Measurements of the anodic and cathodic diffusion-limited current densities ilCl- and ilCuCl2-.
\r\n\tOne basic topic is that of expression manipulation: combining, expanding etc, and the applications of this scholar topic needs focusing on.
\r\n\r\n\tThe general topic of "polynomials" is very large, and here the focus is both on scholar/student basics of it, and on applications of some special polynomials in science and research.
\r\n\r\n\tAn important topic of the book is "algebraic curve". Here the approaches are multiple: basic/scholar on one hand, and applications on the other hand. It must be noticed the use of algebraic curves properties in the field of differential equations, for example for finding the singularities.
\r\n\r\n\tGrobner basis is a very modern and applied topic of algebra. Here we must outline the great importance of Grobner basis and polynomial ideals manipulation, in the differential equations field, an example being in fast finding normal forms of differential systems.
\r\n\r\n\tRelated to this last topic of the book, but applying to all specified topics, it must be noticed the importance of numeric algorithms. The importance of software algorithms in all fields of science is continuously increasing. Therefore, computational approach of the specified algebraic topics is very useful, with applications in other mathematical and scientific fields.
",isbn:"978-1-83968-393-0",printIsbn:"978-1-83968-392-3",pdfIsbn:"978-1-83968-394-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"2a81efb05ce334905cc672188033b15d",bookSignature:"Dr. Adela Ionescu",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9907.jpg",keywords:"expand, factoring, combining, simplifying, random polynomials, special polynomials, orthogonal polynomials, polynomial factorization, two variables polynomials, homogenization, parameterization, singularity, monomial order, polynomial ideal, leading monomial, normal form",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 26th 2019",dateEndSecondStepPublish:"December 17th 2019",dateEndThirdStepPublish:"February 15th 2020",dateEndFourthStepPublish:"May 5th 2020",dateEndFifthStepPublish:"July 4th 2020",remainingDaysToSecondStep:"10 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,editors:[{id:"146822",title:"Dr.",name:"Adela",middleName:null,surname:"Ionescu",slug:"adela-ionescu",fullName:"Adela Ionescu",profilePictureURL:"https://mts.intechopen.com/storage/users/146822/images/system/146822.jpg",biography:"Dr. Adela Ionescu is a lecturer at the University of Craiova, Romania. She received her PhD degree from the Polytechnic University of Bucharest, Romania. Her research focuses on development and implementation of new methods in the qualitative and computational analysis of differential equations and their applications. This includes constructing adequate models for approaching the study of different industrial phenomena from a dynamical system standpoint and also from a computational fluid dynamics standpoint. By its optimizing techniques, the aim of the modeling is to facilitate the high understanding of the experimental phenomena and to implement new methods, techniques, and processes. Currently, Dr. Ionescu is working in developing new analytical techniques for linearizing nonlinear dynamical systems, with subsequent applications in experimental cases. The bifurcation theory and its applications in related fields is also a domain of interest for her. She has published six monographs and few scientific papers in high-impact journals. She is also a member of few scientific international associations and has attended more than 45 international conferences.",institutionString:"University of Craiova",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"University of Craiova",institutionURL:null,country:{name:"Romania"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"15",title:"Mathematics",slug:"mathematics"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"287827",firstName:"Gordan",lastName:"Tot",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/287827/images/8493_n.png",email:"gordan@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"6217",title:"Computational Fluid Dynamics",subtitle:"Basic Instruments and Applications in Science",isOpenForSubmission:!1,hash:"0fb7b242fd063d519b361e5c2c99187b",slug:"computational-fluid-dynamics-basic-instruments-and-applications-in-science",bookSignature:"Adela Ionescu",coverURL:"https://cdn.intechopen.com/books/images_new/6217.jpg",editedByType:"Edited by",editors:[{id:"146822",title:"Dr.",name:"Adela",surname:"Ionescu",slug:"adela-ionescu",fullName:"Adela Ionescu"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3794",title:"Swarm Intelligence",subtitle:"Focus on Ant and Particle Swarm Optimization",isOpenForSubmission:!1,hash:"5332a71035a274ecbf1c308df633a8ed",slug:"swarm_intelligence_focus_on_ant_and_particle_swarm_optimization",bookSignature:"Felix T.S. Chan and Manoj Kumar Tiwari",coverURL:"https://cdn.intechopen.com/books/images_new/3794.jpg",editedByType:"Edited by",editors:[{id:"252210",title:"Dr.",name:"Felix",surname:"Chan",slug:"felix-chan",fullName:"Felix Chan"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3621",title:"Silver Nanoparticles",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"silver-nanoparticles",bookSignature:"David Pozo Perez",coverURL:"https://cdn.intechopen.com/books/images_new/3621.jpg",editedByType:"Edited by",editors:[{id:"6667",title:"Dr.",name:"David",surname:"Pozo",slug:"david-pozo",fullName:"David Pozo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"40141",title:"Analysis of Kinetics Parameters Controlling Atomistic Reaction Process of a Quasi-Reversible Electrode System",doi:"10.5772/51896",slug:"analysis-of-kinetics-parameters-controlling-atomistic-reaction-process-of-a-quasi-reversible-electro",body:'For understanding the mechanism of electrolysis it is important to estimate kinetics parameters controlling the atomistic reaction process of metal electrode that is polarized in an electrolyte solution, but it seems not to have been performed satisfactorily. The reason for this is attributed to the fact that because actual electrode reactions proceed quasi-reversibly via consecutive two processes which consist of surface reaction and volume diffusion of ions involved in the reaction, the expression for its current density/overpotential relationship have become complex and not been presented explicitly. This is also related to the subjects of studies concerning the process of deposition or dissolution of atoms in crystal growth or its dissolution.
It is well known that the etch pits having a crystallographic symmetry are formed at dislocation sites of the low indices surfaces of a crystal which was etched under a specified condition (e.g. Gilman et al., 1958; Young, Jr., 1961). The dislocation etch pit is thought to be formed via a nucleation and growth process of two-dimensional pits at the dislocation site or via a spiral dissolution of the surface step which is caused by screw dislocation (Burton et al., 1951; Cabrela and Levine, 1956). Therefore elucidation of its formation mechanism is important for understanding of the surface step motion which is thought to play major role in the dissolution process of a crystal, and dissolution kinetics of crystals in the etch pit formation has been investigated and discussed by some researchers (e.g. Ives and Hirth, 1960; Schaarwächter, 1965; Jasper and Schaarwächter,1966; Van Der Hoek et al., 1983) so far.
However the research concerning parameters controlling surface step motion in the dissolution of crystals has not been satisfactorily performed. Especially it has not been examined quantitatively except for a few studies (e.g. Onuma, 1991). This is principally due to the reason that because the dissolution of a crystal proceeds generally via a dissolution reaction of surface atom and diffusion process of the dissolved atom (ion) into interior of solution, it is difficult to experimentally inspect the dissolution kinetics of surface step which depends on both processes. Since the dissolution rate of a metal crystal which is anodically dissolved under polarization in an electrolyte solution can be investigated by measurement of current density, dissolution mechanism of metal crystals has been researched electrochemically (e.g. Despic and Bockris, 1960; Lee and Nobe, 1986). However because of the same reason as the above mention, discussions on the results have become complex and not always contributed to understanding of surface step motion.
Recently, however, it has been proposed by the author that an expression to analyze the relationship between anodic current density and overpotential of a quasi-reversible electrode system including both the consecutive reaction processes is derived explicitly on the basis of an appropriate assumption (Imashimizu, 2010, 2011). According to the analysis, if the anodic and cathodic diffusion-limited current densities are measured for a given quasi-reversible electrode system, we can experimentally determine the kinetics parameters controlling dissolution process of crystals of the metal electrode, by assuming expressions for the activation and concentration overpotentials which are driving forces of surface reaction process and volume diffusion process respectively.
Thus the dissolution rates at dislocation-free and edge dislocation sites of (111) surface when a copper crystal was anodically dissolved in an electrolyte solution are investigated and discussed based on the above thinking, in this chapter. The relationships between anodic current density and overpotential are analyzed and discussed electrochemically by using the method developed for anodic dissolution processes of quasi-reversible electrode as described above. Activation enthalpy, transfer coefficient and surface concentrations of the ions involved in the dissolution process are experimentally estimated, and kinetics parameters controlling anodic reaction of the copper crystal/electrolyte system are quantitatively examined. An expression for the vertical dissolution rate at dislocation site is proposed based on a nucleation model of two-dimensional pit, and the critical free energy change at nucleation is quantitatively examined.
Single crystals of copper with [111] direction about 10 mm in diameter were prepared from the starting material of re-electrolyzed copper of 99.996 % purity by using the pulling method. They were divided into the cylindrical crystals approximately 15 mm length by a strain-free cutting. A terminal for detection of electric current and potential was soldered to an end surface of the cylindrical crystals. Another end surface was chemically polished so that the deviation of surface orientation from [111] direction is within 8.7×10-3 rad, and was further electrolytically polished in a high concentrated phosphoric acid solution. The crystal specimen was embedded in a Teflon holder with paraffin so that its polished surface is exposed. Then it was supplied for the electrolysis experiment after the boundary portion between the paraffin and the periphery of polished surface was covered with a vinyl seal having a hole 6 mm in diameter (Watanabé et al., 2003).
Schematic diagram of the electrolytic cell for this experiment is shown in Fig.1 (Watanabé et al., 2003). The crystal specimen was immersed in the electrolyte solution which consists of 5 kmol m-3 NaCl, 0.25 kmol m-3 NaBr and 10-4 kmol m-3 CuCl (Jasper and Schaarwächter, 1966) so that (111) surface of copper is located at approximately 5mm below the surface of electrolyte solution, and was held at a specified temperature. Then, the crystal specimen was set under a constant overpotential, and (111) surface of the crystal was anodically dissolved for a prescribed time, while anodic current density/time curve was recorded. The potentiostatic electrolysis experiments were performed at a range of lower overpotential and at a range of higher overpotential. After that the structure of dissolved surfaces were observed by use of the optical microscope system equipped with lens for interferometry.
