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Soft Matter
EDITORIAL
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Department of Science Teaching, Weizmann
Science, Rehovot, Israel, 76100. E-m
† This article is part of a collection of edSo Matter Education.
Cite this: Soft Matter, 2013, 9, 5316
DOI: 10.1039/c3sm90028b
www.rsc.org/softmatter
5316 | Soft Matter, 2013, 9, 5316–53
The challenge of teaching soft matter at theintroductory level†
Edit Yerushalmi
Teaching somatter at the high school orintroductory undergraduate level mightseem a strange choice: could studentsstruggling to understand ideal gaseslearn to model the complex phenomenaof molecules that self-assemble intomesoscopic or larger-scale aggregates,such as polymers or membranes? On theother hand, the traditional focus ofdisciplinary science curricula on idealsystems of non-interacting particles doesnot expose introductory-level students tothe wide variety of fascinating andimportant phenomena that exist ininteracting molecular and macromolec-ular systems. Neglecting a quantitativediscussion of cooperative behavior ininteracting multi-particle systems fails toequip students with the conceptual toolsthat are fundamental to the under-standing of many phenomena at theheart of physics, chemistry, biology andmaterials science. In particular, it fails toprovide an important part of the intel-lectual foundation that science andengineering students are likely to need intheir future elds of study.
Can one dene a set of powerfulenough concepts that can be feasiblytaught in introductory level courses,
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which would allow students to simplifyand analyze complex multi-particlesystems? Moreover, can one introduce aninterdisciplinary topic such as somatterin a quantitative and systematic manner,thus, serving to remedy the compart-mentalized manner in which introduc-tory science courses are commonlytaught at the high-school level and topromote recognition of the importance ofinterdisciplinary approaches in currentscientic research and technology? And,last but not least, how should one incor-porate such content into the already busyprogram of high school or introductorylevel students?
Based on my experience in leading thedevelopment, research and teaching of aninterdisciplinary program for high schoolstudents entitled “So andmessy matter”,I maintain that so matter is an appro-priate choice for an introductory levelinterdisciplinary course that supplementsthe core science courses that students takein the eld in which they major. On apractical level, I note that the centralmethods used to teach the theory can bepresented in a manner suited to themathematical background of high schoolstudents. In addition, the concepts do notrequire extensive scientic backgroundsuch as complex mechanics, electrody-namics or quantum mechanics. They alsofocus on everyday materials near roomtemperature and atmospheric pressure,which are familiar to students.
This
The program on “So and messymatter” is an ongoing project that involvesa group of scientists and science educatorsat the Weizmann institute. It introduces aunied and quantitative approach toanalyze the statistical thermodynamic andstructural properties of systems of inter-acting particles of interest to applicationsin chemistry and biology, such as colloidaldispersions, amphiphilic self-assemblyand polymer networks. It was taught inthree cycles to interested and capable 11th
and 12th grade science students, whosemajor subject was either advanced levelphysics and/or chemistry. To bypassthe constraints of rigidly xed schoolcurricula, the course was taught as aregional program within the well-equip-ped labs of a university outreach center.1 Itencompassed bimonthly aernoon meet-ings and granted matriculation credit forindependent experimental projects.
In addition to this more specializedprogram, the place of so materials inintroductory level courses is also relatedto calls for reforms of undergraduate lifescience education (2004 National Acade-mies report Bio2010,2 2009 ScienticFoundations of Future Physicians3).These reports advocate greater integra-tion of biology in the introductory physicscourse for life science students, includingpedagogies centered on solving complex,real-world scientic problems thatrequire interdisciplinary tools. Follow-ups to these reports were meetings such
journal is ª The Royal Society of Chemistry 2013
Editorial Soft Matter
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as the 2009 conference on Physics inUndergraduate Quantitative Life ScienceEducation and projects such as NEXUS,4
a multi-university multi-disciplinaryproject focused on the development of anintroductory physics course appropriatefor the analysis of biological systems.
