Fromwaterfatemulsionstoradarcrosssectioncontrol从水的.ppt

,*,The ASU College of Engineering,by,E.Dan Hirleman,Associate Dean for Research,College of Engineering and Applied Sciences,09 October 1996,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Fromwaterfatemulsionstoradarcrosssectioncontrol从水的脂肪乳剂对雷达截面控制,Fromwaterfatemulsionstoradarcrosssectioncontrol从水的脂肪乳剂对雷达截面控制Fromwaterfatemulsionstoradarcrosssectioncontrol从水的脂肪乳剂对雷达截面控制The engineered artificial material,or composite,has wide applicabilityMechanical Engineering(concrete),Thermal management(pitch fiber),Geophysical modeling(soil modeling for geosensing),Biomedical applications,In particular,the electromagnetic composite has been of interest in optics and electrical engineering for over a century.,Over this time,the two engineering tasks of Analysis and Synthesis have been developing hand in hand.,The ultimate question:How do we design and manufacture an artificial material with prescribed advantageous properties?,The engineered artificial material,or composite,has wide applicability,Mechanical Engineering(concrete),Thermal management(pitch fiber),Geophysical modeling(soil modeling for,geosensing,),Biomedical applications,In particular,the electromagnetic composite has been of interest in optics and electrical engineering for over a century.,Over this time,the two engineering tasks of Analysis and Synthesis have been developing hand in hand.,The ultimate question:How do we design and manufacture an artificial material with prescribed advantageous properties?,Over this time,we see recurring motifs in the problems addressed,Analysis,Explanation of the optical properties of emulsions and suspensions,Measurement of the butter-fat content of milk or the red blood cell count of mammalian blood.,EM properties of metal insulator composites.,Microwave properties of composites and exotic materials,and their measurement.,Reverse engineering of the same.,Synthesis,Artificial dielectric lenses,Hi-K low loss artificial substrates for printed antennas.,Artificial structures as“matching”devices(w/or w/o dispersion).,Lossy materials for antenna backlobe suppression,anechoic chambers,radar cross section control.,Design of exotic materials(chiral,non-reciprocal,non-linear,optically active salts.),The motifs are question that we keep asking ourselves.,How can a measurement of the composite A+B yield the individual fractions of A and B?,Can a measurement of a composite A+B of known fractions of A and B yield the(unknown)properties of A?,How can a material with an extreme property(high dielectric constant,high loss,high conductivity,etc.)be made,reliably,cheaply?,What are the physically realizable limits of such materials?,The answer might be found in a truly general theory of effective media.,Focusing on the binary material,a practical theory must:,Include the shape of the components.,Contain fitting parameters.,Possess a well defined region of applicability.,Lets follow a Historical Perspective to see how close we have come to this goal:,The role of particle shape and the effective field.,The issue of the internal morphology.,The encompassing nature of the morphology function.,The history can be divided along two principal paths of research.,The random mixture,Spheres in a host,Spheres and spheres,Coated spheres,Coated ellipsoids,Randomly oriented ellipsoids,Stochastic models of aggregates,Fractal clusters,Percolation theory,Cluster theory,Structured dielectrics,Arrays of spheres,Arrays of ellipsoids,Arrays of slabs,Arays of rods,disks,spirals,etc.,Arrays of panels of the sameFSS,2D Arrays of planar structures (Honeycomb),2D Arrays of volumetric structures (Absorber pyramids),3D arrays=PBG,We will start along the random mixture path and end with structured dielectrics,It all started with an attempt at understanding natural dielectrics,by seeking to relate the macroscopic,permittivity,to microscopic dipole moments.,In a binary medium with,polarizable,inclusions,Maxwell(1873),Rayleigh,Clausius,-,Mossotti,(1879),Lorentz,-Lorenz(1880),Maxwell-Garnett(1904),Bottcher,(1946)agree that the simplest expression is:,This CM formula spans the range from,e,host,to,e,inc,uniformly,The problem is that for natural materials,in which the molecules possess intrinsic polarization,it blows up.,Onsager fixed that in 1936,highlighting as crucial the issue of the mean field.,This opened up the way for much of the early work in the development of a rigorous theory of mixtures.,CM,LL,Rayleigh addressed the question for“spheres”.,Then Polder-Van Santen(1946),and Taylor(1965)squarely addressed it for ellipsoidal shapes.,But before either of them,there was Hugo Fricke(1924),He looked at the same kind of problem(a heterogeneous medium of filler particles in a surrounding host)in a different way.,Instead of asking,“what is the mean field seen by an arbitrarily shaped particle?”,he assumed a typical unit cell of the medium could be locally represented by a microscopic capacitor inside which the particle had