By Barrat J.-L., Hansen J.-P.

Proposing a unified procedure, this booklet specializes in the theoretical innovations and techniques beneficial for figuring out the physics and chemistry of the fluid nation. vital rules are offered concisely and illustrated with examples from easy molecular beverages and extra complicated delicate condensed topic structures corresponding to polymers, colloids, and liquid crystals.

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**Example text**

In the opposite limit of high densities, which is much more relevant for the condensed (liquid or solid) states of matter, calculation of the free volume is a much more difﬁcult task, due to the numerous overlaps of the excluded volumes associated with each particle. On average each particle is trapped in a cage of neighbouring spheres, and the free volume per particle v = V /N is much less than the volume per particle v = V /N . The free volume v accessible to any one particle trapped in its cage may then be calculated with a cell model, whereby the nearest neighbours of the particle are assumed to be ﬁxed at some favourable average position.

In other words all measurable, macroscopic properties of a given substance, say its speciﬁc heat, its thermal expansivity or its viscosity, are well deﬁned functions of these state variables. 1 State variables and thermodynamic equilibrium species in the substance. g. the mass (in kilograms or moles) of each species, only two further variables are needed to characterize completely the state of that substance; in practice the most common choices are temperature T and pressure P or total volume V of the sample.

37) p where p = − / ln(cos α) 2 /α 2 is the persistence length, and the second equality is valid for small α. p is the length scale above which the correlation between orientations along the chain becomes negligible. Again, the Kratky–Porod chain can be ‘coarse-grained’ into a freely jointed model with identical large-scale properties. 37) that the orientations of successive subunits are essentially uncorrelated. Hence the chain can be described as a succession of rigid subunits, each of length p , with random relative orientations.