Mesoscopic stresses

Mesoscopic stresses occur between particle splats inside a lamella and are responsible for reduced coating cohesion. These stresses result principally from frozen-in contraction of the rapidly quenched molten particles at the substrate interface. 

As stressed by Mermin and collaborators [9 - 18] it is far too restrictive to define the structural indistinguishability of two mesoscopically homogeneous materials with reference to identical densities. Instead of the densities themselves one should study the properties of the correlationfunctions,... 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

The pressure p includes both the partial pressure of the gas of Brownian particles n(N +1 )T and the partial pressure of the carrier monomer liquid. We shall assume that the viscosity of the monomer liquid can be neglected. The variables xt k in equation (9.19) characterise the mean size and shape of the macromolecular coils in a deformed system. The other variables ut k are associated mainly with orientation of small rigid parts of macromolecules (Kuhn segments). As a consequence of the mesoscopic approach, the stress tensor (9.19) of a system is determined as a sum of the contributions of all the macromolecules, which in this case can be expressed by simple multiplication by the number of macromolecules n. The macroscopic internal variables x -k and u"k can be found as solutions of relaxation equations which have been established in Chapter 7. However, there are two distinctive cases, which have to be considered separately. 

Stresses can be predicted Irom the mesoscopic theory by inserting Eqs. (11-34) for the mesoscopic birefringence into the equation for the stress tensor, Eq. (11-32), to give the following approximate expressions for the stresses ... 

Figure 11.26 Reduced sheai stress = u/Ocyo versus shear strain / = yt, after a"step up in shear rate from /, to Yf with yt/yf =0.1, and after a reversal in shear direction, predicted by the mesoscopic theory with s = 0.03 and CfC = (a) 1.122, (b) 1.5, and (c) 2.0. (From Larson and Doi 1991, with permission of the Journal of Rheology.)...

The macroscopic properties of liquid suspensions of fumed powders of silica, alumina etc. are not only affected by the size and structure of primary particles and aggregates, which are determined by the particle synthesis, but as well by the size and structure of agglomerates or mesoscopic clusters, which are determined by the particle-particle interactions, hence by a variety of product- and process-specific factors like the suspending medium, solutes, the solid concentration, or the employed mechanical stress. However, it is still unclear how these secondary and tertiary particle structures can be adequately characterized, and we are a long way from calculating product properties from them [1,2]. 

Although these simple considerations help to frame in a general logic the behavior of these bimetallic surface, there are at present no such simple models to explain the more complex mesoscopic reconstructions, such as the pyramids observed on Pt3Sn(100) or the hill and valley structure observed on PtsSnCl 10). These phenomena are obviously related to the tendency of the system to relax in-plane stress, in turn resulting from the different atomic radius of the elements involved in the presence of concentration gradients. This relaxation appears to take place on the (111) oriented plane simply by an outward relaxation of the tin atoms. On the other two low index surfaces, instead, it takes a more complex route leading to reconstruction phenomena (pyramids on the (100) and hill and valley on the (110)) which are so far unique to the Pt-Sn system. 

Another approach towards a thermodynamics of steady-state systems is presented by Santamaria-Holek et al.193 In this formulation a local thermodynamic equilibrium is assumed to exist. The probability density and associated conjugate chemical potential are interpreted as mesoscopic thermodynamic variables from which the Fokker-Planck equation is derived. Nonequilibrium equations of state are derived for a gas of shearing Brownian particles in both dilute and dense states. It is found that for low shear rates the first normal stress difference is quadratic in strain rate and the viscosity is given as a simple power law in the strain rate, in contrast to standard mode-coupling theory predictions (see Section 6.3). 

A comparison of mesoscopic simulation methods with MD simulations has been performed by Denniston and Robbins.423 They study a binary mixture of simple Lennard-Jones fluids and map out the required parameters of the mesoscopic model from their MD simulation data. Their mapping scheme is more complete than those of previous workers because in addition to accounting for the interfacial order parameter and density profiles, they also consider the stress. Their mapping consists of using MD simulations to parameterise the popular mesoscale Lattice Boltzmann simulation technique and find that a... 

Besides the outstanding chemical characteristics of certain mesoscopic structures, they also possess a number of surprising physical characteristics. Typical examples are the initiation of premelting near dislocations, twin boundaries or grain boundaries (e g. Raterron et al. 1999, Jamnik and Maier 1997) and the movement of twin boundaries under external stress which leads to non-linear strain-stress relationships. It is the purpose of this review to focus on some of the characteristic features of mesocopic structures and to illustrate the generic results for the case of ferroeleastic twin patterns (Salje 1993). 

During plasma spraying, the particle-substrate interactions characterised by momentum and heat transfer from the solidifying particle after impacting the surface of the substrate lead eventually to the development of residual stresses in the coating. These stresses can be divided into microscopic, mesoscopic and macroscopic stresses. 

In alloys of the other category, the preferentially sputtered component is segregating towards the surface. Here PtsSn serves as an example, in which Sn is segregating and preferentially sputtered (wsn < mpt and Tsn < 7pt). The PtsSn exhibits a strict chemical order of the LI2 type, that is, fee structure with Pt at the comer sites and Sn at the face sites of the unit cell. The depletion in Sn in the surface region leads to a smaller lattice constant (apt < JptsSn)- All three low-indexed surfaces of PtsSn respond to this depletion by formation of metastable phases with characteristic stress compensation features (Table III). A mesoscopic dislo-... 

Without any precautions, islands typically agglomerate at rather random positions on the surfaces, governed by nucleation and agglomeration processes. Ordered nanostructures can be obtained when the film is grown on mesoscopic network structures arising from reconstructions or stress compensation. An early... 

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