Melting of lamellar phases in temperature sensitive colloid-polymer suspensions

Size: px
Start display at page:

Download "Melting of lamellar phases in temperature sensitive colloid-polymer suspensions"

Transcription

1 Melting of lmellr phses in temperture sensitive colloi-polymer suspensions A. M. Alsye, Z. Dogic, n A. G. Yoh Deprtment of Physics n Astronomy, University of Pennsylvni, Philelphi, Pennsylvni (Dte: Ferury 4, 2004) We investigte the ehvior of novel suspension compose of ro-like f virus n thermosensitive polymer Poly(N-isopropylcrylmie) whose phse igrm is temperture n concentrtion epenent. The system exhiits rich vriety of stle n metstle phses, n, more importntly, provies unique opportunity to irectly oserve melting of lmellr phses n single lmelle. Typiclly lmellr phses swell with incresing temperture efore melting into the nemtic phse. The highly swollen lmelle cn even e superhete s result of topologicl nucletion rriers tht slow formtion of nemtic phses. Using opticl forces we prepre metstle nemtic n multilyer structures strting from single colloil memrne, n then oserve the system evolve ck into single memrne. PACS numers: M v My Melting of three-imensionl (3D) crystls is mong the most uiquitous phse trnsition in nture [1]. In contrst to freezing, melting of 3D crystls hs no ssocite energy rrier. Bulk melting is initite t pre-melte surfce, which then cts s heterogeneous nucletion site n elimintes the nucletion rrier for the phse trnsition [2 4]. In this pper we investigte pthwys for melting of lmellr phses. In contrst to 3D crystls, lmellr phses hve one-imensionl (1D) qusi-long-rnge orer [5 7]. Aitionlly while 3D crystls hve only one surfce etween coexisting mei the lmellr phse is microphse seprte stte in which the entire ulk is spnne y interfces etween immiscile phses. These phses re frequently uilt from mphiphilic molecules such s surfctnts n lock copolymers in solution. Although lmellr phses re very common, melting trnsitions of lmellr into nemtic phses re rrely oserve. Here we crete novel system tht exhiits lmellr-nemtic melting, n we show melting of lmellr phse is funmentlly ifferent from melting of 3D crystlline solis. We hve evelope temperture sensitive queous colloil suspension in orer to crry out these stuies. The suspension is compose of lyotropic monoisperse ros of f virus [8, 9], n thermosensitive Poly(N-isopropylcrylmie) (NIPA) polymer. The thermotropic chrcter of the f/nipa mixture stems from the temperture epenent soluility of NIPA polymer in wter [10]. Below its Θ-temperture of 31 C, wter is goo solvent n NIPA polymer ssumes swollen coil form. Aove the Θ-temperture wter is poor solvent n NIPA hs collpse gloule form [11]. The resultnt mixture forms isotropic, lmellr n nemtic phses epening on temperture n constituent concentrtion. The lmellr phses resemle those of f with hr spheres, in which lyers of spheres re interclte etween lyers of ros [12]. Our temperture sensitive queous suspension, however, enles us to irectly stuy trnsitions from one phse to nother with opticl microscopy. These f/nipa solutions re unusul new mterils whose lmellr phses iffer from those of mphiphilic molecules. The lmelle cn swell consierly n melt into nemtic phse, trnsition lmost never oserve in lock-copolymer lmellr systems. The ifferent phse ehviors rise primrily ecuse of the ro-like chrcter of the f component, n lso ecuse of the sence of covlent cross-links etween f n NIPA polymer. The kinetic pthwys exhiite y these f/nipa mixtures re lso more complex then those foun in temperture-epenent (thermotropic) moleculr liqui crystls n concentrtion-epenent (lyotropic) mphiphilic systems [13, 14]. For exmple the lmellr phses of f/nipa mixtures cn e swollen to the point where isolte lyers (lmelle) of ros re oserve. These isolte memrne-like structures of non-mphiphilic mesogens re stle ginst mechnicl perturtions, melt into nemtic roplets, n rise questions out the simplest intercting mesogens cple of ssemling into two-imensionl (2D) memrnes. Most of the ssemly into 2D memrnes is riven y hyrophoic-hyrophilic interctions [15 17], while our work inictes tht much simpler system of ros with uniform ttrctions is cple of ssemling into memrnes uner specific conitions. Finlly, our temperture sensitive f/nipa solutions offer powerful new moel system for stuies of melting. Lyotropic suspensions such s collois hve proven to e iel for rel-time stuies of freezing [18 20]. Melting trnsitions, however, re much more ifficult to investigte with lyotropic collois. Once stle orere phse is otine, microscopic oservtion n concurrent concentrtion vrition re require to monitor melting, chllenging experimentl tsk. The vntge of our wekly thermotropic f/nipa polymer se suspension is tht simple chnges in temperture enle us to prepre the lyotropic colloil system in metstle orere stte, n then stuy its melting trnsition in situ. Generlly smll increse of temperture increses monomer-monomer ttrctions n thus ecreses the osmotic pressure of the semi-ilute NIPA polymer solution. As result, wter from polymer-rich