Schematic diagram of electrolytic cell. S: sample; E: electrolyte; WE: terminal for potential and current; RE: saturated calomel electrode; CE: counter electrode of platinum wire; B: salt bridge; I: thermobath; R: Regulator; and T: thermometer.
Figure 2 shows typical anodic current density/time curves which were recorded while the copper crystal was anodically dissolved for 360 s or 600 s at the respective overpotentials. Anodic current density under any condition decreases steeply immediately after start of electrolysis and reaches a nearly constant current density is when it was carried out at an overpotential lower than about 125 mV as shown by the curve of 87 mV in Fig.2. Figures 3 (a), (b) and (c) are the optical micrographs of the (111) surfaces which were dissolved for 600 s at overpotentials in a range of 60 mV to 125 mV being held at 298K. The surfaces are rather smooth though etch pits tend to be formed as overpotential increases.
Anodic current density/time curves under potentiostatic electrolysis at 298K.
Optical micrographs of the surfaces which were anodically dissolved at lower overpotentials of (a): 58 mV, (b): 88 mV, and (c): 108 mV.
On the other hand, the current density reaches a minimum current density ism that is pointed by arrow after the initial steep decrease when an overpotential higher than about 125 mV was applied. Then it tends to increase gradually along with fluctuating and take a higher steady value as shown by the curve of 176 mV. Figures 4 (a), (b), and (c) are optical micrographs of the surfaces which were dissolved for 300 s at 156, 166, and 176 mV respectively being held at 298K. One can see that etch pits are significantly formed.
Optical micrographs of the surface that were anodically dissolved under potentiostatic electrolysis at higher overpotentials of (a): 156 mV; (b): 166 mV; (c): 176 mV.
The initial steep decrease of current density is principally due to the fact that a diffusion layer of the dissolved atoms (ions) forms in the neighborhood of crystal surface in process of time so as to decrease the undersaturation which is driving force for the dissolution. Therefore an approximately constant current density after its initial steep decrease is thought to be a steady current density is which flows accompanying with the consecutive two dissolution processes consisting of surface reaction and volume diffusion of dissolved atoms. This shows that the copper crystal/electrolyte system is a quasi-reversible electrode. Also the steady anodic current densities at lower overpotentials are thought to have only a little influence of formation of dislocation etch pits. Thus we assume that is is related to the vertical dissolution rate vs at dislocation-free site of surface, which is given by the following expression (Schaarwächter and Lücke, 1967):
where e [C] is elementary charge (electronic charge), n [1] the charge number transferred at reaction and Ω [m3] the atomic volume.
In this experiment, the potentiostatic electrolysis at overpotentials in a range from about 60 mV to 125 mV were carried out for 600 s at each temperature of 268, 283, 298 and 308 K and the relationships between the steady anodic current densities is and applied overpotentials η were investigated.
On the other hand, the current density reaches a minimum after an initial steep decrease as shown in the curve of 176 mV in Fig.2 when an overpotential higher than about 125mV was applied. Then it tends to increase gradually together with fluctuating and take a higher steady value as described in Section 2.3. This is thought to be due to the fact that etch pits remarkably formed at dislocation sites and grew along with time under higher overpotential as shown in Fig.4 (Schaarwächter and Lücke, 1967; Imashimizu and Watanabé, 1983). That is, it is because nucleation and growth of etch pits at dislocation site resulted in an increase of the anodic current density which represents an average dissolution rate of whole surface exposed to electrolyte solution as the areas occupied by etch pits increase. Based on the above knowledge, we assume that the initial minimum current density ism under potentiostatic electrolysis at higher overpotentials is approximately equal to a current density that is equivalent to the dissolution rate of dislocation-free site of surface because the contribution to anodic current density of dislocation etch pit formation is thought to be a little in the initial stage of electrolysis. That is, an average value of ism was assumed to give the vertical dissolution rate at dislocation-free site of surface approximately as represented by the relation:
Thus the electrolysis experiment was carried out for a prescribed time from 60 s to 360 s at each overpotential of 156, 166, 176 and 186 mV keeping the temperature at 298 K and at each temperature of 268, 283, 298 and 308 K under an overpotential of 176 mV. The initial minimum current densities ism were obtained from the anodic current density/time curves measured under every condition.
It needs to estimate activation overpotential ηa and concentration overpotential ηc for analyzing the relationship between anodic current density and applied overpotential as described in Section 1. Thus the polarization curves in a range of overpotential of about -400 mV to 400 mV were measured three times at each temperature of 298K and 308K by the potential step method. Then the anodic and cathodic diffusion-limited current densities were estimated.
After the (111) surface of a copper crystal specimen was anodically dissolved at every condition of specified overpotrntials and temperatures as described in Section 2.4.2, it was observed by use of the optical microscope equipped with objective lenses for two-beam interferometry and multiple interferometry.
Figure 5 (a) shows the micrograph of a part of boundary region between the crystal surface exposed to the electrolyte solution and the peripheral portion covered with vinyl seal, which was photographed with two-beam interferometry mode. The vertical dissolution amounts s of surface shown by the illustration was measured from a deviation of the interference stripes caused by the step which was formed at that boundary region after dissolved. The vertical dissolution amounts s of surface under each condition was plotted against dissolution time t. The increasing rate
Figures 5 (b) and (c) show a pair of micrographs of identical dislocation etch pits formed on dissolved surface which were photographed with optical mode and multiple interferometry mode. In this work, the depth d of the dark (deep) pits that were formed at positive edge dislocation sites (see Appendix A1) were measured by drawing the vertical cross sections of the pits that is shown by the illustration with use of the micrograph pairs such as Figs.5 (b) and (c). Also the width w (average distance from center to the three sides of pit) of those dark pits that is shown by the illustration were measured on the micrograph such as Fig.5 (b). Measurements of the depth and width of pit were performed about more than 20 dark pits formed on the surface dissolved under every condition, and the respective average values d and w were obtained. The depth d and the width w of dark pits were plotted against dissolution time t.
a): Two-beam interferometry micrograph at the boundary between dissolved and undissolved surfaces; (b): Optical micrograph; (c): Multiple interferometry micrograph of the same view as b.
The increasing rate
where vs means the vertical dissolution rate at dislocation-free site of the surface. Also the increasing rate
Under potentiostatic electrolysis of the copper/electrolyte system in the present experiment, the copper crystal is thought to be dissolved accompanying an anodic current according to a simple electrode reaction expressed by the following equation (Lal and Thirsk, 1953; Jasper and Scaarwächter, 1966):
where the contribution to current density of reaction of Br- ion involved in dissolution process as inhibitor is assumed to be disregarded. The anodic current density is flowing steadily at an applied overpotential η is generally expressed by a relation:
where exchange current density i0 is represented by
(Tamamushi, 1967; Maeda 1961). ks is surface density of kink that is active site at dissolution of surface atom, α the transfer coefficient, ΔH0 the activation energy (enthalpy) at dissolution of an atom, ν the atomic frequency, and β a supplementary factor of rate constant of electrode reaction. Also, CCl- and CCuCl2- are the surface concentrations of Cl- and CuCl2- ions involved in a steady anodic dissolution, and C0Cl- and C0CuCl2- the ones in equilibrium state. They are represented as a relative surface density as follows.
If the electrolyte solution contacting with crystal surface contained X ions of m kmol m-3, the surface concentration CX [1] can be expressed by the following relation:
where NA is the Avogadro constant, bb* the area occupied by an atom and ξ the thickness of electrolyte solution layer contacting with the crystal surface (Imashimizu, 2011).
The anodic dissolution of copper crystal in this experiment is thought to proceed quasi-reversibly with a surface reaction and volume diffusion of dissolution atom as described in Section 2.4.1. So we assume that the activation overpotential ηa and the concentration overpotential ηc are written by
where the folloing relations:
are given, if ilCl- and ilCuCl2- are the anodic and cathodic diffusion-limited current densities of the electrode reaction respectively (Tamamushi, 1967). Thus activation overpotential ηa and concentration overpotential ηc are assumed to be given by Eqs.(9) and (10), when the anodic dissolution of copper crystal proceeds steadily at an applied overpotential η by a quasi-reversible electrode reaction of Eq.(5). Also surface undersaturation σ is defined by
Then, the Eq.(6) is reduced to
by using Eqs. (7), (9) and (11). Also Eq.(12) leads to the following relation:
Thus if the anodic and cathodic diffusion-limited current densities ilCl− and ilCuCl2- are obtained, the experimental relationship of is/η would be represented with use of Eqs.(10) and (11) by Eq.(13). Then α and i0(T) would be estimated from the gradient and the constant term of the linear relationship of ln{is(CCl-/C0Cl-)-2σ\n\t\t\t\t\t-1} vs. neη/kT. Also ΔH0 would be estimated from the gradient of the linear relationship of ln{i0(T)} vs. 1/T.
On the other hand, concerning the complex term consisting of surface concentrations of Cl− and CuCl2− ions,
\n\t\t\t\tis lead from Eq.(9). Therefore applying Eq.(14) to Eq.(12) lead to
where ΔH is given by the relation:
We can see that Eqs.(15) and (16) are formulae for the steady current density expressed with use of the parameters β, ks, CCl-, CCuCl2-, σ, α and ΔH involved in the surface reaction process when the anodic dissolution progresses steadily by a quasi-reversible electrode reaction.
Thus undersaturation σ, transfer coefficient α and activation enthalpy ΔH0 for the anodic dissolution reaction of copper crystal/electrolyte system will be estimated from experimental results, and a supplementary factor β and kink density ks will be examined by a model of crystal dissolution in this study.
