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Orientational transitions in block-copolymer melts under shear flow

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Orientational transitions in block-copolymer melts under shear flow
Orientational transitions in block-copolymer melts under shear flow
Morozov, Alexander Nicolaevitch
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to
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Publisher's PDF, also known as Version of record
Publication date:
2002
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Morozov, A. N. (2002). Orientational transitions in block-copolymer melts under shear flow: a theoretical
study [S.l.]: [S.n.]
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Download date: 30-03-2017
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Ó ƒoÔrÕ_3ÖÂ_:× f"u m ]yp _ Ø{Ù ] Ú Ù p/ÛbVkc„Û h d Ü m h cÝ Þ h l h m pu]„\^Û _ ûqßd h \bn—à£j-VY…"]o\^ÛbV a pÚ¤\b]oÛ^ۄá
ûqßd h \^n‰á;µq]„âÆã h \^Ý:á Ø h ÝKp h á ƒQä"ä[å_
Óçæ ÔHèe_ _ ܚf a ]oۊf"j-né _¡×H_(è \^]„n-\^VYcÝÛ h j _ Ü m h cÝ1Þ h l h m pu]„\ Ø{Ù ]„\^u h npj)fuVYcoÛo`
Ø{Ù ] á h \bpf"j-nêWß l ]o\bVkuŠ]oj a _ ë j-jZ)f m³ì ]y…Vk]„â h dWÚ Ù pÛ^VYc'f m Þ Ù ]ouŠVkÛ a \bpáší ƒ ` v æ v'î
v[v" ƒQä[ä"ï_
Óñð Ô é _[×r_[è \^]„n-\^VYcÝÛ h jŠf"j-n èe_ _ ܚf a ]oÛ _:ò pj)f"uŠVkcoÛ h dÜ m h cÝ˜Þ h l h m pu]„\^ۄ` Ø{Ù ] h \bp
f"jn—êWß l ]„\^VYu]„j a _ ë j-jZ)f m ì ]„…VY]„â h d¤ó—f a ]o\bV«f m coVY]oj-c„][á æ"ô ` v"ïƒ|îv[v"ï á ƒQä[ä ô _
Ó í Ô ´ _ë uFZ-jn-Û h j‰á-ê _× ] m dgf"j-nõáö _-÷ Z-f"jõá/f"j-n _/òF_ uV a Ùõ_‰ë¦m VYX[j-uŠ]oj aOh d m fu] m t
mæ"f"ô-\ù ø m h ` cæÝDô c h l æ h m pð uŠá ]o\Šuð VYco\^VYÛ a \^Z-c a Z-\b]~VYjžf"jž] m ]„c a \bVkc)] m n _ ó~f"co\ h u h m ]oc„Z m ]„Ûoá
ƒ[·ƒ 1 ä[å?î "ï ƒQä[ä _
Ó vzÔ ´ _)ë˜_ ´ h ll V!á:ó _)Ø Vk\^\b] mYm á è_ _ ܚf a ]oۄᴠ_-ëqm uŠn)f m á-f"j-n ì_:×H_ Þ h m øKp _Oú f"u] m t
m f"\i] fj-h co\^]VY]oj a á f æa V ù h jVk` jní pj)f"uŠô Vkcofá mkm p~Û æ Ù ]'f\^]onsn-Vkø m h cݗc h l h m pu]„\”u] m a Û _ û_ Ú Ù p/Û _
è Õ^Õ ƒ[·ƒ 1 ƒ'ä ƒy'ä ï ƒQä[ä _
Óñô ԘüW_ t ì_ Þ Ù ]oj‰á û_,ëH_ ´ h \bj)] m nõá _qòF_ uŠV a Ù á û_,ؔ_ é\ h"a Ù f"Z-Ûoá•f"j-n¢ó _ ó _