2 Lyer spcing µm 2 c 4 3 ntensit o C 7 o C 10 o C e c le (egr f 13 o C 16 o C g h 17 o C 17 o o C heting cooling Temperture o C FIG. 1: Melting ehvior of smple S1 (50 mg/ml f n 7.5 mg/ml NIPA). () Lmellr phse t low temperture exhiits visile isloction efects () At 7 C the isloction efects ct s site for nucletion of the nemtic phse. (c) Nemtic omins grow, expelling NIPA polymer into lmellr phse, which les to swelling of lmellr lyers. () Swollen lmellr phse (e) Coexistence etween nemtic phse n highly swollen lmellr phse. Lmellr phse hs the shpe of n elongte stripe while the nemtic phse fills the rest of the spce. (f-g) Isolte monolyer-eforme isotropic tctoi. (h) Isotropic-nemtic coexistence oserve t high temperture. (i-l) Illustrtion of the propose melting processes of the lmellr ro/polymer mixture. Scle rs re 5 µm. lyers flows into ro-rich lyers until osmotic equilirium is re-estlishe. This phenomen ilutes the ro concentrtion loclly, which in turn cn le to melting of the lmellr phse. NIPA polymer ws synthesize t 22 C y polymeriztion of of N-isopropylcrylmie (7 gm) issolve in 100 ml of 20mM (ph=8.15) tris uffer. Ammonium persulfte (61 mg) n tetrmethyleneimine (TEMED) (280 µl) were e s inititor n ccelertor [10]. Bcteriophge f is negtively chrge semi-flexile ro with imeter of 6.6 nm, contour length of 880 nm n persistence length etween 1000 nm n 2200 nm [9, 21]. It forms isotropic, cholesteric(nmetic) n smectic phses with incresing concentrtion [8]. A stnr protocol ws use to grow f virus [9]. The f/nipa mixtures were suspene in uffer (ph=8.15, 20 mm tris) n were plce etween the coverglss n coverslip n then sele. All oservtions were me with n inverte FIG. 2: Melting of the lmellr smple S1 stuie y smll ngle light scttering. The rel spce imges of the melting ehvior re shown in Fig. 1.() Smll ngle light scttering pttern of n orienttionlly isorere lmellr phse t 5 C () Angulrly verge intensity profile t 5 C n 13. (c) Lmellr perioicity for smple uring heting (fille circles) n cooling (open circles). There is lrge hysteresis of lyer spcing etween heting n cooling cycles. microscope (Leic DM IRB) equippe with DIC optics using n oil immersion lens (100X, N.A. 1.4). The temperture of the smple n the ojective ws controlle with wter circultor. Imges were cpture y CCD cmer n igitize using NIH-imge softwre. The opticl trp for the melting experiments ws crete with IR light (λ = 1054 nm) s escrie elsewhere [22]. The melting ehvior of f/nipa mixture with high ro concentrtion is illustrte in Fig. 1. Herefter we refer to this smple s S1. At low temperture (5 C), the mixture forms lmellr phse where lyers of ros re interclte with lyers of polymers; the polymers re in the semiilute regime (Fig. 1). The mesure lyer perioicity (1.2 µm) is much lrger then the perioicity of the smectic phse (0.9 µm) in isolte f suspensions. Disloctions n grin ounries re oserve t low temperture (Fig. 1 n i); with incresing temperture they ct s nucletion sites for formtion of nemtic tctois (Fig.1). The shpe of the nemtic tctoi in the smectic ckgroun is very similr to the shpe of the nemtic tctoi in the isotropic ckgroun [23]. Although polymer is mcroscopiclly miscile with ros in the lmellr phse, it is highly immiscile with ros in nemtic phses [24]. Therefore s the nemtic tctois grow, they expel polymer into coexisting lmellr phse which in turn les to swelling of the lmellr

3 3 lyers (Fig. 1c n j). In swollen lmellr phse there re regions where iniviul lyers re tightly oun n regions where they re well seprte (Fig. 1). Aove 15 C most of the smple is melte into nemtic phse which coexists with highly swollen lmellr phse. The lmellr phse ssumes form of elongte stripes (Fig. 1e n k). Upon incresing the temperture further, the lmellr stripes trnsform into polymer rich isotropic tctois which re frequently eforme y few isolte lmellr lyers (Fig. 1f-h). Finlly, ove 17 C isolte lyers melt, n the isotropic tctois in the nemtic ckgroun ssume their chrcteristic shpe (Fig. 1h n l) [23]. Lmellr perioicity is lso otine from the iffrction pttern of lmellr phses (Fig. 2). With incresing temperture the pek simultneously roens n shifts to lower ngles (Fig. 2 n c) inicting swelling of the lmellr phse. Aove 15 C most of the smple hs melte into the nemtic: in this cse only lrge forwr scttering is oserve. At this temperture we still oserve highly swollen lmellr stripes with n opticl microscope (Fig. 1e). When the smple is coole from the high temperture nemtic phse, the lmellr phse forms t 13 C. Tken together, the oservtion of coexistence n hysteresis in the heting/cooling cycle suggest lmellr melting into the nemtic phse is first orer phse trnsition with significnt nucletion rriers. Moreover the structure of the lmellr phse epens on smple history. The lmellr spcing of smples prepre t high temperture n susequently coole is smller thn the lmellr spcing of smples prepre t low tempertures n susequently hete. In orer for the polymer to form n isotropic roplet the lmellr lyers must melt. In the next prt of the pper we show there is kinetic rrier for melting of isolte lmelle into nemtic. Therefore with incresing temperture, the smple forms metstle highly swollen lmellr phse until the iniviul lmelle overcome nucletion rrier for melting. In the experiments with smple S1, we oserve swelling of the lmellr phse. The concentrtion of lmellr lyers in these smples ws high, n thus swelling ws limite y steric interctions. In orer to etermine the mximum swelling of the lmellr system, we repete the melting experiments t much lower f concentrtion (Fig. 3). Herefter we refer to this smple s S2. At low tempertures most of the smple is n isotropic polymer solution. At tempertures etween C we oserve coexistence etween lmellr roplets (Fig. 3) n isolte lmelle (colloil memrnes) (Fig. 3c). The spcing of the lyere roplets is 1.2 µm, inicting lmellr phse similr to S1. The colloil memrnes we oserve re compose of single liquilike lyer of highly ligne ros; similr memrnes hve een oserve in therml ro/polymer mixtures n perhps in queous solutions of β-feooh ros [9, 19, 25]. Over time isolte lmelle grow from the interfce of the isotropic-lmellr roplet into the isotropic phse; this 21 o C 26 o C c e f 27 o C 30 o C 30 o C 30 o C FIG. 3: Melting ehvior of smple S2 (7.5 mg/ml f n 37 mg/ml NIPA). () At 24 C lmellr roplets form in ckgroun isotropic phse. Simultneously, the formtion of isolte lyers (shown in imge c) is oserve. () At higher temperture, lmellr roplets melt into nemtic phse y the mechnism escrie in Fig. 1. (c) An isolte memrne is stle for tempertures from C. (-f) Sequence of imges showing nucletion n growth of 3D nemtic nemtic tctoi from n isolte superhete 2D memrne. (gj) Illustrtion showing the ove escrie melting processes. At tempertures elow 10 C, the smple forms miscile isotropic phse. The reson for this in not unerstoo. Scle rs re 5 µm. inictes tht single memrnes re more stle thn lmellr roplets. The coexistence of isolte memrnes n lmellr roplets with well efine spcing implies nother first orer trnsition, this time from oun to unoun lyers. Relte ining-unining trnsitions hve een stuie theoreticlly in the context of lipi ilyers; the orer of these trnsitions ws foun to e sensitive to the rnge of the intermoleculr interctions [26, 27]. It is lso notle tht the suspension of f ros usully contin low volume frction of imers. The imers cn ffect the swelling kinetics of smectic lyers n proly increse the stility of the multilyer structure since they issolve more esily in ilyer thn in monolyer. We hve investigte melting n lyer reucing ynmics ssocite with isolte memrnes (smple S3). At tempertures ove 25 C lmellr roplets melt into nemtic phse. The mechnism for this melting is similr to melting of the ulk lmellr phse (Fig. 3). The isolte colloil memrnes, however, remin stle t tempertures well ove the melting temperture of the multi-lyer lmellr roplets. Only upon ris-

