth, such as the source TXS 0506+056. From
a theoretical perspective, the properties of these sources as neutrino emitters
are not yet well understood. In this work we model a sample of 324 blazars
detected by the Fermi Large Area Telescope (LAT), most of which are
flat-spectrum radio quasars (FSRQs). This amounts to 34% of all FSRQs in the
latest Fermi catalog. By numerically modelling the interactions of cosmic-ray
electrons and protons, we explain the emitted multi-wavelength fluxes from each
source and self-consistently predict the emitted neutrino spectrum. We
demonstrate that the optical and GeV gamma-ray broadband features are generally
well described by electron emission. For 33% of the blazars in our sample, a
description of the observed X-ray spectrum benefits from an additional
component from proton interactions, in agreement with recent studies of
individual IceCube candidate blazars. We conclude that blazars that are
brighter in GeV gamma rays tend to have a higher neutrino production efficiency
but a lower best-fit baryonic loading. The predicted neutrino luminosity shows
a positive correlation with the observed GeV gamma-ray flux and with the
predicted MeV gamma-ray flux. By extrapolating the results for this sample, we
show that the diffuse neutrino flux from the population of gamma-ray-bright
blazars may be at the level of about 20% of the IceCube flux, in agreement with
current limits from stacking analyses. We discuss the implications of our
results for future neutrino searches and suggest promising sources for
potential detections with future experiments.