In determining the most powerful butstill manageable set of concepts thatwould allow introductory level studentsto study multi-particle systems, we fol-lowed the proposal of prominent scienceeducators (Reif5 and Chabay and Sher-wood6) to use a microscopic, statisticalpresentation as a way to help studentsassociate concrete meaning with abstractthermodynamic concepts. Pioneeringintroductory physics curricula such asMatter and Interactions7 have imple-mented this approach, emphasizing theatomic nature of matter, intertwiningmechanics and thermal physics. Thisapproach was successfully implementedwith both rst-rate students at upper tieruniversities, as well as with more averagestudents. Inspired by this approach, weanchored many of the topics in the “Soand messy matter” program to lattice gasmodels, initially to introduce entropy,and later to model the phase behavior ofuid mixtures, wetting of interfaces, self-assembly of surfactants, and polymersfrom a statistical perspective.
Students enter high-school (andcommonly graduate education) thinkingthat there are only three states of matter(liquid, gas or solid), based both on theirexperience and on what they are taught.Thus, we began the program withdiscussions of unconventional materialssuch as silly putty, which takes on theproperties of a solid or uid, dependingon the time scale of the applied force. Toallow for variations in the prior, middleschool education of the students, we tooka spiral approach, rst discussing in aqualitative manner fundamental princi-ples and concepts of statistical thermo-dynamics. We applied this terminology tohave students explain an experiment on“Egyptian ink”, described in the popularbook by P. G. de Gennes and J. Badoz.8
This experiment required students toexplain that in some cases the colloidalparticles remain dispersed (entropy-dominated) and in other cases the parti-cles aggregate, due to large attractive
This journal is ª The Royal Society of Chemistry 20
interactions between them, which domi-nates the entropy of dispersion.
We then moved on to a more quanti-tative analysis of the phenomena. Wediscussed congurational entropy interms of a lattice model in the context ofbinary mixtures; this has not only scien-tic but also pedagogical advantage overthe more traditional presentation ofentropy associated with energy distribu-tions in the context of a continuum idealgas. The lattice model allows for concretevisualization, which supports theabstract derivations used later on thatpredict the equilibrium properties ofsystems of interacting particles via freeenergy minimization (i.e. phase separa-tion). Moreover, this construction allowsus to make explicit the simplifyingassumptions that are needed to derivethe mean-eld expression for the internalenergy of the system. These simplica-tions allow us to approximate the freeenergy change upon mixing withoutconsidering the partition function,making it appropriate for introductorystudents.
We further applied the principles of afree energy minimization to specic somatter systems in which inter-particleinteractions are important, such aswetting/capillarity, self-assembly, andpolymers. To scaffold students' under-standing we used concept maps, whichmake explicit the major steps in applyingstatistical thermodynamics principles toconstruct simplied, theoretical modelsfor the equilibrium behavior of commonso matter phenomena.9 All these mapsinvolved a common set of steps, whichinclude appropriately dening thephenomenon of interest and its experi-mental manifestation, identifying themacroscopic degrees of freedom, andthe construction of a simplied model ofthe system. The internal energy andentropy are calculated and combined toyield the free energy, which is then mini-mized with respect to the relevantdegree(s) of freedom to predict the ther-modynamic behavior of the system (for anexample, see Fig. 5 and 9 in ref. 9). Such anapproach allows students to understandhow the competition between interactionsand entropy is resolved, to determine howmolecules self-organize to form meso-scopic structures.
13
The problem of phase separation ofsimilarly sizedmolecules required quite asignicant time investment by the intro-ductory level students. To keep themmotivated, it is important to show themthat what they learned can be extended tothe analysis of more complex so-mattersystems. However, treating more complexsystems in detail would burden studentswith even more tedious derivations. Webypassed this challenge by presenting thecore of the derivation mapped ontopreviously studied theory. As an exampleof how one can extend the problem ofsimilarly sized molecules to polymers insolution, we introduced a research paperby Shultz and Flory10 using the method ofadapted primary literature (APL).11 APL isa text genre that retains the authenticcharacteristics of primary literature,while making it accessible to high schoolstudents; this allows the instructor toacquaint students with authentic scien-tic discourse. Specically, we re-struc-tured the text, mapping the theory ofpolymer solutions onto the model forbinary mixtures of small molecules ofequal size that was already studied inclass.12
However, we found that when studentswere asked to identify the major stepsbehind the theory presented in the adap-ted research paper by Flory they focusedalmost exclusively on the stages that entailquantication of the interactions and theentropy. The stages related to the selectionof the relevant degrees of freedom and theconstruction of the simplied model wereeither absent or mentioned only in animplicit manner in students' worksheets.These ndings suggest that one mustprovide more instructor support so thatstudents understand how the degrees offreedom are chosen and themodel itself isdeveloped.