4 4 c e g FIG. 4: Lyer reucing trnsition of colloil memrne oserve in smple S3 (12 mg/ml f, 31 mg/ml NIPA). The smple temperture is 28 C, elow the melting of the ulk lmellr phse (29 C). () A memrne is repetely puncture y 2.1 µm silic sphere trppe with lser tweezers. () A metstle nemtic roplet forms ue to sher melting. (c) Upon removl of the lser em the nemtic roplet freezes into multilyer smectic structure. (-f) The structure unergoes sequence of lyer reucing trnsitions. (gh) In seprte experiment formtion of isloction in the min memrnes in visile. The isloction susequently isppers s lyers slie over ech other which reucing the numer of lyers y one. ing the temperture to lmost 30 C is nucletion of three-imensionl nemtic tctoi oserve in the twoimensionl memrne (Fig. 3-f). Once nemtic tctoi is nuclete it quickly grows until the whole memrne melts. If the smple is susequently coole, the formtion of single lyer smectic will e oserve only t tempertures elow 27 C. These oservtions suggest colloil memrnes re metstle superhete structures etween C. Nucletion of 3D nemtic tctoi from 2D memrne requires lrge collective fluctution in which mny ros protrue into the thir imension. Our experiments inicte the topologicl rrier for nucletion of nemtic tctoi is very lrge. In this sense the melting ehvior of lmelle re very ifferent from melting of 3D solis. Finlly we explore the stility of isolte colloil memrnes ginst externl mechnicl perturtions (Fig. 4). These experiments were one t tempertures elow the ulk lmellr melting trnsition so tht the f h memrnes were stle. A silic e ws trppe with n opticl tweezer n the colloil memrne repetely puncture (Fig. 4). This mechnicl perturtion prouce locl sher melting of the memrne into nemtic roplet (Fig. 4). We were only le to sher melt memrnes t tempertures close to ulk lmellr-nemtic phse trnsition. At lower tempertures the puncture memrne rpily returne to its equilirium shpe. After the memrne melte, the lser em is kept in close vicinity of the nemtic roplet, loclly heting the smple. When the lser em is on, the nemtic roplet coexists with the memrne. The temperture is reuce when the lser em is turne off, n the nemtic roplet quickly freezes into multilyer smectic structure (Fig. 4c). This multilyer smectic structure is unstle n unergoes sequence of lyer reucing trnsitions until the initil equilirium memrne configurtion is otine. This experiment provies itionl evience tht colloil memrnes re equilirium structures in this temperture rnge. By irectly visulizing the smectic lyers we cn iscern the mechnism y which lyer reucing trnsition tkes plce. The numer of lyers cn e reuce when iniviul lyers slie over ech other (Fig 4e-f) or y spontneous formtion of isloctions in the min memrne n their susequent nnihiltion (Fig. 4g-h). These trnsitions re relevnt to lyer reucing trnsitions in superhete smectic films of thermotropic liqui crystls [28]. To conclue, we hve crete novel f/nipa lmellr phse which cn simultneously melt into nemtic phse n swell into iniviul lmelle. The interply etween these two processes cretes multiple melting pthwys of unexpecte complexity. The lmellr phse iffers from conventionl 3D crystl in tht interfces etween micophse seprte lyers of ligne ros n polymers in isotropic phse spn the entire smple. As result, melting of these interfces correspons to melting of the entire ulk smple n it is possile to superhet the lmellr structure. Another unique feture of our experiment is the ility to control the phse ehvior of lyotropic suspension y temperture, which in turn controls the solvent qulity of the polymer phse. This strtegy cn e use in the future to stuy phse trnsitions of other systems in soft conense mtter. We thnk Tom Luensky n Dennis Discher for useful iscussions. This work ws supporte y the NSF through grnt DMR n the PENN MRSEC, DMR We lso cknowlege support from NASA (NAG8-2172). [1] H. Lowen, Phys. Rep. 237, 249 (1994). [2] J. G. Dsh, Rev. Mo. Phys. 71, 1737 (1999). [3] R. W. Chn, Nture 323, 668 (1986). [4] J. F. vn er Veen, Surf. Sci , 1 (1999). [5] F. S. Btes, Science 251, 898 (1991). [6] J. T. Chen, E. L. Thoms, C. K. Oer., n G. P. Mo, Science 273, 343 (1996). [7] M. Muthukumr, C. K. Oer, n E. L. Thoms, Science 277, 1225 (1997). [8] Z. Dogic n S. Fren, Phys. Rev. Lett. 78, 2417 (1997). [9] Z. Dogic n S. Fren, Phil. Trns. R. Soc. Lon. A. 359, 997 (2001).