been placed.,By estimating the charges induced on the non-spherical particle he obtained a physical model that:,Sidestepped the issue of the mean field.,And yielded a formula very much like Wieners(1912),self-consistently including the ellipsoidal shape of the particle.,Where,x,is the shape factor.,This HF model is as uniform as CM but includes the collective shape effect.,The behavior of the suspension depends on the shape and the volume fraction:,There is enhancement at low volume fractions directly proportional to the polarizability of the individual particles.,But as the volume fraction increases,particles start stealing flux from each other.,Assuming a reasonable model for red corpuscles as oblate spheroids of aspect ratio 1/4.25,he obtained agreement with experimental data of the order of 1%over a range of volume fractions from 11%to 91%.,HF HF,CMCM,Frickes model illustrates the three major requirements to be met by an effective medium theory.,(1)It includes the shape of the particle.,(2)This shape is not taken literally,but rather it is allowed to be a fitting parameter in the model.,(3)The resulting model is valid(plausible)over a useful range of volume fractions.,The objection can be raised that,just as CM,it implies 100%filling is possible.But this is not a rigorous objection since materials exist(such as sintered ceramics)for which 100%filling is indeed possible.,It is,admittedly,an approximation.,So,how much better can rigorous models fare?,Before Polder and Van Santens rigorous mean field theory,the general approach to rigor was to change the question from,“what is the mean field?”to“what is the mean environment?”,Bruggeman(1935),Maxwell-Garnett(1904),Bottcher(1946),Looyenga(1965),Ping-Sheng(1980)all obtain simulations of the average medium by considering the particles as coated,to some extent,by the host,or the average medium,or each other.,The question is,what extent is appropriate?,Niklasson and Granqvist illustrate these alternatives for us,To every set of assumptions corresponds a new EMT,The result is that we can have symmetric or asymmetric theories.,The validity can depend on the contrast between the particle and the host properties or it can be independent of it.,There is no connection between the assumption used and a physical process that justifies it above any of the others.,And there may be no accounting for the shape of the particles.,The variety of assumptions certainly are equivalent to a variety of fitting parameters,but the range of validity thus obtained is unknown.,How much better can we do with rigorous mean field theories?,Sillars(1937)developed a theory for dielectrics containing semi-conducting prolate spheroid particles following Wagners 1914 work on spheres.,Polder and Van Santen(1946)obtained a formal solution to Laplaces equation on the ellipsoidal boundary,including randomness,while ignoring correlation effects.,Taylor(1965)put Polder and Van Santens work on the sound basis of generalized boundary conditions obtaining a theory valid for complex,e,.,So,whats the problem?,They prove that ellipsoidal particles of high aspect ratio have a much stronger effect on the materials properties than an equivalent volume of spheres.,For this very reason they have a limited range of validity:,f,2,1,so that,f,can be arbitrarily small.,But if we try to apply the same reasoning to obtaining magnetic susceptibility from non-infinite,m,i,we find the limitation to,f,2,1 extremely restrictive.,Take Nickel,with,m,i,at microwave frequencies of the order of 30.At,f,=2%,the maximum effective permeability that high aspect ratio slivers can give is,m,eff,=1.2.,And even,f,=2%is pushing the limit of validity.,A random mixture of any kind of particle has a finite probability of generating chains and clusters,Chains of spheres can behave like high aspect ratio objects(Percolation theory-Lagarkov et al 1992),Under dynamic mixing,the lowest energy configuration of slivers may be spherical clusters(Doyle and Jacobs 1992 ),And so the discussion of the most useful artificial material reaches a surprising conclusion,Even though the morphology of the individual constituent is a crucial factor,it is the internal morphology of the mixture that controls the materials final property.,And this transition from individual to collective must be a function of the particle shape and,f,.,Frickes model recognized this:At low,f,the particles contribute their full enhancement,as in the RM limit.But at high,f,they switch over to the CM limit.,The collective behavior has its own characterizable morphology,Isolated slivers resemble an early percolating system,Clustered slivers resemble a late percolating system,So we must change our focus from the morphology of the particle to the morphology of the mixture,Which is unknown The first approach to guess is Percolation Theory,regularized to dielectric particles(Sihvola et al(1994),McLachlan et al(1992),Merrill(1996)following Lagarkov,where,p,c,is the percolation threshold.,The