Finally, our program also providesstudents with an opportunity to conductexperimental or computational inquiryprojects that allow them to apply theconcepts they have learned. In a nalpaper, they are expected to discuss theirexperimental observations in the light oftheoretical analysis. However, we do notexpect students in high school toconstruct the analytical analysis in anautonomous manner. We resolved thistension by having students determine the
Soft Matter, 2013, 9, 5316–5318 | 5317
Soft Matter Editorial
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phenomenon and research question theywould study and set up the experiment ormodel the phenomenon computationallyin a simulation. However, the analyticalscientic explanation was reconstructedfrom an explanation presented in aprimary source (published scienticpaper). Examples of these projectsinclude observations of changes inwetting and in micellization as thesystem properties were changed, as wellas simulations of lipid ras.
To help the students link the simpleanalytical models taught to more complexsystems, we are currently exploring the useof computational modeling tools with astrong visual component. This alsosupports the development of basic physicsconcepts, even before they are introducedin a more formal, analytical presentation.Computational modeling also allowsstudents to develop some intuitionregarding the dynamical approach toequilibrium, the meaning of entropy etc.Integrating computational models ofvarious types (molecular dynamics, MonteCarlo) to represent simple phenomenasuch as random walks will also allowstudents to explore the nature of modelsin physics.
Our program has shown that studentswho take a supplementary, introductorylevel course in so matter can learnto quantitatively understand basicstatistical thermodynamics and itsapplications to cooperative behavior ininteracting multi-particle systems,
5318 | Soft Matter, 2013, 9, 5316–5318
which are important in current researchin a wide cross-section of physics,chemistry, biology and materialsscience. Being able to understand thespontaneous formation of the complexand beautiful structures in the worldsurrounding them is not only motivatingfor young minds, it also equips themfrom the start with a language and visionof science that is coherent rather thanfragmented.
Edit Yerushalmi, Weizmann Institute ofScience, Israel
References
1 School of Contemporary Science at theDavidson Institute of ScienceEducation, Weizmann Institute ofScience.
2 National Research Council, Bio 2010:Transforming Undergraduate Educationfor Future Research Biologists, NationalAcademy of Sciences, Washington,DC, 2003.
This
3 Scientic Foundations of FuturePhysicians, AAMCHHMI Committee,Washington, DC, 2009.
4 http://www.hhmi.org/grants/office/nexus/.5 F. Reif, Thermal physics in theintroductory physics course: Why andhow to teach it from a unied atomicperspective, Am. J. Phys., 1999, 67, 1051.
6 R. W. Chabay and B. A. Sherwood,Bringing atoms into rst-year physics,Am. J. Phys., 1999, 67, 1045.
7 R. W. Chabay and B. A. Sherwood,Matter and Interactions: ModernMechanics, John Wiley & Sons, NewYork, 2002, vol. 1.
8 P. G. de Gennes and J. Badoz, FragileObjects: So Matter, Hard Science, andthe Thrill of Discovery, Copernicus,New York, 1996.
9 E. Langbeheim, S. Livne, S. A. Safranand E. Yerushalmi, Introductoryphysics going so, Am. J. Phys., 2012,80, 51–60.
10 A. R. Shultz and P. J. Flory, Phaseequilibria in polymer–solvent systems,J. Am. Chem. Soc., 1952, 74, 4760.
11 A. Yarden, G. Brill and H. Falk, Primaryliterature as a basis for a high-schoolbiology curriculum, J. Biol. Educ.,2001, 35, 190–195.
12 E. Langbeheim, S. Safran andE. Yerushalmi, Design guidelines foradapting scientic research articles:an example from an introductorylevel, interdisciplinary program onso matter, AIP Conf. Proc., 2013,1523, 23–26.
journal is ª The Royal Society of Chemistry 2013