5 5 [10] X. Wng n C. Wu, Mcromolecules 32, 4299 (1999). [11] C. Wu n X. Wng, Phys. Rev. Lett. 80, 4092 (1998). [12] M. Ams, Z. Dogic, S. L. Keller, n S. Fren, Nture 393, 349 (1998). [13] P. G. e Gennes n J. Prost, The Physics of Liqui Crystls (Oxfor Science, 1993), 2n e. [14] F. C. Lrche, J. Appell, G. Porte, P. Bssereu, n J. Mrignn, Phys. Rev. Lett. 56, 1700 (1986). [15] S. A. Jenekhe n X. L. Chen, Science 279, 1903 (1998). [16] S. Prk, J. H. Lim, S. W. Chung, n C. A. Mirkin, Science 303, 348 (2004). [17] B. Discher, Y.-Y. Won, D. Ege, J.-M. Lee, F. Btes, D. Discher, n D. Hmmer, Science 284, 1143 (1999). [18] V. J. Anerson n H. N. W. Lekkerkerker, Nture 416, 811 (2002). [19] Z. Dogic, Phys. Rev. Lett. 91, (2003). [20] U. Gsser, E. R. Weeks, A. Schofiel, P. N. Pusey, n D. A. Weitz, Science 292, 258 (2001). [21] A. W. C. Lu, K. H. Lin, n A. G. Yoh, Phys. Rev. E 66, (2003). [22] J. C. Crocker, J. A. Mtteo, A. D. Dinsmore, n A. G. Yoh, Phys. Rev. Lett. 82, 4352 (1999). [23] P. Prinsen n P. vn er Schoot, Phys. Rev. E 68, (2003). [24] Z. Dogic, D. Frenkel, n S. Fren, Phys. Rev. E 62, 3925 (2000). [25] H. Me n Y. Me, Phys. Rev. Lett. 90, (2003). [26] R. Lipowsky, in Generic interctions of flexile memrnes., eite y R. Lipowsky n E. Sckmnn (Elsevier, 1995), pp [27] R. Lipowsky n S. Leiler, Phys. Rev. Lett. 56, 2541 (1986). [28] S. Pnkrtz, P. M. Johnson, A. Pulson, n C. C. Hung, Phys. Rev. E 61, 6689 (2000).

Controllable Microfluidic Production of Multicomponent Multiple Emulsions

Controllable Microfluidic Production of Multicomponent Multiple Emulsions Supplementry Mteril (ESI) or L on Chip This journl is The Royl Society o Chemistry 0 Controllle Microluiic Prouction o Multicomponent Multiple Emulsions Supplementry Mteril Wei Wng, Rui Xie *, Xio-Jie

More information

Conservation Law. Chapter Goal. 6.2 Theory

Conservation Law. Chapter Goal. 6.2 Theory Chpter 6 Conservtion Lw 6.1 Gol Our long term gol is to unerstn how mthemticl moels re erive. Here, we will stuy how certin quntity chnges with time in given region (sptil omin). We then first erive the

More information

Supplementary Figure 1 Supplementary Figure 2

Supplementary Figure 1 Supplementary Figure 2 Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully

More information

Supporting Online Material for

Supporting Online Material for Correction: 1 December 007 www.sciencemg.org/cgi/content/full/318/5857/1750/dc1 Supporting Online Mteril for Mott Trnsition in VO Reveled by Infrred Spectroscopy nd Nno- Imging M. M. Qzilbsh,* M. Brehm,

More information

Physics Lecture 14: MON 29 SEP

Physics Lecture 14: MON 29 SEP Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce Von Kleist ws le to store electricity in the jr. Unknowingly, he h ctully invente novel evice to store potentil ifference. The wter in the

More information

APPENDIX. Precalculus Review D.1. Real Numbers and the Real Number Line

APPENDIX. Precalculus Review D.1. Real Numbers and the Real Number Line APPENDIX D Preclculus Review APPENDIX D.1 Rel Numers n the Rel Numer Line Rel Numers n the Rel Numer Line Orer n Inequlities Asolute Vlue n Distnce Rel Numers n the Rel Numer Line Rel numers cn e represente

More information

Designing finite automata II

Designing finite automata II Designing finite utomt II Prolem: Design DFA A such tht L(A) consists of ll strings of nd which re of length 3n, for n = 0, 1, 2, (1) Determine wht to rememer out the input string Assign stte to ech of

More information

Rates of chemical reactions

Rates of chemical reactions Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Synthesis of metl oxide with roomtemperture photoreversile phse trnsition Shin-ichi Ohkoshi 1 *, Yoshihide Tsunouchi, 1 Tomoyuki Mtsud, 1 Kzuhito Hshimoto, 2 Asuk Nmi, 1 Fumiyoshi

More information

Silicon Nanowire Based Single-Molecule SERS Sensor

Silicon Nanowire Based Single-Molecule SERS Sensor Supporting informtion Silicon Nnowire Bsed Single-Molecule SERS Sensor Hui Wng, Xuemei Hn, Xuemei Ou, Chun-Sing Lee, Xiohong Zhng* nd Shuit-Tong Lee S1, A series of Si nnowires coted with compct ggregtes

More information

Period #2 Notes: Electronic Structure of Atoms

Period #2 Notes: Electronic Structure of Atoms Period # Notes: Electronic Structure of Atoms The logicl plce (for civil engineers) to begin in describing mterils is t the tomic scle. The bsic elements of the tom re the proton, the neutron, nd the electron:

More information

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy

More information

Graphene chiral liquid crystals and macroscopic assembled fibres

Graphene chiral liquid crystals and macroscopic assembled fibres Receive Jun 0 Accepte Nov 0 Pulishe 6 Dec 0DOI: 0.038/ncomms583 Grphene chirl liqui crystls n mcroscopic ssemle fires Z h e n Xu & Ch o G o Chirlity n liqui crystls re oth wiely expresse in nture n iology.

More information

Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene

Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.

