| Summary: | Dilute mixtures of nanoparticles (NPs) and nematic liquid crystals (LCs) are considered. We focus on cases where NPs enforce a relatively weak disorder to the LC host. We use a Lebwohl-Lasher semi-microscopic-type modeling where we assume that NPs effectively act as a spatially-dependent external field on nematic spins. The orientational distribution of locally favoured “easy„ orientations is described by a probabilistic distribution function <i>P</i>. By means of a mean field-type approach, we derive a self-consistent equation for the average degree of nematic uniaxial order parameter <i>S</i> as a function of the concentration <i>p</i> of NPs, NP-LC coupling strength and <i>P</i>. Using a simple step-like probability distribution shape, we obtain the <i>S</i>(<i>p</i>) dependence displaying a crossover behaviour between two different regimes which is in line with recent experimental observations. We also discuss a possible origin of commonly observed non-monotonous variations of the nematic-isotropic phase temperature coexistence width on varying <i>p</i>.
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