The polarization characteristic of the copper crystal/electrolyte system at 298K is shown in Fig. 6. The anodic and cathodic diffusion-limited current densities ilCl- and ilCuCl2- shown in the diagram were obtained by averaging the values measured three times. Table 1 shows those diffusion-limited current densities obtained from the polarization characteristics measured at 298 and 308 K by a similar method.
Polarization curve of the copper crystal/elecrolyte system. ilCl- and ilCuCl2- mean the anodic and cathodic difffusion-limited current densities.
T /K | ilCl-/A m-2 | ilCuCl2-/ A m-2 |
298 | 827 | -0.0732 |
308 | 1072 | -0.156 |
Measurements of the anodic and cathodic diffusion-limited current densities ilCl- and ilCuCl2-.
The undersaturation σ were estimated from experimental polarization characteristics such as Fig.6 with use of Eqs.(10) and (11). The diagram that plotted σ against neη/kT in a range of (neη/kT) about 0 to 6 is shown in Fig.7. The black dots in the diagram show the values of σ which are calculated from the (is/ilCl-)/(neη/kT) relationship that was derived by substituting the experimental values i0, α, ilCl and ilCuCl2 into Eq.(6).
The experimental relationships of σ/(neη/kT) at 298K and 308K approximately consist with each other, and also with the calculated relationship. However, the experimental curves of σ/(neη/kT) deviate from the calculated curve in a range of (neη/kT) larger than about 5. This is because the experimental current density includes an increase of current density attributed to significant formation of etch pits at higher overpotentials than about 125 mV. We assumed that the σ/(neη/kT) relationship does not almost depend on temperature from the result of Fig.7.
Plots of undersaturation σ against normalized overpotential neη/kT. σ(298) and σ(308) designate experimental values at 298K and 308K respectively. σ(cal) is the calculated one.
Figure 8 is the diagram that plotted the steady current densities against overpotentials lower than 127 mV which were measured at 268K, 283K, 298K and 308K. Figure 9(a) is the diagram that plotted ln(isσ−1) obtained from Fig. 8 against neη/kT at every temperature taking account of (CCl-/C0Cl-)−2 ≈1. The linear relationships at every temperature in the diagram are drawn so that they have a same gradient given by averaging. The transfer coefficient α was estimated from the gradient of their linear relationships. Then also the exchange current densities i0(T) at each temperature were estimated from the constant terms of them. Figure 9(b) is the diagram that plotted ln{i0(T)} against 1/T. The activation enthalpy for the anodic dissolution reaction of copper crystals was estimated from the gradient of the linear relationship shown in Fig. 9(b).
Plots of steady current densities against overpotentials lower than about 125 mV
a): Plots of ln(isσ-1) against neη/kT; (b): Plot of ln{i0(T)} against 1/T.
Then, because surface concentrations C0Cl-and C0CuCl2 of Cl− and CuCl2− ions are calculated by Eq.(8) when (111) surface of a copper crystal is in equilibrium with the electrolyte solution consisting of 5 kmol m-3 NaCl and 10-4 kmol m-3 CuCl, the complex term C0Cl-2(1-α)C0CuCl2-α in Eq.(7) giving exchange current density can be evaluated by using the transfer coefficient α estimated above.
Thus the estimations of parameters controlling exchange current density are summarized in Table 2. The value of βks was evaluated by substituting i0, ΔH0 and C0Cl-2(1-α)C0CuCl2-α into Eq.(7), where the atomic frequency ν = 6.21×1012 [s-1], elementary electric charge, e = 1.602× 10-19[C] and n = 1 were assumed.
α | ΔH0 / eV | i0 /10-2A m-2 | C0Cl-2(1-α)C0CuCl2-α | β ks /1016 m-2 |
0.84 | 0.33 | 8.2* | 2.36×10-6 | 1.32 |
Estimation of transfer coefficient α, activation enthalpy ΔH0, exchange current density i0 at 298K, and a factor β ks affecting reaction rate constant.
Figures 10 (a) and (b) are examples of the anodic current density/time curves which were recorded when the copper crystal was dissolved for 240 s at higher overpotential. The vertical dissolution rate vsm at dislocation-free site of surface under every condition was determined from an average of the initial minimum current densities ism pointed by arrow of i/t curves (measured for five different dissolution time in a range of 60 s to 360 s under each condition) shown in Fig.10 as described in Sections 2.4.2.
Examples of anodic current density/time curves. (a): The effect of overpotential; (b): The effect of temperature. Initial minimum ism was obtained in every curve.
Figures 11 (a) and (b) are the diagrams that plotted vertical dissolution amounts s of surface against dissolution time t as described in Sections 2.6.1. The vertical dissolution rates
Vertical dissolution amounts of surface vs. dissolution time. (a): Effect of overpotential at 298K; (b): Effect of temperature at 176mV
Figures 12 (a) and (b) are the diagram that plotted the depth d of the dark etch pits which were formed at positive edge dislocation sites on the surface dissolved under each condition against dissolution time t, as described in Sections 2.6.2. Also Figs.13 (a) and (b) are the diagrams that plotted similarly the width w of the same dark etch pits as the above mention against dissolution time t. The increasing rate
Depth of dark etch pit vs. dissolution time. (a): Effect of overpotential at 298K; (b): Effect of temperature at 176mV
Width of dark etch pit vs. dissolution time. (a): Effect of overpotential at 298K; (b): Effect of temperature at 176mV.
Figures 14 (a) and (b) are the diagrams that plotted the logarithm values of the dissolution rates. It can be seen that the value of log vsm approximately consists with that of log
a): Plots on a logarithmic scale of dissolution rates vsm, s˙, ved, and vw against overpotential η; (b): Similar plots of vsm, s˙, ved, and vw against temperature T
It can be seen that both log vsm and log vw tend to increase rather homogeneously with an increase of η, from Fig.14 (a). However, the tendency of log ved are somewhat different and in accelerative. Also, it can be seen from Fig.14 (b) that though log vsm and log vw tend to similarly increase with an increase of T, the tendency of log ved are somewhat little, compared to the former two. This is seen from the fact that the increasing rate (Δlog ved/ΔT = 5.4×10-3) of the latter is less than that (Δlog vsm/ΔT = 1.1×10-2, Δlog vw/ΔT =1.4×10-2) of the former two.
Concerning the dissolution of a crystal, the atomistic model illustrated in schematic diagram of Fig.15 has been proposed (Burton et al., 1951; Schaarwächter, 1965). The dissolution of crystals proceeds via a lateral retreat motion of surface step of an atomic height that is induced by dissolving of surface atom from the kink sites into the solution. The vertical dissolution rate vs of surface is given by lateral retreat rate vh and surface density tanθ of surface step, which is expressed by the following equation:
where θ is an average inclination of crystal surface to a low index face, a an atomic height of surface step, and λ the mean distance between adjacent surface steps. The lateral retreat rate vh of surface step is expressed by
where ΔHs is the activation enthalpy for dissolution of an atom at kink site of surface step, ν the atomic frequency, k* the retreat rate constant of surface step, and b* the unit retreat distance. σs is surface undersaturation, which is written as
where Δμ is the chemical potential difference of dissolution atom between two phases of a crystal/ solution system (Schaarwächter, 1965).
Atomistic model for dissolution process of a crystal surface. Atom dissolves from kink site of surface step into solution. K: Kink; S: Surface step; T: Terrace; A: Ad-atom
The dislocation etch pit is thought to be formed via a successive nucleation and growth processes of two-dimensional pits at the dislocation site (Schaarwächter, 1965) or via a spiral dissolution of the surface step which is caused by screw dislocation (Cabrera and Levine, 1956). We discuss the dissolution rate at edge dislocation site of (111) surface of copper crystals, based on a nucleation and growth model of two-dimensional pits (Schaarwächter, 1965) that is illustrated in Fig 16, in the following.
Since the lateral dissolution rate vw is thought to represent horizontal growth rate of two-dimensional pit nucleated at edge dislocation site of surface, it may be corresponding to the lateral retreat rate vh of surface step along (111) face. Thus we assume that vh is given by vw as shown in the following relation:
On the other hand the vertical dissolution rate at positive edge dislocation site would be examined by the nucleation rate of two-dimensional pit at dislocation site as follows.
Illustration for dislocation etch pit formation by successive nucleation and growth of two-dimensional pits. D: Dislocation; S: Surface step; K: Kink.
According to the classical nucleation theory, if ΔGed* is the critical free energy change at nucleation of a two-dimensional pit at edge dislocation site, a steady state nucleation rate I of two-dimensional pit would be expressed by
where r is a separation rate of an atom from an active site of the two-dimensional pit into the solution and Z the Zeldovich factor (Toschev, 1973). Since the separation rate r is assumed to be a similar quantity to the dissolution rate of an atom from kink site of surface, it depends on the surface concentrations of Cl− and CuCl2− ions as known from the Eq. (15) in Section 2.7, and is expressed by
Accordingly, the vertical dissolution rate ved at edge dislocation site of surface is expressed by
where a is the depth of "two-dimensional pit and Ks is an undetermined constant including Zeldovich factor and others (see Appendix A2.).
According to the nucleation theory of dissolution of crystals, ΔGed* is small compared to ΔGs* which is the critical free energy change at nucleation of a two-dimensional pit at dislocation-free site of surface, because of strain energy of dislocation core. It is expressed by
and
where γ is the interfacial free energy of the crystal and solution at step of the two-dimensional pit, G the shear modulus and q and αc the constants (Schaarwächter, 1965).