More information

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light. 1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the

More information

Structures of some surfactant polyelectrolyte complexes

Structures of some surfactant polyelectrolyte complexes PRAMANA cfl Indin Acdemy of Sciences Vol. 61, No. 2 journl of August 2003 physics pp. 447 454 Structures of some surfctnt polyelectrolyte complexes REMA KRISHNASWAMY 1, V A RAGHUNATHAN 1 nd A K SOOD 2

More information

Particle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/)

Particle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/) Sutomic Physics: Prticle Physics Lecture 3 Mesuring Decys, Sctterings n Collisions Prticle lifetime n with Prticle ecy moes Prticle ecy kinemtics Scttering cross sections Collision centre of mss energy

More information

CHEMICAL KINETICS

CHEMICAL KINETICS CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy

More information

Supplementary Information

Supplementary Information Supplementry Informtion Spontneously mplified homochirl orgnic-inorgnic nno-helix complex vi self-prolifertion Hlei Zhi, Yn Qun, Li Li, Xing-Yng Liu, Xurong Xu c nd Ruikng Tng*,c Centre for Biomterils

More information

ELETROSTATICS Part II: BASICS

ELETROSTATICS Part II: BASICS GROWING WITH ONPTS: Physics LTROSTTIS Prt II: SIS Presence of chrge on ny oject cretes n electrosttic fiel roun it n in turn n electricl potentil is experience roun the oject. This phenomenon hs foun ppliction

More information

Examples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field

Examples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field Suslt illumintion studies through longitudinl nd trnsversl wve propgtion Riz Ali *, Jn Thorecke nd Eric Verschuur, Delft University of Technology, The Netherlnds Copyright 2007, SBGf - Sociedde Brsileir

More information

6. Photoionization of acridine through singlet and triplet channels

6. Photoionization of acridine through singlet and triplet channels Chpter 6: Photoioniztion of cridine through singlet nd triplet chnnels 59 6. Photoioniztion of cridine through singlet nd triplet chnnels Photoioinztion of cridine (Ac) in queous micelles hs not yet een

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. THE PHYSICS OF SOFT CONDENSED MATTER

Data Provided: A formula sheet and table of physical constants is attached to this paper. THE PHYSICS OF SOFT CONDENSED MATTER Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. Ancillry Mteril: Grph pper (liner) DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn Semester (2015) THE PHYSICS OF SOFT CONDENSED

More information

Chapter 4rth LIQUIDS AND SOLIDS MCQs

Chapter 4rth LIQUIDS AND SOLIDS MCQs Chpter 4rth LIQUIDS AND SOLIDS MCQs Q.1 Ioni solis re hrterize y () low melting points () goo onutivity in soli stte () high vpour pressure () soluility in polr solvents Q.2 Amorphous solis. () hve shrp

More information

Polymers: Melts, Crystals, Mixtures and Gels

Polymers: Melts, Crystals, Mixtures and Gels 7-9-9 Polymers: Melts, Crystls, Mixtures n Gels nres. Dhlin Lecture 5/6 Jones: 5., 6.-6., 7.7, 8.-8., 9. Hmley:.5,.7-.8,.-. hlin@chlmers.se http://www.hlin.com/ 7-9-9 Soft Mtter Physics Outline From the

More information

Reverse Engineering Gene Networks with Microarray Data

Reverse Engineering Gene Networks with Microarray Data Reverse Engineering Gene Networks with Microrry Dt Roert M Mllery Avisors: Dr Steve Cox n Dr Mrk Emree August 25, 2003 Astrct We consier the question of how to solve inverse prolems of the form e At x(0)

More information

Section 20.1 Electric Charge and Static Electricity (pages )

Section 20.1 Electric Charge and Static Electricity (pages ) Nme Clss Dte Section 20.1 Electric Chrge nd Sttic (pges 600 603) This section explins how electric chrge is creted nd how positive nd negtive chrges ffect ech other. It lso discusses the different wys

More information

Fully Kinetic Simulations of Ion Beam Neutralization

Fully Kinetic Simulations of Ion Beam Neutralization Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion

More information

Parse trees, ambiguity, and Chomsky normal form

Parse trees, ambiguity, and Chomsky normal form Prse trees, miguity, nd Chomsky norml form In this lecture we will discuss few importnt notions connected with contextfree grmmrs, including prse trees, miguity, nd specil form for context-free grmmrs

More information

Chemistry Department. The Islamic University of Gaza. General Chemistry B.(CHEMB 1301) Time:2 hours الرقم الجامعي... اسم المدرس...

Chemistry Department. The Islamic University of Gaza. General Chemistry B.(CHEMB 1301) Time:2 hours الرقم الجامعي... اسم المدرس... The Islmic University of Gz Chemistry Deprtment Generl Chemistry B.(CHEMB 1301) Time:2 hours 60 اسم الطالب... الرقم الجامعي... اسم المدرس... R = 8.314 J/mol.K, or = 0.0821 L.tm/mol.K Q1- True ( ) or flse(

More information

AMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE

AMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE AMPERE 2000 th 30 CONGRESS AMPERE on Mgnetic Resonnce nd Relted Phenomen Lison, Portugl, 23-2 July 2000 Under the uspices of The GROUPEMENT AMPERE Edited y: A.F. MARTINS, A.G. FEIO nd J.G. MOURA Sponsoring

More information

Stereoselective Synthesis

Stereoselective Synthesis Stereoselective Synthesis Dr Michel Perkins, Fliners University Reference Texts: Stereochemistry of orgnic compouns Ernest L. Eliel New York : Wiley & Sons, c1994. Chpter 12 on stereoselective synthesis

More information

ANSWERS TO REVIEW PROBLEM SET CH F

ANSWERS TO REVIEW PROBLEM SET CH F ANSWERS T REVIEW PRBLEM SET C41-018F [1] () The chirl isomer is stilized y intrmoleculr hydrogen onding etween the two guche groups. Such n rrngement lso keeps the ulky tert-utyl groups frther prt s they

More information

Temperature influence compensation in microbolometer detector for image quality enhancement

Temperature influence compensation in microbolometer detector for image quality enhancement .26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*

More information

Poly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents

Poly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents SUPPLEMENTARY INFORMATION Poly(vinylmine) Microgels: ph-responsive Prticles with High Primry Amine Contents Sineent Thioonro, Cory Berkln, Amir H. Milni, Rein Ulijn c n Brin R. Suners, * Polymer Science

More information

PHY 140A: Solid State Physics. Solution to Midterm #1

PHY 140A: Solid State Physics. Solution to Midterm #1 PHY 140A: Solid Stte Physics Solution to Midterm #1 TA: Xun Ji 1 October 24, 2006 1 Emil: jixun@physics.ucl.edu Problem #1 (20pt)Clculte the pcking frction of the body-centered cubic lttice. Solution:

More information

Flexible Beam. Objectives

Flexible Beam. Objectives Flexile Bem Ojectives The ojective of this l is to lern out the chllenges posed y resonnces in feedck systems. An intuitive understnding will e gined through the mnul control of flexile em resemling lrge

More information

2.4 Linear Inequalities and Interval Notation

2.4 Linear Inequalities and Interval Notation .4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or

More information

Physics 1402: Lecture 7 Today s Agenda

Physics 1402: Lecture 7 Today s Agenda 1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:

More information

School of Business. Blank Page

School of Business. Blank Page Integrl Clculus This unit is esigne to introuce the lerners to the sic concepts ssocite with Integrl Clculus. Integrl clculus cn e clssifie n iscusse into two thres. One is Inefinite Integrl n the other

More information

SUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION

SUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION Physics 8.06 Apr, 2008 SUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION c R. L. Jffe 2002 The WKB connection formuls llow one to continue semiclssicl solutions from n

More information

Last Time emphasis on E-field. Potential of spherical conductor. Quick quiz. Connected spheres. Varying E-fields on conductor.