f a Ý h â,ÛbÝV ÚWf a âef'pÛ aih uˆf"c„\ h Ûbc'f ] h \^n-]„\qVYj~j-f"j h Û a \^Zc a Z\^]on—ø m h cÝCc h l h m pt
uŠ]o\bÛ _ coVY]o_ j-c„][á æÙ " ` ƒ æ í å? æ v ð á ƒQä[äKm _
Ó zԘüW_ t ì_ Þ Ù ]„j f"j-n û_)ë˜_ ´ h \bj)] m n _(èWm h âštŸVkjn-Z-co]„n›f m VYX[j-uŠ]oj a{h d m f"uŠ] mYm f"\Oø m h cÝ
c h l h m pu]„\{u] m a Û _ Ú h m puŠ]o\oá ð ä ù ƒ'ä21 `ñí ô "äQî í ô ä[ä á ƒQä"ä[å_
Ó åÔrÕ_7ÖÂ_³× f"u m ]yp _ŒØ{Ù ]]„ý]oc aFh d{Û Ù ]'f\ h j h \^n-]„\^]„n$ø m h cݏc h l h m pu]„\rÛ h m Z a V h j-Û _
ÞeZ-\b\ _ û l VYj _ Þ h mYm!_ Õ j a _ coV _ á v ù v 1 ` ð í ƒ|î ð í ä á æ ï[ï"ï_
Ó äÔrÕ_zÖÂ_K× f"u m ]yp _ Õ j a \ h n-Z-c a V h j aih Û h d a uˆf a^a ]„\ ` l h m pu]„\^ۄá c h mYm h VYn-Ûoá f"u l-Ù V l-Ù V m ]oÛ
f"jn m VkþZ-Vkn c„\bpÛ a f m Û _7Ö V m ]„p[á)Þ Ù Vkc Ù ]„Û a ]o\oá æ ï"ï[ï_
Ó ƒQïÔHû_:×r_:ì h Ûb]on)f m ]f"j-n èe_ _ ܚf a ]oÛ _Oì£Ù ] h m h X"p h Àd û•\^n]o\^]„n f"jn ò VYÛ h \bn-]o\b]on put
uŠ] a \^VkcŽÚ h m p ù ] a Ù p mæ"]„ð-j-ù ] l \ æ"h ð[l æp m ]ojæ"] ð"1 ð tŸÚ h m p ù ] a Ù p m ] a Ù p m ]oj-] 1ò VYø m h cÝ¬Þ h l h m pu]„\^Û _
ó—fco\ h u h m ]oc„Z m ]„Ûoá 2å 1 ` ä?î å á ƒQä[ä[ï_
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Ó ƒ[ƒoÔëH_ ´] mkm ]o\oá-ê _ Ú³]on-]„u h j a ]"áf"j-n èe_ ó _-Ö V mYm u h Z a Ùõ_ ó—f"c„\ h m f aba VYco]•d–\ h uÛ^]„X[\^]|t
XKæ"fð a ]où næfu ð h \ l-Ù ð h ZÛ l-Ù f"Ûb]oÛ h df a Ù \^]„]ø m h cݛc h l h m puŠ]o\ _ Þ h mkm h Vkn Ú h m pu _ coV _ á
å ƒ t 1 ` åKv'î å[ä á ƒQäKï_
Ó ƒ æ Ô ó _³û_õè h m Ý"]„Ûoá ëH_ ´”] mkm ]o\„áõf"j-n èe_ Ú _ cof m VYÛ^V _rë js]|ß a \^ZÛ^V h j a ]oc Ù jVkþZ-]d h \ a Ù ]
læ \b] l ù f\if` a V hí-j á h d[ð ÛbVkj-X m ]yt‡co\bpÛ a f m Û^ h dø m h cݗc h l h m puŠ]o\^Û _ Þ h mYm h VYn Ú h m pu _ coV _ á
vƒ ·ƒ 1 ƒ|î ƒ'äK _
Ó ƒ ð Ô é _ × f"n oVYV h fj-j h Zõá ëH_ ó—f a Ù VkۄáDf"j-n ë˜_ Ý h Z m V h Û _ ó h j h c„\^VYÛ a fZ/ß/¶n-]
c h l h m pu ]„ \^]„Û a \bVkÛ ]„ þZ-]oj-c ]o Û”Û a p/\ ]o j-] æ VkÛ h l \ ]o j-æ[] æ Û a p\ ]„ j-] l \]o Ûb]oj a fj a m fˆÛ a \^Z-c a Z-\b]
cyp m Vkj-n\^VkþZ-] _ Þ h mkm h Vkn Ú h m p/u _ c„V _ á v[ ` ƒ?v'î á ƒQäK"ä_