When the copper crystal is anodically dissolved by the simple electrode reaction of Eq.(5) the vertical dissolution rate vs of dislocation-free surface at lower overpotentials and the vsm at higher overpotentials would be estimated by Eq.(1) and Eq.(2) respectively as described in Section 2.4. Thus it is experimentally estimated with use of Eqs. (1), (2), and (15) by the following expression:
According to the dissolution model of crystals, the dissolution rate at dislocation-free site of surface is expressed from Eqs. (17) and (18) by
Therefore, the following relations are obtained from Eqs.(16), (26) and (27) concerning the rate constant of the lateral retreat rate of surface step and activation enthalpy for the dissolution.
and
is obtained. It can be seen that the rate constant k* of lateral retreat motion of surface step is electrochemically expressed by Eq.(28) and that it increases with an increase of concentration overpotential ηc.
As mentioned above the dissolution rate vsm at dislocation-free site of surface under higher overpotentials is expressed by an approximate equation:
from Eqs. (14) and (26), where we assumed is << ilCl-, that is,
Thus concerning the dissolution rate at dislocation-free site of surface which have a constant kink density ks, a following approximate expression is lead from Eq.(31) (Imashimizu, 2011).
Figures 17 (a) and (b) are the diagrams that plotted the dissolution rate vsm shown in Figs.14 (a) and (b) on a natural logarithmic scale against η (T = 298K) and 1/T (η =176mV) respectively. It can be seen that the values of (αne/kT) and ((ΔH0 −αneη)/k) are estimated by comparing the Eq.(33) with gradients of the linear relationships drawn in Figs. 17 (a) and (b), because the overpotential and temperature dependences of σ in the range of 156 mV to 186 mV are assumed to be a little. Thus, α and ΔH0 were also obtained from overpotential dependence of vertical dissolution rate vsm of surface at higher overpotentials and temperature dependence of that. The estimations are shown in Table 3, showing α and ΔH0 are in good agreement with those values in Table 2.
Vertical dissolution rate vsm at dislocation-free site of surface on a natural logarithm scale. (a): The plot against overpotential η; (b): The plots against the inverse 1/T of temperature.
According to atomistic dissolution model of a crystal surface illustrated in Fig.15, the relation of θ = tan-1(a/λ) = tan-1(vs/vh) is lead from Eq. (17), which represents the inclination angle of surface to (111) face. Since it is approximately given by θ ≈ θ * = tan-1(vsm/vw) with use of Eqs.(20) and (26), the values of θ* obtained from Fig.14 were plotted against η and T in Figs.18 (a) and (b). It can be seen that the tendencies of change in θ * against η and T are not clear and not reasonable. The average value of θ *av is 2.1×10-2 rad, which is a little large compared to a deviation 8.7×10-3 rad from [111] direction that was aimed when we prepared the surface of specimen as described in Section 2.1. This is probably attributed to the fact that actual surface exposed to electrolyte solution was slightly spherical as a whole and was having microscopic swells. That is, the variation of their values seems to be due to experimental error. Thus the vertical dissolution rate at dislocation-free site of surface is assumed to be given by retreat rate of the surface steps which preexists on the prepared surface, which gives following relation:
Accordingly
Inclination of surface to (111) face, which is given by θ *= tan-1(vsm/vw).
α | ΔH0/eV | vsm/m s-1 | β b/x0 | ved/m s-1 | ΔGed*/eV | |
Ks = 1 | Ks = 0.2 | |||||
0.85 | 0.33 | 1.6×10-9† | 0.034† | 5.7×10-9† | 0.16† | 0.12† |
Estimations of kinetics parameters controlling dissolution rate at edge dislocation site of surface of copper crystals.
As mentioned in Section 4.1.2 the dissolution rate ved at edge dislocation site is expressed by Eq. (23), but if Eq. (14) is applied it is reduced to
Accordingly, if we assume CCl-/C0Cl- ≈ 1, ΔGed* is given by
Thus ΔGed* under each condition was estimated by Eq.(36) with use of experimental value of ved as well as estimations of α and ΔH0 which were obtained in Section 4.2.2. The ΔGed* estimated with use of two assumed values of undetermined constant Ks for a specified condition (η = 176 mV and T = 298K) are shown together with the values α and ΔH0 in Table 3, where a = 2.09×10-10 m and ν = 6.21×1012 s-1 were used.
According to the precedent theoretical study (Schaarwächter 1965), in which the conditions for the formation of visible etch pit at dislocation site were investigated on the basis of a proposed nucleation model, the critical free energy change is estimated to be 0.115 eV. The present estimation of ΔGed* approximately consists with that value as shown in Table 3, though the exact value of Ks can not be evaluated in this study. This is seemed to be reasonable as described in Appendix A2.
On the other hand, however, it was admitted that the value of ΔGed* varies with overpotential and temperature as mentioned below.
Figures 19 (a) and (b) are the diagrams that plotted the square root of ΔGed* estimated assuming Ks = 1 by Eq. (36) against η and T respectively. It can be seen that ΔGed*1/2 is not constant but changes in different manners with increases in η and T. The reason for this is probably that ΔGed*1/2 is proportional to the interfacial energy γ as known from Eqs. (24) and (25).
Square root of the critical free energy change for the formation of a two-dimensional pit. (a): The overpotential dependence; (b): The temperature dependence.
It is known that the interfacial energy varies with electrode potential according to so-called electrocapillary curve (Tamamushi, 1967). Therefore, the change in ΔGed*1/2 with η is surmised to be due to the potential dependence of γ, because the overpotential dependences of the undersaturation σ and therefore that of Δμ = neηa = −kTln(1-σ) in an overpotential range of 156 to 186 mV are assumed to be a little as described in Section 4.2.2. This is supported by the fact that Fig.19 (a) indicates a quadratic dependence similar to the electrocapillary curve. Also, it is inferred from Fig.19(b) and\n\t\t\t\t\t\tEq.(24) that γ should increase with an increase in Τ, becauseΔμ tend to increase with increase in T. This is probably attributed to a decrease in specific adsorption of anion accompanied by an increase of interfacial energy with rising of temperature.
The overpotential dependence of log ved is in accelerative, and somewhat different from that of both log vsm and log vw. Also the increasing rate of log ved with increase in temperature is smaller than that of both log vsm and log vw as shown in Figs.14 (a) and (b). The reason for this seems to be attributed to the overpotential and temperature dependences of the interfacial energy of the electrode surface as mentioned above.
Following conclusions were obtained from the results and discussion:
The transfer coefficient, activation enthalpy and surface concentrations of the ions which control the dissolution reaction were estimated from measurements of the relationships between steady anodic current densities and applied overpotentials when copper crystals are dissolved in an electrolyte solution under potentiostatic electrolysis.
The values of a supplementary factor and kink density affecting rate constant of dissolution reaction were examined.
The dissolution rate at edge dislocation site of (111) surface of copper was discussed quantitatively by a nucleation model of two-dimensional pit based on the classical nucleation theory.
The present estimation of the critical free energy change ΔGed* for nucleation of a two-dimensional pit at edge dislocation site reasonably consisted with the evaluation by the precedent study.
The overpotential and temperature dependences of dissolution rate at edge dislocation site were somewhat different from those dependences of dissolution rate at dislocation-free site. The reason for this is probably that ΔGed* changes according to the overpotential and temperature dependences of interfacial energy.
The surface of copper specimen on which some small glass spheres 300 μm in diameter were dropped beforehand was anodically etched by the present method. Fig.20 (a) is an optical micrograph of dissolved surface in which Rosseta pattern composed of dark and light etch pits was formed at the portion that was hit by a small glass sphere. This proves that dark and light etch pits are formed at the sites of positive and negative edge dislocations respectively because the six arms of Rosseta pattern are composed of rows of a pair of positive and negative edge dislocations.
Optical micrographs for identifications of dark and light pits. The surfaces dissolved by the present method; (a): Rosetta pattern composed of etch pits; (b): a distribution of etch pits. (c): etch pits formed by a chemical etchant in the same portion as that observed in b.
In another experiment, the surface of prepared copper specimen was anodically etched first by the present method, and a distribution of etch pits were observed by the optical microscope. Subsequently after electropolished the etched surface of specimen, the surface was etched for 10 s by a modified Young\'s etchant prepared by Marukawa (Marukawa, 1967), and the same portion as the previous portion was observed. Figs.20 (b) and (c) are a pair of optical micrographs of the surfaces etched by such two methods. It has been reported by Marukawa that the dark (deep) and light (shallow) pits are formed at screw dislocations and edge dislocations on the surface etched by the modified Young\'s etchant respectively. Accordingly it can be seen that the light etch pits are formed at the sites of screw dislocations on the surface that was anodically etched by the present method, by comparing the kinds of etch pits which are observed in these micrographs. Thus Table 4 is obtained concerning dislocation characters related to dark and light etch pits.
Etching | Edge dislcation | Screw dislcation | |
(positive) | (negative) | ||
Chemical† | Light | Light | Dark |
Electrolytic†† | Dark | Light | Light |
Relations between the dislocation characters and the kinds of etch pits which are formed by two etching methods
In this work, the depth and width of the dark (deep) pits were measured to investigate the dissolution amounts at positive edge dislocation sites.
As described in the Section 4.1.3, if the separation rate r of an atom at nucleation of two-dimensional pit is a quantity similar to the dissolution rate of an atom from kink site of surface, it would need to take account of supplementary factor β affecting the exchange current density as a parameter involved in the separation rate r. Then the dissolution rate ved at edge dislocation site derived from the nucleation rate Eq. (21) is represented afresh by
Thus, we assume that the undetermined constant Ks is approximately given by a relation:
We have assumed in the Section 2.7 that the exchange current density i0 is given by Eq. (7) for simplification, but to be exact i0 should be expressed with use of the activities of the ions involved in the electrode reaction instead of the concentrations. Also, transmission coefficient should be taken account of as pre-exponential factors in Eq. (7). Therefore it is generally hard to estimate β including some unknown factors. However, concerning β of the present electrode reaction, β (b/x0) = 0.034 was estimated experimentally as shown in Table 3. Also it can be seen from an observation of etch pit by optical microscope that surface steps have a structure along a crystallographic direction of the crystal. Accordingly if (b/x0) is assumed to be a quantity of 0.02 to 0.2, it would give an estimation of β = 0.17~1.7.