Last Time emphasis on E-field. Potential of spherical conductor. Quick quiz. Connected spheres. Varying E-fields on conductor. Lst Time emphsis on Efiel Electric flux through surfce Guss lw: Totl electric flux through close surfce proportionl to chrge enclose Q " E = E = 4$k e Q % o Chrge istribution on conuctors Chrge ccumultes

More information

The development of nanoscale morphology in polymer:fullerene. photovoltaic blends during solvent casting

The development of nanoscale morphology in polymer:fullerene. photovoltaic blends during solvent casting Supplementry informtion Supplementry Mteril (ES) for Soft Mtter The development of nnoscle morphology in polymer:fullerene photovoltic lends during solvent csting To Wng, * Aln D. F. Dunr, Pul A. Stniec,

More information

p-adic Egyptian Fractions

p-adic Egyptian Fractions p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction

More information

Thin Film Scattering: Epitaxial Layers

Thin Film Scattering: Epitaxial Layers Thin Film Scttering: Epitxil yers Arturs Vilionis GAM, Stnford University SIMES, SAC 5th Annul SSR Workshop on Synchrotron X-ry Scttering Techniques in Mterils nd Environmentl Sciences: Theory nd Appliction

More information

Lecture 10: PN Junction & MOS Capacitors

Lecture 10: PN Junction & MOS Capacitors Lecture 10: P Junction & MOS Cpcitors Prof. iknej eprtment of EECS Lecture Outline Review: P Junctions Therml Equilibrium P Junctions with Reverse Bis (3.3-3.6 MOS Cpcitors (3.7-3.9: Accumultion, epletion,

More information

Chapter 2 USING THE SWITCHABLE QUALITY OF A LIQUID CRYSTAL SOLVENT TO MEDIATE SEGREGATION BETWEEN COIL AND LIQUID CRYSTALLINE HOMOPOLYMERS

Chapter 2 USING THE SWITCHABLE QUALITY OF A LIQUID CRYSTAL SOLVENT TO MEDIATE SEGREGATION BETWEEN COIL AND LIQUID CRYSTALLINE HOMOPOLYMERS 22 Chpter 2 USING THE SWITCHABLE QUALITY OF A LIQUID CRYSTAL SOLVENT TO MEDIATE SEGREGATION BETWEEN COIL AND LIQUID CRYSTALLINE HOMOPOLYMERS Chpter 2... 22 2.1 Introduction...22 2.2 Experimentl...24 2.3

More information

THE ULTRATHIN POLYMER FILMS BASED ON POLYANILINE AS SPR SENSITIVE DIAGNOSTIC SYSTEMS

THE ULTRATHIN POLYMER FILMS BASED ON POLYANILINE AS SPR SENSITIVE DIAGNOSTIC SYSTEMS THE ULTRATHIN POLYMER FILMS BASED ON POLYANILINE AS SPR SENSITIVE DIAGNOSTIC SYSTEMS ISAKOVA Alexndr 1, OMELCHENKO Olg 1, GARINA Ekterin 2, INDENBOM Andrey 1,3 1 A.N. Frumkin Institute of Physicl Chemistry

More information

a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2

a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2 18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions

More information

BOND ORDER (BO): Single bond Þ BO = 1; Double bond Þ BO = 2; Triple bond Þ BO = 3 Bond Order Þ bond strength and bond length

BOND ORDER (BO): Single bond Þ BO = 1; Double bond Þ BO = 2; Triple bond Þ BO = 3 Bond Order Þ bond strength and bond length EMISTRY 104 elp Sheet #1 hem 103 Review (Text: h 6, h 7) Do topics pproprite for your lecture Prepred y Dr. Tony Jco http://www.chem.wisc.edu/res/clc (Resource pge) Nuggets: Electronegtivity (6.7), Bond

More information

Rugby High School Physical Science I Can & Evidence Statements

Rugby High School Physical Science I Can & Evidence Statements Rugy High School Physicl Science I Cn & Evidence Sttements RHS-PS1-1 Students who demonstrte understnding cn: RHS-PS1-1. Use the periodic tle s model to predict the reltive properties of elements sed on

More information

Crystals. Fig From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005)

Crystals. Fig From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005) Crystls Mterils will often orgnize themselves by minimizing energy to hve long rnge order. This order results in periodicity tht determines mny properties of the mteril. We represent this periodicity by

More information

Heavy tail and stable distributions

Heavy tail and stable distributions Hevy til nd stle distriutions J.K. Misiewicz Deprtment of Mthemtics nd Informtion Science Technicl University of Wrsw X or its distriution hs hevy til if E(X ) =. X or its distriution hs hevy til of order

More information

Here we consider the matrix transformation for a square matrix from a geometric point of view.