Ó ƒ í Ô é _µ× f"n „VkV h f"j-j h Z‰á ë˜_ ó—f a Ù VkÛoá f"j-n ë˜_ Ý h Z m V h Û _ ø a ]„j a V h j n-]
[u h j h co\bVkÛ a f"Z/ß/Šn-]˜c h l h m pu ]o \^]„Û a \^VkÛ ]o þZ-æ ]„j-c ]„ ەð[ôÛ a p\ ð ]„ j-] zVkÛ h l \ ]„ j-] Û a p\ ]o j] l f\
c„VkÛifV mkm ]ouŠ]oj a lm f"j _ Þ h mkm h Vkn Ú h m pu _ coV _ á v[ ` ƒ î:ƒ ä á ƒQäK"ä_
Ó ƒ?vzÔ ´ _£ë˜_ ´ h ll V!áró _qØ Vk\b\^] mYm á”fj-n èe_ _ Üef a ]„Û _ Ù ]'f"\tŸVYj-n-Z-c„]on¢VkÛ h"a \ h l VYcyt a^h t
m f"u] mkm f"\ a \if"jÛ^V a V h j _ Ú Ù pÛ _ ì ]„… _ ú ] aba _ á "ï ù ƒQ2ï 1 ` ƒ í[í ä? í v æ á ƒ'ä[ä ð _
Ó ƒ ô Ôrì_ ó _ ´rfj-j)f"j f"j-n û_rëH_ ´ h \^j)] m n _ ꡅ h m Z a V h j h dŒuŠVkco\ h Û a \^Z-c a Z-\b]fj-n
…VkÛbc h ] m f"Û a VkcoV a p n-Z-æ \bVkj-ù X h â f m VkX[j-ô uŠ]oj a1h df m f"u] mkm f"\+n-VYø m h cÝ c h l h m pu]„\ _
ó—fco\ h u h m ]oc„Z m ]„Ûoá v 1 ` ƒ[ƒQ[Q[ƒ'å á ƒQä[ä í _
Ó ƒ?zÔ ã _¦ü‰Ù f"j-Xžfj-n¹à _,Ö VY]oÛbj-]o\ _ p/uŠuŠ] a \bVkcn-VYø m h cݬc h l h m pu]„\^ÛZ-j-n-]„\ m f"\^X[]
f"u ð)l-ù m V a Zn-] h Û^coV mkm f aið h \§p1Û Ù ]'f"\ h â`sê¤j a f"j-X m ]ouŠ]oj a ]yý‰]„c a _ û_ Þ Ù ]ou _ Ú Ù pÛ _ á
ƒQï ƒ[‹ƒ 1 `ñí "å í î í "ä á ƒQä[ä[v/_
Ó ƒQåÔ ã _(ü‰Ù f"j-Xá(à _WÖ VY]oÛ^j]o\oáOf"jn ×r_ ÖÂ_ l Vk]„Û^Û _sè \^]„þZ]oj-cyp­n-] l ]oj-n]oj-c„] h d h \bV€t
]„æ j a ùfð a V h j Vkj npj)f"uŠVkc'f mkm p¹Û Ù ]of"\^]„n nVkø m h cÝÂc h l h m pu]„\^Û _ ó~f"co\ h u h m ]oc„Z m ]„Ûoá
å 1 ` [å?î"åƒ á ƒQä[ä[v/_
Ó ƒQäÔ ã _˜ü‰Ù f"j-X-á*à _Ö VY]oÛbj-]o\„á*ã _ ãf"j-X-á ؔ_ ÚWf"ÝZ m fáŠf"j-n ×H_•ÖÂ_ l VY]oÛ^Û _ ë jt
j-]of m VYj-X]„ý]oc a Û h j æ h \bù Vk]oô j a f a V æ h jsVYjsð n/p/j-f"uô VYc'f mYm p~Û Ù ]of"\^]„n$n-VYø m h cÝ c h l h m pu]„\^Û _
ó—fco\ h u h m ]oc„Z m ]„Ûoá ä ƒ 1 ` v í Qîv í ƒ á ƒQä[ä _
Óñæ ïÔ ã _:ü‰Ù f"j-XFf"j-n›à _Ö Vk]oÛbj-]o\ _ puŠu] a \^VYc¦n-VYø m h cÝ*c h l h m p/uŠ]o\bۚZ-j-n]o\ m f\^X[]¦f"u*t
l-m V ô)a Z-ù n-] ` æ h Û^ô c„V mkm f æ aih ô \bp”á Û Ù ]'f"\ h â` ò Z)f m d–\b]oþZ-]ojc„pF]|ß l ]„\^VkuŠ]oj a Û _ û_ Þ Ù ]ou _ Ú Ù pÛ _ á
ƒQï 1 ä ƒyî ä ä ƒQä[äK_
Óñæ ƒoÔ à _[Ö Vk]oÛbj-]o\ _‰ú f"uŠ] mYm f"\³n-VYø m h cݘc h l h m pu]„\^Û¤Z-jn-]o\ m f\^X[]{fu l-m V a Z-n-] h Û^coV mkm f aih \§p