On the other hand, if we assume the free energy change ΔGed (j) for formation of a two-dimensional pit consisting of j vacancies at edge dislocation site, it is written as
Then the critical size j* of two-dimensional pit and the critical free energy change ΔGed*( j*) are given by
respectively. It can be seen that ΔGed*(j*) is expressed by the same relation as Eq. (24), and that the factor p’ has the same contents with Eq. (25), that is, p’ = p. Then, Zeldovich factor is expressed from the definition (Toschev, 1973) by
Accordingly, Z = 0.76 is estimated, if p = 0.18 (Schaarwächter 1965), Δμ = 0.027 eV(σ = 0.65) (Imashimizu, 2011), ΔGed* = 0.12 eV (Table 3) and kT = 0.0257 eV (T = 298K) are used.
Thus Ks = 0.13~1.3 is estimated from Eq. (38), which suggests the reasonability of the assumed value of Ks shown in Table 3.
Our twenty-first century world is awash with information. One need only look at the amount of information on the Internet about any topic, and the likelihood is that the number of sites is in the tens of thousands, if not more, at least for topics which are popular. It is not the lack of information which is the bane of our century, but the plethora, metaphorically the fire hose of information.
Our thinking to deal with such an abundance of information is either to shut out most of it, or do some type of directed search for the topic. One cannot absorb the totality of information in a popular subject, nor perhaps even form a reasonable opinion based upon deep knowledge, unless perhaps one has specialized in the topic and has amassed a great deal of information after years of practice. There are of course tools which sift ideas, such as Google® for conventional websites, and Google Scholar® for academic papers. These sifting tools aggregate data “on the fly,” presenting the raw material as different sites to explore. One can then use the Google® tools to get a sense of what is “au courant,” although the effort to do so may be more daunting in the execution than in the expectations before the effort is made.
With the foregoing introduction, the next question is how does the novice, whether scientist or simply interested layman, learn about the mind of a consumer toward a specific product? For instance, let the product be “milk.” A Google® search of consumer + milk shows a mere 130 million sites. Refining the focus for Consumer Attitudes Regarding Milk, again on Google® revealed 6,280,000 hits. A more focused search, this time for academic papers, on Google Scholar®, for Consumer Attitudes Towards Milk, revealed 90,700 hits. Certainly, enough for a number of PhDs, and for a lifetime of reading, but what about the practical problem of the small, even a start-up company, wanting to develop a new product? The “plethora of choice” in the world of information is simply paralyzing, so that the expeditious answer is to guess, to solicit the advice of an expert, to buy a book of trends in food, to run a focus group, or perhaps to spend a great deal of money developing products and concepts with the full confidence that it MUST BE GOOD [1, 2].
Whether the foregoing picture presents a positive development, a negative development, or perhaps just a development without valence is not the issue. The issue for this chapter is whether one can use the mass of information to understand issues, say in dairy, with these issues relating to the attitudes of consumers. Simply stated, can we create a system to rapidly and profoundly understand the mind of the consumer regarding a specific topic, and, where possible, incorporate the contribution of the “Big Data of Relevant Information?”
For a century now, the norm for understanding subjective reactions to products has been to ask people to talk about these products in focus groups or other qualitative methods [3], and for those who are quantitatively oriented, to ask questions of people in a survey. Often surveys begin with topics about what one does in general, such as food preferences and food habits [4], now evolving down to a momentary survey after a relevant experience to ask ‘How did we do?, or ‘Would you recommend us to someone with whom you do business?’ the now-ubiquitous NPS, (Net Promoter Score), analyzed by [5].
As the amount of information increases, and as companies run surveys about the attitudes and usages of product, whether dairy or other food products, it is becoming increasingly obvious that data are cheap to obtain, but true knowledge of the so-called actionable nature is expensive. By actionable, we mean the use of the data to effect some change, whether that be convincing someone to try or buy a product, or learning how to change the ingredients of a product to increase acceptance. Surveys are limited to the respondent’s conscious efforts to answer the interviewer’s questions. Often, they require knowledge to which the respondent may not be privy, or may require “politically correct” answers. An example of the former, information to which the respondent is not privy, is what to do to change the fat content of milk, or to make the milk taste like it is full fat. The latter, “politically correct” answers come from the desire to give the correct or socially approved answer. For example, a person who loves whipped cream in great amount on cake as a delicious dessert may simply not describe dessert preferences, or when doing so may consciously or perhaps even unconsciously forget one’s lifelong obsession with mountains of whipped cream when allowed to consume it.
The sheer abundance of data, this so-called “hydrant effect” may seduce one into thinking that the “answers are there” but the reality is that one learns far more from simple experiments. In recent years, author HRM has introduced the new, now more rapidly emergent science of Mind Genomics [6, 7]. The name Mind Genomics is metaphorical. It posits that knowledge about decision-making comes from presenting people with combinations of ideas of different types, measuring their responses, and determining which ideas or sets of ideas (mind-genomes) drive the decision-making. To further the metaphor, each topic area of experience comprises a variety of aspects. The aspects of a topic to which a person attends while making a decision are the so-called “mind genomes.” Furthermore, each topic area has a limited set of these mind-genomes, almost mind-alleles, in some sense.
Mind Genomics has already been applied to the dairy world in a number of different, easy-to-do experiments. For example, one study looked at the different ways of making a decision about what a dairy product (yogurt) is worth. Through the Mind Genomics method, it became possible to extract various mind-genomes about yogurt, with each person embodying one of a set of mutually exclusive genomes. The objective of that study was to identify a group of individuals who valued texture or mouthfeel as the basic criterion for decision-making [8].
Other studies of dairy have involved products such as milk, yogurt, cheese and so forth.
We live in an age of instant gratification, of superficial thinking, of information abundance, and most sadly, a belief that whatever we do has to be made simple, dumbed down. When our focus is to understand the mind of the consumer toward a dairy product, this might mean running a few focus groups to get a “sense” of today’s customer, or doing a general survey about dairy using any of the widely available survey platforms like Survey Monkey® [9]. One could also mine the Web for information, and produce a summarized report of trends. The aforementioned approach provides a great deal of information, often delightfully presented in newsletters, at conferences, at webinars. Yet, there is something missing, the translation of the information into product concepts.
One of the most common, traditional methods of using the data is to present the information from these surveys, focus groups, and so forth to the agency and marketing professionals, often called “creatives.” It becomes the job of the creative to synthesize the information, and with her or his skill, experience, and insight, to emerge with the final “idea,” whether the idea be fully formed or even modestly sketched out.
We are accustomed to experiments in the world of physical features. These experiments may range from a simple change in a product, and the measurement of the consumer response to the product (so-called “cook and look”), all the way up to DOE, Design of Experiment [10]. DOE specifies different combinations of ingredients, and then measures the response to the combination in order to identify what each product ingredient contributes, and how a specific combination performs in a consumer test. DOE is usually in the purview of R&D, and represents a dramatic investment of time and money, but also an increase in the opportunity for a corporate success.
We deal in this chapter with consumer knowledge, ideas. How does one experiment with ideas about dairy? The answer to this question is quite simple. One can present ideas, simple or compound, about a dairy product, and obtain ratings about the ideas. Figure 1 shows an example of three advertisements about yogurt from Chobani®, presented in the original language, and deconstructed as a preparation for analysis by experimental design:
Comparison of three text advertisements for Chobani® yogurt taken from the Web (December, 2018), and their deconstruction for study by experimental design (Mind Genomics).
The choice of concepts in Figure 1 is simply that. The reasons behind the choice must be left to probing questions asked of those who evaluated the concepts, and/or left to the talented researcher who can “connect the dots” and tell an engaging, and possibly insightful story.
A better way to understand the world of dairy from the mind of the consumer involves experimentation, preferably easy, fast, and inexpensive experimentation that anyone can do [11]. We illustrate the strategy with data from a study that required a total of 6 hours, done at a very low cost, dealing with yogurt. The emphasis on speed, cost, and simplicity is important for the tenor of the chapter. Our goal is to present a new paradigm, more powerful than other previous approaches, as well as far faster, and significantly more economical, all leitmotifs for today, as of this writing (December, 2018). The strategy is very simple, encapsulated in Table 1.