Here we consider the matrix transformation for a square matrix from a geometric point of view. Section. he Mgnifiction Fctor In Section.5 we iscusse the mtri trnsformtion etermine mtri A. For n m n mtri A the function f(c) = Ac provies corresponence etween vectors in R n n R m. Here we consier the

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory 2. Diffusion-Controlled Reaction

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory 2. Diffusion-Controlled Reaction Ch. 4 Moleculr Rection Dynmics 1. Collision Theory. Diffusion-Controlle Rection Lecture 17 3. The Mteril Blnce Eqution 4. Trnsition Stte Theory: The Eyring Eqution 5. Trnsition Stte Theory: Thermoynmic

More information

Simulated climate vegetation interaction in semi-arid regions affected by plant diversity

Simulated climate vegetation interaction in semi-arid regions affected by plant diversity SULMNTARY INFORMATION DOI: 0.038/NGO96 Simulted climte vegettion interction in semi-rid regions ffected y plnt diversity M. Clussen,,*, S. Bthiny, V. Brovkin nd T. Kleinen []{Mx lnck Institute for Meteorology,

More information

QUB XRD Course. The crystalline state. The Crystalline State

QUB XRD Course. The crystalline state. The Crystalline State QUB XRD Course Introduction to Crystllogrphy 1 The crystlline stte Mtter Gseous Stte Solid stte Liquid Stte Amorphous (disordered) Crystlline (ordered) 2 The Crystlline Stte A crystl is constructed by

More information

The Thermodynamics of Aqueous Electrolyte Solutions

The Thermodynamics of Aqueous Electrolyte Solutions 18 The Thermodynmics of Aqueous Electrolyte Solutions As discussed in Chpter 10, when slt is dissolved in wter or in other pproprite solvent, the molecules dissocite into ions. In queous solutions, strong

More information

The Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics

The Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics Proceedings of the 5th Smll Systems Simultion Symposium 2014, Niš, Seri, 12th-14th Ferury 2014 The Influence of Interfce nd Semiconductor Bulk Trps Generted Under HEFS on MOSFET`s Electricl Chrcteristics

More information

Homework Assignment 3 Solution Set

Homework Assignment 3 Solution Set Homework Assignment 3 Solution Set PHYCS 44 6 Ferury, 4 Prolem 1 (Griffiths.5(c The potentil due to ny continuous chrge distriution is the sum of the contriutions from ech infinitesiml chrge in the distriution.

More information

Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary

Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed

More information

A study of fluid flow simulation in convergentdivergent

A study of fluid flow simulation in convergentdivergent IOP Conference Series: Mterils Science nd Engineering PAPER OPEN ACCESS A study of fluid flow simultion in convergentdivergent nozzles To cite this rticle: I Olru 2015 IOP Conf. Ser.: Mter. Sci. Eng. 95

More information

Simulation of Eclipsing Binary Star Systems. Abstract

Simulation of Eclipsing Binary Star Systems. Abstract Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.

More information

XX-th ARS SEPARATORIA Szklarska Poręba, Poland 2005

XX-th ARS SEPARATORIA Szklarska Poręba, Poland 2005 XX-th ARS SEPARATORIA Szklrsk Porę, Polnd 25 DIALYSIS OF METAL IONS THROUGH ULTRAFILTRATION POLYSULFONE MEMBRANES ENHANCED BY POLY(ACRYLIC ACID) Gryzeld POŹNIAK Wroclw University of Technology, Deprtment

More information

Triangular hysteresis loops in the spin-rotation region of orthoferrites

Triangular hysteresis loops in the spin-rotation region of orthoferrites Fizik Nizkikh Tempertur, 010, v 36, Nos 8/9, p 1001 1005 Tringulr hysteresis loops in the spin-rottion region of orthoferrites YB Bzliy 1, nd LT Tsyml 3 1 Institute of Mgnetism of the Ntionl Acdemy of

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI: 1.138/NMAT3984 Supplementry Informtion for Improved performnce nd stility in quntum dot solr cells through nd lignment engineering Chi- Ho M. Chung 1, Ptrick R. Brown 2, Vldimir Bulović 3 & Moungi

More information

Minimal DFA. minimal DFA for L starting from any other

Minimal DFA. minimal DFA for L starting from any other Miniml DFA Among the mny DFAs ccepting the sme regulr lnguge L, there is exctly one (up to renming of sttes) which hs the smllest possile numer of sttes. Moreover, it is possile to otin tht miniml DFA

More information

Mass Creation from Extra Dimensions

Mass Creation from Extra Dimensions Journl of oern Physics, 04, 5, 477-48 Publishe Online April 04 in SciRes. http://www.scirp.org/journl/jmp http://x.oi.org/0.436/jmp.04.56058 ss Cretion from Extr Dimensions Do Vong Duc, Nguyen ong Gio

More information

Section 4: Integration ECO4112F 2011

Section 4: Integration ECO4112F 2011 Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

Rel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited

More information

Thermal Stability of Ti-C-Ni-Cr and Ti-C-Ni-Cr-Al-Si Nanocomposite Coatings

Thermal Stability of Ti-C-Ni-Cr and Ti-C-Ni-Cr-Al-Si Nanocomposite Coatings Journl of Physics: Conference Series PAPER OPEN ACCESS Therml Stility of Ti-C-Ni-Cr nd Ti-C-Ni-Cr-Al-Si Nnocomposite Cotings To cite this rticle: A V Andreev et l 2015 J. Phys.: Conf. Ser. 652 012057 View

More information

UNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences

UNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences UNIVERSITY OF OSLO Fculty of Mthemtics nd Nturl Sciences Midterm exm in MENA3100 Dy of exm: 19 th Mrch 2018 Exm hours: 14:30 17:30 This exmintion pper consists of 4 pges including 1 ppendix pge. Permitted

More information

DFA minimisation using the Myhill-Nerode theorem

DFA minimisation using the Myhill-Nerode theorem DFA minimistion using the Myhill-Nerode theorem Johnn Högerg Lrs Lrsson Astrct The Myhill-Nerode theorem is n importnt chrcteristion of regulr lnguges, nd it lso hs mny prcticl implictions. In this chpter,

More information

Section 6: Area, Volume, and Average Value

Section 6: Area, Volume, and Average Value Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find

More information

Strategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?

Strategy: Use the Gibbs phase rule (Equation 5.3). How many components are present? University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the three-phse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the

More information

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block

More information

1B40 Practical Skills

1B40 Practical Skills B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

TRIB HEIGHT- DEPENDENT ASPERITY RADII OF CURVATURES IN A CONTACT AND FRICTION MODEL

TRIB HEIGHT- DEPENDENT ASPERITY RADII OF CURVATURES IN A CONTACT AND FRICTION MODEL Proceeings of 4 ASME/STLE Interntionl Joint Tribology Conference Long Bech, Cliforni USA, October 4-7, 4 TRIB4-6449 HEIGHT- DEPENDENT ASPERITY RADII OF CURVATURES IN A CONTACT AND FRICTION MODEL George

More information

Li ion diffusion mechanism in the crystalline electrolyte γ-li 3 PO 4

Li ion diffusion mechanism in the crystalline electrolyte γ-li 3 PO 4 Li ion diffusion mechnism in the crystlline electrolyte γ-li 3 Yojun Du nd N. A. W. Holzwrth The structure of thin film bttery 3 Solid stte electrolyte could be mde very thin to overcome to the low ionconductivity.