second alternative is the spherical cluster theory of Doyle and Jacobs(1990)generalized to dielectrics(Diaz et al 1998),Let,p,be the volume fraction of particles and,p,c,be the percolation limit.Assume that of the,p,particles,f,are clustered into percolated spheres and(1-,f,)are isolated.,Then the average polarizability is,And the effective permittivity is,Similarly,for nonspherical particles,we start with the,b,for metal particles derived in DJ,JAP,71,(8),3926,1992,and proceed in the same way.,The result is that we have two theories that could meet Frickes three requirements,In DJ,shape is accounted for by the shape factor,u,0,.,In ML,(McLachlans GEM version of Percolation Theory)the shape is accounted for implicitly since the depolarization factor is related to the percolation threshold,f,c,.,In DJ,there are two adjustable(or fitting)parameters:the shape factor,u,0,and the percolation limit,p,c,.,In ML,the two adjustable factors are the critical exponent,t,and the percolation threshold,f,c,.,In DJ the formulation is valid up to,p,c,.,In ML the formulation is valid to either side of,f,c,.,Both theories are modeling the internal morphology and,of course,.,They disagree.,Consider a mixture of,e,i,=1000 in,e,h,=1.,Let,f,c,=,p,c,=0.63,u,0,=10,and,t,=1.8.,The two theories model two completely different behaviors.,Note the trend from RM to CM or,viceversa,.,It is time to draw some practical conclusions,Rigorous Mean Field or Average Environment theories can be,extended,into multi-parameter EMTs that are useful(meet all three of Frickes requirements).,There are at least two(and perhaps more)families of these multi-parameter theories(exemplified by the DJ and ML formulations)with different asymptotic limits.,But,given a material,before knowing which family to apply to it,and how to select its parameters,we must know something about its internal morphology.,Then,why not start with a theory of morphology?,An analytic framework for the modeling of effective media,Diaz,Merrill,Alexopoulos,JAP,84,(12)6815,1998.,It is shown that binary mixtures have analytic properties that describe the internal geometry of the mixture and are independent of the components.,All EMTs of such materials can be described in terms of analytic functions in the,u=i,/(,e,i,-1)plane.,These functions take the form of Debye poles in which the strength of the pole and its relaxation frequency are equivalent to the geometric parameters describing a partially filled capacitor.,An EMT merely describes the way this ideal capacitor is filled.,The most general partially filled capacitor contains three types of regions:(a)empty,(b)fully filled,and(c)partially filled.,These correspond to portions of the medium where:(a)the host is fully connected,(b)the inclusions are percolated,(c)the inclusions and the host are both disconnected and in series with each other.,Why does this work?,Because the solution to Laplaces equation in a heterogeneous medium is merely a description of how the Electric Flux is conducted from one capacitor plate to the other.,And when,all,multipoles are taken into account the result is a parallel sum of series capacitors.,What is it good for?A workable framework.,When all possible factors are taken into account,“Rigorous”deterministic theories become unworkable.,The morphology framework is a,thermodynamic,simplification.,Inclusion and host(frequency dependent)permittivity,Particles mean morphology,Statistical dstribution about this mean,Statistical distribution of the spatial orientation of the inclusions,Mean morphology of the clusters and/or chains formed by the inclusions,Statistical distribution of the same,Including distribution of sizes,number of particles included,packing density.,Spatial distribution of clusters and individual particles,The effect of volume fraction on all these parameters.,Because it is a consequence of causality,Whatever the process was that was used to produce the material,whatever the inclusion particles and the surrounding host were,regardless of the microscopic complexity of the finished product,The internal morphology of the mixture must be expressible as a sum of these poles,or partially filled capacitors.,If this is true.,We have three powerful tools for the analysis and design of artificial materials,There is a one-to-one correspondence between the frequency dependence of a material filled with resistive particles and the internal morphology.Measurement of the first will reveal the second.,Once the morphology function is found(the sum of capacitors),the properties of the medium can be determined trivially for arbitrary properties of host and inclusion(electric or magnetic).,An engineering estimate of the flux paths in a structure or mixture suffice to obtain a practical effective medium description of the material.,The morphology function is ideal for structured dielectrics.,Many useful materials can be described by periodic arrays of unit cells containing dielectric segments or structures.,A unit cell of the