Step | Activity | Rationale |
---|---|---|
1 | Identify the topic | The topic may be product, service, or literally anything where human experience and judgment play a key role. |
2 | Interrogate the Web and social media using artificial intelligence | The Web and social media present an almost inexhaustible number of ideas. Mine the Web and social media to extract “ideas” in rough form, simple if possible. Consider these to be “nuggets of ideas,” a semi-structured reservoir of raw material. |
3 | Put the Web output aside, and concentrate on the topic, by formulating four questions | The objective is to find four aspects of the topic that can be put as questions which together, and in sequence, tell a story. The topic is the description of the product, for this study of yogurt. |
4 | Edit the four questions, and set them up to be answered | The questions require the user to “think” about the story of what the product is. The questions will never be shown to the respondent. The questions will be used simply to promote creative thought. |
5 | Answer each question with four answers | Return now to the information extracted by artificial intelligence. With the four questions as a guide, and with the semi-structured reservoir of raw material, provide four answers or phrases for each question. One’s mind, one’s creative intuitions from the semi-structured reservoir of ideas, and one’s ability to craft a sentence allow one to generate the necessary four answers to each of four questions, or sixteen answers in total. |
6 | Create an introduction for the respondents to read | Make the introduction simple, with little information other than what the study is about, and what the respondent should do. The information will come from the answers to the questions (the messages, the elements). |
7 | Create a rating scale | The scale comprises a question and an anchored scale (lowest and highest scale points each have a defining phrase). What do you want the respondent to consider when making a judgment? The easiest is an evaluative attribute, such as: How interested are you in this product? |
8 | Select respondents | The entire objective of the exercise is to have respondents judge these ideas. The respondents who participate may come from the corporation’s customers, or from a commercial panel. It is always easier to work with panelists who are compensated for their participation. The fastest, easiest, and often the most productive way is to work with a commercial company. |
9 | Get classification information | Find out age, and gender. Put in a third classification question dealing with the topic. The APP used here is limited to three classification questions to make the system quick and inexpensive to execute. |
10 | Present the respondent with 24 vignettes, one after another | Each respondent evaluates a UNIQUE SET OF 24 VIGNETTES. This unique set is important. It means that increasing the number of respondents allows the researcher to test more of the “space of the combinations” rather than simply testing the same combinations again and again. |
11 | Collect the rating from each vignette and measure response time | The response time is the time from the presentation of the vignette on the screen to the response. The time is measured in seconds. |
12 | Ask the respondent another question, open-ended, about a relevant aspect of the topic | Optional, to obtain more information from the respondent about her or his feelings. |
13 | Transform the 9-point ratings to binary | For the typical, most-used, 9-point scale, convert the rating of 1–6 to 0. Convert the rating of 7–9 to 100. Then add a very small random number to the now-converted value of 0 or 100, respectively. The reason for the transformation is that although the rating scale is easy to use, it is not clear what a scale value means. It is a lot easier to use a binary scale. The key is how to bisect the 9-point rating scale. We are somewhat stringent, with “no” corresponding to the bottom 2/3 of the scale, and “yes” corresponding to the top 1/3 of the scale. |
14 | At the level of the individual respondent, use OLS (ordinary least-squares) regression to relate the presence/absence of the 16 answers to the binary ratings (0/100) | The vignettes were constructed according to a basic experimental design. The design was permuted for each respondent. The experimental design allows us to estimate the coefficients of the model for each respondent. The equation created is of the form: Binary Rating = k0 + k1(A1) + k2(A2) … k16(D4). For other, bigger designs, also created in this fashion, using a permuted individual-level design, there may be more questions and more answers per question. The mathematics is precisely the same. The only difference is the number of coefficients. There is one coefficient for each answer. |
15 | OLS relates the presence/absence of the 16 answers to the response time | Using the same mathematics, create another model for each respondent, this time using response time as the dependent variable. Prepare the data by recoding any response time of 30 seconds or over as 30 seconds because the longer time probably represents an interruption in the experiment. The equation does not have the additive constant, k0. We write it as follows: Time (seconds) = k1(A1) + k2(A2) … k16(D4). |
16 | The unit of analysis is the individual coefficient | By applying OLS regression to the data from each respondent, we ensure that each respondent generates an individual set of 16 coefficients, and for interest, an additive constant as well. We use that coefficient as the basis of understanding the pattern of responses for each participant, as well as averaging the coefficient across subgroups to understand the average of the subgroup, and thus the pattern of their thinking about the topic. |
17 | The coefficients tell us about how the respondents react to individual elements | We can combine the additive constant with up to four answers or elements and add their values to estimate the performance of the combination. Recall from above (#16) that the additive model is written as: Binary Rating = k0 + k1(A1) + k2(A2) … k16(D4). The additive constant, k0, tells us the likely rating on the scale of 0–100 that would be achieved if the vignette had no elements, no answers. The coefficient tells us the contribution of each element or answer. Each of the 16 answers has an average coefficient. Positive coefficients mean that adding the answer to a combination or vignette increases the proportion of respondents who rate the concept 7–9. A negative coefficient means that adding the answer to a combination or a concept decreases the proportion of respondents who rate the concepts 7–9. It is not that they do not like the idea. It is just that the element is not a particularly strong positive. We consider results from base sizes as few as 8–10 respondents. Below that base for a subgroup, the average coefficient is not stable. |
18 | Combine groups of respondents based on any criteria | To find subgroups, we simply combine the coefficients from the people who fall into the group. This could be gender, age, pattern of usage, etc. Then, across the respondents selected for the subgroup, average their respective additive constants, and corresponding coefficients, to estimate group performance. Alternatively, we can simply put raw data together for all the relevant respondents in a subgroup, and run one OLS regression. This is called the Grand Model. The parameters of the Grand Model typically correlate highly with the corresponding average parameters estimated by averaging the individual models. |
19 | Previous studies suggest norms | When the coefficient is … here is how to interpret +15 or higher major positive +10 to +15 strong positive +5 to +10 positive 0 to +5 does not hurt, but not important 0 to −5 negative, only slightly damaging −5 to −10 negative, could be damaging −10 or lower strong negative |
20 | Within any topic, Mind Genomics allows us to uncover basic groups of responses, so-called Mind-Sets | These might be considered the basic mental alleles of judgment of a topic. They are not exhaustive, but suggest groups with different thoughts about what is important and relevant (positive or negative) versus irrelevant. |
21 | Use conventional statistics (clustering) to uncover Mind-Sets, but judgment to name them | To find Mind-Sets, we array the coefficients from our respondents (but not the additive constant), creating a matrix. The columns are the elements (our 16 elements). The rows are the respondents (our 50 respondents). We compute a measure of distance between each pair of respondents, using an accepted distance measure. In our case, we use the value (1-Pearson R). The Pearson R, or correlation varies from a high of +1 (perfect linear relation, meaning a distance of 0 between the two respondents), down to a low of −1 (perfect inverse relation, meaning a distance of 2 between the two respondents). Clustering then reveals non-overlapping groups of meaningfully different respondents, showing different Mind-Sets. We choose the fewest number of clusters or Mind-Sets (parsimony), such that these Mind-Sets tell a meaningful story (interpretability). |
22 | Create a set of questions from the experiment, the pattern of answers to which assigns a new person to one of the Mind-Sets uncovered in the experiment | The set of answers in the study (the original set of 16) now are filtered to identify which answers most efficiently differentiate among Mind-Sets. The PVI, personal viewpoint identifier, emerging from the experiment typically comprises 3–7 such answers from the original 16, now recast as statements. The different answers (aforementioned 3–7) are presented in random order for each person to be mind-typed and assigned to one of the Mind-Sets. The person to be assigned either agrees with the statement or disagrees with the statement (or feels the statement is important or unimportant). Thus, the response is binary, no/yes, unimportant/important, disagree/agree. The pattern of responses assigns the person to one of the Mind-Sets, the “best guess” assignment. |
The paradigm explicated using yogurt.
A good way to understand the features of the paradigm and what it delivers to the user comes through the demonstration with a common product that can be moderately modified, with that innovation driven by the consumer requirements. This is the typical situation, wherein there is no major technical innovation, but there is the corporate need to offer something new and attractive. The ingoing assumption is that the “new product” is somewhere “out in the ether.” The features of the new product must be discovered, and not slogans, but real ideas. The effort may be too slow or cumbersome when fighting against other internal priorities, or when the assignment must be to an outside, not-necessarily quickly responsive organization. Nor, in fact, is there the desire to wait until some start-up corporation develops a product, and then “snatch up” the corporation, making up by acquisition what one lacks in creation and innovation.
Our case history here is yogurt, although the precise steps can be used for virtually any dairy product, any food product, and indeed any product or service about which people write and talk. The specifics for yogurt are thus meant only as didactic examples.
The specific study on which we elaborate began on December 19, 2018, and finished on December 23, 2018. Of that time, the first 2 days were devoted to refining an existing software which scoured the Internet, discovering and reporting on trends, with these trends specified to be in the food industry. On December 23, we ran the study, and emerged with the results. After the holiday period, on January 4, 2019, we developed the PVI, the personal viewpoint identifier. Altogether, the paradigm, from knowledge development to testing to the personal viewpoint identifier can be said to have required approximately 48 hours of real time, taking into account the development time, as well as the disrupting time respectively. The objective is to show how to “do it” by actually doing it. In the elaboration, we present the different steps following the outline in Table 1.
Figure 2 shows an example of the summary information for “Yogurt” yielded by the artificial intelligence system created by authors Choudhuri and Upreti and named “SamanthaSM" for this early stage. Figures 3 and 4 show examples of the output of Samantha, using the artificial intelligence system.
The matrix of information about the products. The matrix emerges from the artificial intelligence platform, “SamanthaSM,” previously designed to deal with the entire vertical of food and beverage.
Korean smoothie deconstructed by SamanthaSM.
A health-oriented yogurt deconstructed by SamanthaSM.
Figure 2, shows a matrix of information about the products. This matrix, with circles and a short phrase, gives a sense of the different ideas. It is important to note that the effort from artificial intelligence is not to create the final questions and answers, but rather to provide hints, suggestions, from which the questions and answers are crafted. We will see the nature of the crafting later.
Mind Genomics works by presenting the respondents with combinations of ideas, messages, or in our case, combinations of answers to four questions created from the raw material shown in part in Figures 1–3. As we noted earlier, the role of artificial intelligence, and particularly the SamanthaSM platform, is to present suggestions that the researcher can use to elaborate. The output from the artificial intelligence system comprises both a set of words in Figure 2 to “jog the mind,” as well as links to deeper information (Figures 3 and 4). Thus, the Mind Genomics system gives room for suggested topics, as well as for the human elaboration of those topics.
Table 2 presents the set of four questions, extracted from the information provided by the artificial intelligence platform, and then elaborated and edited to move from information to questions. Each question, in turn, generates four answers, or more correctly, the researcher provides four answers to each question. The answers may be taken directly from the information provided by the artificial intelligence platform, or the answers may be polished and edited information, or perhaps even new ideas sparked by the information provided, by not actually part of the information provided. The reality is that it does not really matter where the information comes from. The Mind Genomics effort is attempting to discover “what works.” The information provided to it is the raw material. The goal is to get the best information and identify “what works.”