More information

Intro to Nuclear and Particle Physics (5110)

Intro to Nuclear and Particle Physics (5110) Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41

More information

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

Chapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd

Chapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd Chpter 36 Diffrction In Chpter 35, we sw how light bes pssing through ifferent slits cn interfere with ech other n how be fter pssing through single slit flres-iffrcts- in Young's experient. Diffrction

More information

INVESTIGATION OF BRAGG GRATINGS RECORDED IN POLYMER- DISPERSED LIQUID CRYSTALS

INVESTIGATION OF BRAGG GRATINGS RECORDED IN POLYMER- DISPERSED LIQUID CRYSTALS Journl of Optoelectronics nd Advnced Mterils Vol., No. 3, Septemer, p. 799-83 INVESTIGATION OF BRAGG GRATINGS RECORDED IN POLYMER- DISPERSED LIQUID CRYSTALS K. Beev *, S. Sinov, T. Angelov, A. G. Petrov

More information

Review of Gaussian Quadrature method

Review of Gaussian Quadrature method Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge

More information

Packaging consideration of two dimensional polymer-based. photonic crystals for laser beam steering

Packaging consideration of two dimensional polymer-based. photonic crystals for laser beam steering Pckging considertion of two dimensionl polymer-sed photonic crystls for lser em steering Xinyun Dou, Xionn Chen, Mggie Yihong Chen, IEEE Senior Memer, Aln Xiolong Wng, Wei Jing c, Ry T. Chen *, IEEE Fellow

More information

On the application of explicit spatial filtering to the variables or fluxes of linear equations

On the application of explicit spatial filtering to the variables or fluxes of linear equations Journl of Computtionl Physics 225 (27) 2 27 www.elsevier.com/locte/jcp Short Note On the ppliction of explicit sptil filtering to the vriles or fluxes of liner equtions Christophe Bogey *, Christophe Billy

More information

D. Harel, Statecharts: A visual formalism for complex systems, Science of Computer Programming 8, 1987, pp

D. Harel, Statecharts: A visual formalism for complex systems, Science of Computer Programming 8, 1987, pp Sttechrts y Kenr ooper ontents Introuction Stte igrms epth (hierrchy) Orthogonlity (concurrency) rocst ommuniction Exmple Prolems Introuction Sttechrts were introuce y vi Hrel in 1987. Hrel, Sttechrts:

More information

Interpreting Integrals and the Fundamental Theorem

Interpreting Integrals and the Fundamental Theorem Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of

More information

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials:

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials: Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E-8 Ohm.m)

More information

9 th Interntionl Conference on Quntittive InfrRed Thermogrphy July -5, 008, Krkow - Polnd Two-dimensionl therml nlysis of orgnic mterils y micro-scle thermogrphy *Tokyo Institute of Technology, O-okym,

More information

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique? XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=

More information

3-Way Mixing and Sequencing Globe Valves, Flared (5/8 in. O.D.) with Electric, Hydraulic, and Pneumatic Actuators

3-Way Mixing and Sequencing Globe Valves, Flared (5/8 in. O.D.) with Electric, Hydraulic, and Pneumatic Actuators lectric, Hydrulic, nd Pneumtic ctutors TL 1. Select Vlve ody including P ode (Vlve Size, v Rting, Port ode) or select Vlve ssemly correct (refer to Tle 3 nd Tle 3 lso) less ctutor ode (XXX) including the

More information

polyimide Spray-coated ZrP/epoxy film Spray-coated ZrP/epoxy film glass

polyimide Spray-coated ZrP/epoxy film Spray-coated ZrP/epoxy film glass c d e polyimide Spry-coted ZrP/epoxy film glss Spry-coted ZrP/epoxy film f g Supplementry Figure 1. Opticl microscopy of smectic ( = 0.044) α-zrp/epoxy films., Trnsmission opticl microscopy (TOM) of smectic

More information

Thermal Performance of Electrocaloric Refrigeration using Thermal Switches of Fluid Motion and Changing Contact Conductance

Thermal Performance of Electrocaloric Refrigeration using Thermal Switches of Fluid Motion and Changing Contact Conductance Americn Journl of Physics nd Applictions 2016; 4(5): 134-139 http://www.sciencepublishinggroup.com/j/jp doi:.11648/j.jp.20160405.12 ISSN: 2330-4286 (Print); ISSN: 2330-4308 (Online) Therml Performnce of

More information

PH 102 Exam I Solutions

PH 102 Exam I Solutions PH 102 Exm I Solutions 1. Three ienticl chrges of = 5.0 µc lie long circle of rius 2.0 m t ngles of 30, 150, n 270 s shown below. Wht is the resultnt electric fiel t the center of the circle? By symmetry,

More information

dx dt dy = G(t, x, y), dt where the functions are defined on I Ω, and are locally Lipschitz w.r.t. variable (x, y) Ω.

dx dt dy = G(t, x, y), dt where the functions are defined on I Ω, and are locally Lipschitz w.r.t. variable (x, y) Ω. Chpter 8 Stility theory We discuss properties of solutions of first order two dimensionl system, nd stility theory for specil clss of liner systems. We denote the independent vrile y t in plce of x, nd

More information

Reading from Young & Freedman: For this topic, read the introduction to chapter 24 and sections 24.1 to 24.5.

Reading from Young & Freedman: For this topic, read the introduction to chapter 24 and sections 24.1 to 24.5. PHY1 Electricity Topic 5 (Lectures 7 & 8) pcitors nd Dielectrics In this topic, we will cover: 1) pcitors nd pcitnce ) omintions of pcitors Series nd Prllel 3) The energy stored in cpcitor 4) Dielectrics

More information