By Barrat J.-L., Hansen J.-P.
Offering a unified strategy, this e-book specializes in the theoretical thoughts and techniques precious for knowing the physics and chemistry of the fluid nation. vital principles are provided concisely and illustrated with examples from uncomplicated molecular beverages and extra complicated smooth condensed subject structures akin to polymers, colloids, and liquid crystals.
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Extra info for Basic concepts for simple and complex liquids
8). 1 nm in a dense ﬂuid, so that the neighbours forming the cage may be considered as effectively ‘frozen’ for the purpose of calculating the free volume v . 10 the two-dimensional case of hard discs. The most compact packing is achieved by the triangular lattice, where each atom is surrounded by six nearest √ neighbours placed at the vertices of a hexagonal cell, at a distance d = (2/ 3ρ)1/2 from the centre, where ρ is the number of atoms per unit area (number density of the system). 10, resulting from the intersection of the exclusion discs of radius σ = 2R centred on each of the six vertices.
The main deﬁciency of the above free volume approximation is that it is a mean ﬁeld theory which oversimpliﬁes the effect of the strong positional correlations in dense ﬂuids. Such excluded volume correlations will be examined in more detail in chapter 3. A highly coarse-grained model of ﬂuids, accounting for excluded volume effects, is the lattice gas with single occupancy constraint. 11. Two-dimensional lattice gas model of a one-component ﬂuid (left), of a binary mixture (middle) and of a linear polymer in solution.
Note that the corresponding elastic stiffness increases with increasing temperature. 25 26 An introduction to liquid matter The Gaussian chain model In this model, the conﬁguration of the chain is speciﬁed by N + 1 monomer positions, R1 . . 31) i=1 where b has the dimension of a length. 31) is that the statistical weight of a conﬁguration Ri is W (R1 , . . 32) In this model, all the segments Ri+1 − Ri are independent Gaussian variables. 33) Obviously this Gaussian model 7 is logically interpreted as a coarse-grained version of the freely jointed model.
Basic concepts for simple and complex liquids by Barrat J.-L., Hansen J.-P.