Question A—What type of product is this? | |
---|---|
A1 | A frozen yogurt |
A2 | A Greek yogurt |
A3 | A yogurt smoothie |
A4 | A plain yogurt |
Question B—What does this product deliver in terms of sensates? | |
B1 | Flavorful fruit enhances the yogurt |
B2 | The yogurt has a colorful, picturesque appearance |
B3 | The texture of the yogurt is creamy and delicate |
B4 | The rich taste compliments the appetizing aroma |
Question C—When would you eat this yogurt? | |
C1 | For those on the move and in need of a quick breakfast |
C2 | Complements a meal as the perfect side |
C3 | Perfect as a natural energy boost |
C4 | Improves recovery after daily exercise |
Question D—What are the health benefits of this yogurt? | |
D1 | Provides your body with the protein it craves |
D2 | Low sugar… without sacrificing great taste |
D3 | Probiotic-rich and immune system boosting |
D4 | Only the most natural and organic ingredients |
The four questions and four answers from each question, created by inspecting the information provided by the artificial intelligence platform, and generating the relevant statements to be used in the actual field execution.
One could take the 16 answers in Table 2 and rate each of the ideas on a scale of interest. Presenting the answers one at a time and obtaining an answer is the survey method, widely used, but unable to spark the creation of a new product idea in the way it is structured. By presenting the answers one at a time, and then requiring the respondent to rate each idea alone, we are left with ratings of single ideas, but no idea of how ideas interact with and compete with each other, as they drive interest. The respondent may also change the criterion of judgment, judging healthful ingredients more leniently, and the more indulgent features more stringently.
A potentially more productive way mixes and matches the answers, creating vignettes. The answers become the building blocks. Rather than building one answer at a time, starting with the most popular, we create combinations of answers using a recipe book (experimental design). The responses to the mixtures of answers help us understand the performance of the single elements. We do that by deconstructing the response to a blend, our mixture of answers, to the part-worth contribution of each answer. This notion was developed extensively by Norman Anderson [12], formalized as the method of conjoint measurement [13], popularized in business and academic circles by Professor Paul Green of The Wharton School of Business of the University of Pennsylvania [14, 15], and finally expanded, and made available worldwide as a method of knowledge building by author HRM [7].
Mind Genomics works with various experimental designs. For these studies, we work with the so-called 4 × 4 design, namely four questions, each question requiring four answers. Table 2 showed the raw materials, the answers or features (elements, ideas, messages) for this study. The experimental design for the 4 × 4 design comprises 24 different combinations. Each of the 16 answers or elements is statistically independent of every other answer, allowing us to analyze the data by the method of OLS (ordinary least-square regression), discussed later.
Table 3 shows the first six vignettes or test combinations for one respondent, along with the 9-point rating, the transformed value for the rating, and the response time for that vignette (test combination). Each respondent evaluates a totally different set of vignettes. The underlying experimental design is the same in a mathematical sense, but the actual vignettes differ, because a permutation scheme systematically varies the pairs of elements which appear together.
Order | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
A1 | 0 | 0 | 0 | 1 | 0 | 1 |
A2 | 0 | 0 | 0 | 0 | 0 | 0 |
A3 | 0 | 0 | 1 | 0 | 1 | 0 |
A4 | 0 | 0 | 0 | 0 | 0 | 0 |
B1 | 0 | 0 | 0 | 0 | 1 | 1 |
B2 | 0 | 0 | 0 | 0 | 0 | 0 |
B3 | 1 | 1 | 0 | 0 | 0 | 0 |
B4 | 0 | 0 | 1 | 1 | 0 | 0 |
C1 | 1 | 0 | 1 | 0 | 1 | 0 |
C2 | 0 | 1 | 0 | 1 | 0 | 0 |
C3 | 0 | 0 | 0 | 0 | 0 | 0 |
C4 | 0 | 0 | 0 | 0 | 0 | 1 |
D1 | 1 | 0 | 0 | 0 | 0 | 0 |
D2 | 0 | 0 | 0 | 1 | 1 | 0 |
D3 | 0 | 0 | 1 | 0 | 0 | 0 |
D4 | 0 | 1 | 0 | 0 | 0 | 1 |
Rating | 7 | 7 | 8 | 8 | 8 | 5 |
Binary | 101 | 100 | 100 | 101 | 101 | 0 |
Res Time | 13 | 10 | 6 | 5 | 5 | 3 |
The first six vignettes for one respondent. The 4 × 4 design prescribes 24 vignettes of precise design in terms of the elements which each vignette comprises.
At its basic level, the Mind Genomics study is an experiment, albeit couched in the form of a survey. The researcher systematically varies the stimulus inputs, the answers, according to the experiment design (Table 3), records the respondent’s rating as well as time of response, and then analyzes the results. Figure 5 shows what the respondent sees (test vignette) when using a smartphone. The same vignette can be presented in a slightly different configuration to fit the screen of a personal computer or a tablet.
The respondent experience when using a smartphone with a small screen.
The typical Mind Genomics experiment with BimiLeap® takes approximately 4–5 minutes from start to finish. Many respondents begin with the typical strategy of trying to be “correct.” The respondent may spend more time at the start than at the end, reading the vignettes, in order to make sure that they have gotten all the relevant information. By the time the respondent reaches second, and certainly the third vignette, however, this effort begins to subside, and the respondent answers, almost automatically, at an intuitive level, the System 1 of Nobel Laureate Daniel Kahneman [16].
Figure 6 shows the external dynamics of the experiment. The top set of figures shows the average response time in seconds, by position of the vignette. We see that whether we deal with the Total Panel, with males, or with females, the pattern is virtually the same. The average response time after the first vignette tested drops to a constant level. Despite the long time and the extensive number of vignettes, respondents still seem to vary their ratings.
The average time in seconds needed for a respondent to read a vignette and assign a rating (top row of graphs), and the average rating assigned to the test vignette (bottom row of graphs.).
Up to now, we have focused on the setup and execution of the study. The more interesting part of the study comes from the discovery of just how the answers, the stimulus inputs under the researcher’s control, “drive” the response, in this case interest. In this section, we look at the results from our experiment with 50 respondents. We will look at the additive constant to get a sense of baseline interest, then at the coefficients to see which elements or answers drive interest, and then search for Mind-Sets, groups of ideas which “move together.” Each of our 50 respondents will be assigned to a Mind-Set based upon the pattern of coefficients. Table 4 shows the results.
Total Panel shows an additive constant of 56, meaning that in the absence of any elements in the vignette, we expect 56% of the answers to be ratings of 7–9. Basically, yogurt is liked. It will be up to the elements to drive liking much higher.
The “Total Panel,” with all 50 respondents, shows NO very strong elements. This means that if we continue to try these types of ideas, it is likely that for the general population nothing will work, or when some element works, it will be probably by accident.
The answer is dividing the respondents into Mind-Sets. The Mind-Sets are selected from the mathematical clustering to “make sense.” The computer only divides the respondents by the pattern of coefficients. It is the researcher and the marketer who must make sense of the Mind-Sets.
Mind-Set MS1: Modestly interested in yogurt (additive constant 37), but interested in the type of yogurt, especially high protein and convenient. They may like yogurt for its probiotic qualities. We could call these the health-through-a good-tasting-food.
Mind-Set MS2: A yogurt aficionado (higher additive constant of 58), likes the multisensory appeal of yogurt.
Mind-Set MS3: A yogurt aficionado (higher additive constant of 48), but probably looking for a low-calorie snack.
Group | TOT | MS1 | MS2 | MS3 | |
---|---|---|---|---|---|
Tentative name | Health & good taste | Multisensory | Low-calorie snack | ||
Base size | 50 | 22 | 13 | 15 | |
Additive constant | 56 | 37 | 58 | 58 | |
Question A: Type | |||||
A1 | A frozen yogurt… a guilt-free indulgence | -3 | 9 | 8 | −30 |
A2 | A Greek yogurt… high in protein | −3 | 14 | 4 | −34 |
A3 | A yogurt smoothie… no spoon required | −4 | 17 | −1 | −37 |
A4 | A plain yogurt… versatile, customizable | −7 | 8 | 1 | −37 |
Question B: Traits | |||||
B1 | Flavorful fruit enhances the yogurt… taste and health | 4 | −3 | 25 | −4 |
B2 | The yogurt has a colorful appearance | 1 | −5 | 22 | −8 |
B3 | Nutrient-rich nuts improve the texture and flavor-profile of the yogurt | 1 | −3 | 11 | −3 |
B4 | The yogurt is plant-based… a better alternative | −2 | −6 | 22 | −16 |
Question C: Situation | |||||
C3 | Perfect as a natural energy boost | 0 | 5 | −3 | −5 |
C2 | A healthy meal and snack alternative | −1 | −2 | −6 | 4 |
C4 | Improves recovery after daily exercise | −1 | 2 | −9 | 1 |
C1 | For those in need of a quick breakfast | −6 | −8 | −12 | 0 |
Question D: Benefit | |||||
D3 | Probiotic-rich… immune system boosting | 2 | 15 | −14 | −3 |
D2 | Low sugar… without sacrificing great taste | 0 | 9 | −28 | 10 |
D4 | Only the most natural and organic ingredients | −1 | 9 | −15 | −5 |
D1 | Provides your body with the protein it craves… essential for keto diets | −4 | 8 | −21 | −6 |
The results from the study, showing the coefficients for interest (binary transform) both from the Total Panel (ToT), and from the three complementary Mind-Sets (MS1, MS2, MS3).
