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1 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 α-zrp/epoxy films on polyimide show tht voids re present (indicted y red rrows) throughout the film., Smectic α-zrp/epoxy films on glss re void free, suggesting tht void formtion is sustrte dependent. c, Polrized opticl microscopy (POM) of the sme re s, except for the irefringent fringes of voids, film is lck nd fetureless, suggesting tht the nnopltelets is ligned perpendiculr to the direction of oservtion. Scle rs for c represents 50 m. d, POM of cross-sections of smectic α-zrp/epoxy films (thickness 13 µm) on polyimide (thickness 25 µm). Coting displys strong irefringence indicting the nnopltelets is ligned prllel to the direction of oservtion, scle r represents 20 µm. e, POM of cross-sections of smectic α-zrp/epoxy films (thickness 4 µm) on glss (thickness 1 mm). Coting displys strong irefringence, scle r represents 10 µm. f nd g re the TOM nd POM, respectively, of smectic α-zrp/epoxy films spry-coted on polyimide nd dried t 40ºC for one hour. Scle rs for f nd g represent 50 m. 1

2 Supplementry Figure 2. Lrge-re TEM imge of the ( = 0.044) ulk nnocomposite showing the long-rnge orienttionl (oriented in the direction indicted y white rrow) nd positionl order of nnopltelets. Scle r denotes 1 µm. 2

3 Supplementry Figure 3., Reltive permeility of α-zrp/epoxy coted films t vrious concentrtions (dimonds) re plotted for comprison to models proposed y Cussler nd other uthors (see Supplementry Tle 1). Reltive permeility of nnocomposite films reported y Sun et l. (squres) 39 re lso plotted for comprison., Comprison of experimentl dt for smectic ( = 0.044) α-zrp/epoxy with predicted spect rtios sed on different models. 3

4 q (nm -1 ) Intensity c z q (nm -1 y ) q (nm -1 ) Supplementry Figure 4., Schemtic showing the evolution of nded structure. Nnopltelets rotte (R) while sher flow (S) is generted in response to the sher pplied glolly. Dshed rrows indicte direction of sher flow, smll rrows indicte direction of rottion, red rrows indicte direction of glolly pplied sher, lue nd yellow nnopltelets indicte position efore nd fter sher is pplied, respectively., SAXS 2D diffrctogrm of the smectic ( = 0.040) α-zrp/epoxy liquid showing strong orienttion of the smectic phse. c, SAXS 1D diffrctogrm confirms the lmellr structure (d-spcing = 17.1 nm) of the α-zrp/epoxy liquid s q 1 : q 2 /q 1 : q 3 /q 1 : q 4 /q 1 = 1 : 2 : 3 : 4. 4

5 q z (nm -1 ) Intensity Epoxy/ZrP liquid mixed with curing gent ws cst into glss mould consisting of two glss pltes lined with silicone ruer. Curing ws crried out in nitrogen, in n upright position. Nnocomposite plque ws removed from the mould nd sections were cut out for POM c Sections were mounted onto glss slide using epoxy glue nd polished to 50 m thick for oservtion. d e q y (nm -1 ) q (nm -1 ) Supplementry Figure 5. c Mould-csting process for ( = 0.044) α-zrp/epoxy ulk nnocomposites. d, SAXS 2D diffrctogrm of the nnocomposite showing strong orienttion of the smectic phse. e, SAXS 1D diffrctogrm confirms the lmellr structure of the α- ZrP/epoxy nnocomposite s q 1 : q 2 /q 1 : q 3 /q 1 : q 4 /q 1 = 1 : 2 : 3 : 4. d-spcing ws found to e 15.2 nm. 5

6 Supplementry Tle 1. List of permeility models for filled polymer systems. Model Filler Geometry Flke Size, Arry Type Model Dimension Rion Monodisperse, Regulr Arry Nielsen 2D Eqution* Idel Cussler Regulr Arry Rion Monodisperse, Regulr Arry 2D ( ) Cussler Rndom Arry Monodisperse Flkes Rion Monodisperse, Rndom Arry 2D Cussler Rndom Arry Polydisperse Flkes Rion Polydisperse, Rndom Arry 2D [ ] Modified Cussler-Aris Disc Monodisperse, Rndom Arry 3D ( ) Disc Monodisperse, Rndom Arry Fredrickson-Bicerno 3D Gusev-Lusti Disc Polydisperse, Rndom Arry 3D * α = D/t, σ = stndrd devition, = men vlue of D 6

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