The prudent developer might well repeat this step 3–4 times, with different sampling of ideas from SamanthaSM, and with new populations of respondents, perhaps retaining the strong performing ideas, for a final test (e.g., step #5) comprising only strong performing answers or elements which have proved themselves.
We now turn to the second important variable, response time. The BimiLeap® APP from Mind Genomics measured the number of seconds from the presentation of the vignette on the screen to the response. The analysis deconstructs the response time in seconds into the part-worth contribution of each element in the vignette. The model does not have an additive constant, so that the response time is “0” in the absence of any elements. Furthermore, Figure 6 (top panels) suggests that the response time to the first vignette should be discarded. That response time is longer than the other response times, probably because when making that first rating, the respondent is not accustomed to the procedure, and there may be some issues both with eye-hand coordination, and with using the scale. By the second vignette, however, the response time is quite stable.
Our objective here is to discover whether the 16 answers each generate the same response time. The way to do that is again by OLS regression. This time, however, we put all the relevant data into one set, and estimate one “grand” regression model for that relevant data. By “relevant,” we mean first eliminating ALL data from the first vignette (order #1), no matter who the respondent happens to be. We then either divide the data into three groups, depending upon the Mind-Set of the respondent, allowing us to estimate the response time per element for each Mind-Set, or we look at all the data in one group for Total Panel. We run the Grand Models for this analysis, rather than running the individual-level models.
Table 5 shows the coefficients for response time estimated for each of the 16 elements, both for the Total Panel and, respectively, for the three Mind-Sets generated from the ratings assigned to the vignettes. Table 5 shows clear differences in estimated response time (RT) across the elements, and across the Mind-Sets.
Response times from vignettes 2–24 | TOT | MS1 | MS2 | MS3 | |
---|---|---|---|---|---|
Health and good taste | Multisensory | Low-calorie snack | |||
Question A: Type | |||||
A2 | A Greek yogurt… high in protein | 0.7 | 1.1 | 0.9 | 0.1 |
A3 | A yogurt smoothie… no spoon required | 1.0 | 1.1 | 0.9 | 0.9 |
A4 | A plain yogurt… versatile, customizable | 1.0 | 1.2 | 0.8 | 1.0 |
A1 | A frozen yogurt… a guilt-free indulgence | 1.0 | 1.3 | 0.8 | 0.9 |
Question B: Traits | |||||
B1 | Flavorful fruit enhances the yogurt… taste and health | 0.9 | 1.0 | 0.9 | 0.7 |
B3 | Nutrient-rich nuts improve the texture and flavor-profile of the yogurt | 1.0 | 1.5 | 0.5 | 0.7 |
B4 | The yogurt is plant-based… a better alternative | 1.0 | 1.8 | 0.2 | 0.6 |
B2 | The yogurt has a colorful appearance | 1.2 | 1.8 | 0.1 | 1.0 |
Question C: Situation | |||||
C2 | A healthy meal and snack alternative | 0.8 | 0.4 | 0.7 | 1.5 |
C4 | Improves recovery after daily exercise | 1.0 | 0.5 | 1.3 | 1.5 |
C3 | Perfect as a natural energy boost | 1.1 | 0.7 | 1.6 | 1.0 |
C1 | For those in need of a quick breakfast | 1.2 | 0.9 | 1.6 | 1.5 |
Question D: Benefit | |||||
D3 | Probiotic-rich… immune system boosting | 0.3 | −0.2 | −0.3 | 1.4 |
D1 | Provides your body with the protein it craves… essential for keto diets | 0.5 | 0.1 | 0.4 | 1.4 |
D2 | Low sugar… without sacrificing great taste | 0.7 | 0.9 | 0.5 | 0.7 |
D4 | Only the most natural and organic ingredients | 1.3 | 1.4 | 0.7 | 1.6 |
Coefficients for response time both from the Total Panel (TOT), and from the three complementary Mind-Sets (MS1, MS2, MS3) emerging from the rating question.
When we plot response time against interest, with the points corresponding to the 16 coefficients for the 16 elements, Figure 7 suggests differences in response time may not strongly co-vary with the interest in the message estimated from the rating. That is, more interesting messages or elements are not necessarily responded to more quickly. This lack of strong co-variation between interest and response time differs from what has been recently uncovered by author HRM in a study of the same type, dealing with a political issue, the Russian-Ukrainian conflict of 2018, rather than yogurt. It may well be that the studies of RT require topics which are involving. Yogurt simply may be not particularly involving even though the data may make sense.
Scatterplot showing the relation between the coefficient for response time (ordinate) and the coefficient for interest (abscissa). The patterns are shown for the Total Panel, and for the three Mind-Sets, respectively.
Our efforts to create a new yogurt concept through experimental design (BimiLeap®), powered by access to trends through artificial intelligence (SamanthaSM) have uncovered a new way to understand a product category and prepare to create new concepts. We see clearly from the data in Table 4 as well as from the array of previous studies on dairy that people perceive the features of a dairy product in different ways, at least in terms of what they consider to be interesting and important. Our identification of the mental genomes, these alleles of preference, pertains only to the respondents whom we tested, generally small groups of consumers from easy, affordable panels. How do we generalize our findings, either to discovering the distribution of these basic Mind-Sets in the population or, more importantly, discovering individuals who are members of these Mind-Sets, and who can be further studied? The further studies may be as simple as their preferences for concepts created for the product (e.g., yogurt products), on to purchase and consumption patterns, and even beyond to possible health and genetic correlates of segment membership? One approach to predicting Mind-Set membership looks at the pattern of coefficients for the Mind-Sets (Table 4), and selects elements showing the greatest differentiating power, that is, the biggest difference for the average panelist. Each selected element is then edited to become a question, to be answered NO or YES, or some other appropriate pair of responses for the same type of binary decision. The questions are incorporated into a short questionnaire. The pattern of responses shows the Mind-Set to which the respondent probably belongs. The feedback to the respondent or to a marketing company using the data appears in Figure 6, in the three right panels. The personal viewpoint identifier is easy to create using summary data, is quick to administer, and can be configured as either a “fun” tool to engage customers, or as a more serious tool to understand the mind of the consumer. From one study, one can proceed to type up to the millions of respondents, should one wish to study entire populations. For this study on yogurt, the personal viewpoint identifier is shown in demonstration form in this link:
As presented here, the approach we present begins with a combination of social data analysis and experimental science, moving on to new vistas. These vistas include a new way of exploring ideas, uncovering possibly new-to-the-world mind-genomes, and finally, understanding how neurophysiological processes indicated by response time co-vary with interest in the product. We now move beyond the data to suggest opportunities and applications, some of which are already in their nascent stages, and some of which are easily done, but simply have not been implemented.
Trend definition: The objective of trend spotting is to identify general patterns of what is happening, usually from an exploration of websites and conversations, and their distillation into general patterns. The patterns provide broad patterns, not specifics. Thus, for dairy, we might find a trend emerging for cultured milk products like kefir, combined with new flavors and interesting incorporations, such as chia seeds. The trend spotter may guess about the nature of this trend. What would happen if the new ideas could be incorporated in a Mind Genomics study, with the respondents asked to rate the likelihood of each vignette as an emerging trend? The answers would range from absolutely never to current to approximately a year or a two in the future. In this case, the trend is defined not so much by what one observes as by a combination of that which is observed, with some conscious elaborations of what might be.
Product design: This chapter presents the Mind Genomics as an effort to deconstruct the response to individual features of dairy products based upon the response to vignettes. One can also look at the Mind Genomics as a “Mixmaster” of ideas, whether these ideas or elements be based upon yogurt, upon dairy in general, or even other foods and situations. When these elements from disparate sources are combined, elements not only for yogurt, for example, the outcome is a new set of possible products. The promising ideas can be combined. When, for the most part, the ideas from different areas really do not work together, the ratings for the combinations will be low, and there will not be any strong performing elements, suggesting that the raw materials simply do not work together.
Perhaps the most important contribution of Mind Genomics is to combine profound knowledge of a person’s interest in dairy products with both the ability to guide the person to eat better, and to understand how preferences for dairy co-vary with behavior. The full elaboration of the social use of Mind Genomics for health issues and dairy awaits the new generation of researchers, interest in dairy, in health, and in commerce, respectively. We have presented early indications and of these new developments.
Author AG thanks the support of Premium Postdoctoral Research Program of the Hungarian Academy of Sciences.
IntechOpen celebrates Open Access academic research of women scientists: Call Opens on February 11, 2018 and closes on March 8th, 2018.
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\\n\\nAPPLYING FOR THE “INTECHOPEN WOMEN IN SCIENCE 2018” OPEN ACCESS BOOK COLLECTION
\\n\\nWomen scientists can apply for one book topic, either as an editor or with co-editors, for a publication of an OA book in any of the scientific categories that will be evaluated by The Women in Science Book Collection Committee, led by IntechOpen’s Editorial Board. Submitted proposals will be sent to designated members of the IntechOpen Editorial Advisory Board who will evaluate proposals based on the following parameters: the proposal’s originality, the topic’s relation to recent trends in the corresponding scientific field, and significance to the scientific community.
\\n\\nThe submissions are now closed. All applicants will be notified on the results in due time. Thank you for participating!
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\n\nAPPLYING FOR THE “INTECHOPEN WOMEN IN SCIENCE 2018” OPEN ACCESS BOOK COLLECTION
\n\nWomen scientists can apply for one book topic, either as an editor or with co-editors, for a publication of an OA book in any of the scientific categories that will be evaluated by The Women in Science Book Collection Committee, led by IntechOpen’s Editorial Board. Submitted proposals will be sent to designated members of the IntechOpen Editorial Advisory Board who will evaluate proposals based on the following parameters: the proposal’s originality, the topic’s relation to recent trends in the corresponding scientific field, and significance to the scientific community.
\n\nThe submissions are now closed. All applicants will be notified on the results in due time. Thank you for participating!
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