Ûð[Ù ð ]'f"æ !\ h â` h \^n-]„\Ff"jn$npj)f"uŠVkc„Û _ ó—f"co\ h u h m!_ Þ Ù ]„u _ Ú Ù pÛ _ á ƒQä"å ù ƒ[‹ƒ 1 ` ð[ð ƒQä?î
v á ƒQä"äK/_
Óñæ[æ Ôr×r_Wú ]oVYÛ a á òF_ ó—f"\bVkj-X-á ؔ_ Ø{Ù Z-\bj/t ëqm ø-\b]oc Ù a á(fj-n$à _³Ö VY]oÛ^j]o\ _~ò h Z-ø m "] )V l h d
h \bVk]„j a f a V h jCd h \£f m f"uŠ] mkm f"\enVkø m h cÝc h l h m puŠ]o\,Z-j-n]o\£Û Ù ]of"\ _ û_ Þ Ù ]ou _ Ú Ù pÛ _ á
ƒ[ƒ'ï ù ƒ?& 1 ` å æ[æ vQîå æ[æ å á ƒQä[ä"ä_
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h dOÛ Ù ]'f"\n-]yd h \^uf a V h j-Û¦f"j-nø m h cݛc h l h m p/uŠ]o\¦u h \ l-Ù h m h X"p _ ó~f"co\ h u h m ]oc„Z m ]„Ûoá
æ"ô-ù ƒQ2ï 1 ` æ v í æ î æ v í ä á ƒQä[ä ð _
Óñæ í Ô ´ _¦Õ_£Ö Vkj-]yp[á _ _ ÚWf a ] m á ì_ é _•ú f"\^Û h jõá˜f"j-n ×H_£Ö f a f"j)fø] _ ó h \ lÙ h m t
h Xp h d£f m f"uŠ] mYm f"\•nVkø m h c݁c h l h m pu]„\˜f m VkX[j]on l ]o\ l ]„j-n-VYcoZ m f"\ a^h—a Ù ]ˆÛif"u l-m ]
l-ó—m f"fj-co\]h ` u Ø h \^f"]oj-c„ÛbZ u]„VYÛoÛ^á Û^V æ"h ô-j›ù ] ô m ]„c`çí a ð\ h j~ð uí ð VYco\ h á Û^c h l ðp›fj-n Û^uf mYm tfj-X m ],ßtŸ\if'p›Û^cof a^a ]o\bVkj-X _
m m ƒ 1 î [v ƒQä[ä _
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m f"æuùð ] mk`m ð[f"ô]"`¦Ú ð[hô[mð p/á Û a p\^]oí j]yt l h m p/VYÛ h l \^]oj]ŠVYjn h c a p mOlÙ a Ù f m f a ] _ Ú Ù pÛ _ ì ]„… _ ú ] a^a _ á
1 ï?î ƒQä[ä _
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m m 2ï 1 v"v Qîv"v[v[v ƒQä[ä _
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f"jn \ Ù ] h m h X"p h d˜æf mù f"uŠæ ] mkm ð f"\ ð l h mð pÛ a p\^]„j-] îžl h m p/VYÛ h l \^]oj]ø m h cÝc h l h m pu]„\ _
ó—fco\ h u h m ]oc„Z m ]„Ûoá å ƒ 1 `çí ƒ î í ƒQå á ƒQä[äKv_
Óñæ å-Ô ,˜_ ´ _ é”Z l a f/á ì_ ´”\^VkÛ Ù j)f"u hh \ a V!á û_:ë˜_ ´ h \bj)] m nõá™f"j-/n . _™òF_ .uV a Ùõ_ ꤅ h m Zt
a V h j h d)uŠVkco\ h Û a \^Z-c a Z-\b]en-Z\^VkjX¦Û Ù ]'f"\¤f m VkX"j-u]„j a VYjFf l h m pÛ a p\^]„j-]yt l h m pVkÛ h l \^]„j-]
m f"u] mkm f"\nVkø m h cÝc h l h m puŠ]o\ _ ó—f"c„\ h u h m ]„coZ m ]oۄá æ å ù ƒ ð 1 `ñí[í ô í î í[1í 0zí-á ƒ'ä[äKv/_
Óñæ äÔ Ü _-ú(_ì VYVkÛb]"áé _×H_-è \b]on-\bVkcÝÛ h j‰á ìr_ é _ú f"\^Û h jõá)f"jn òF_ . _ Ú ]'f\^Û h j _(ì£Ù ] h m h X"p
f"jnŽÛ Ù ]'f\§tŸVYj-n-Z-c„]onŽæ f ù!m æ"VkðX[j-uŠô ]oj ð a¦h d ô m f"uŠ] mYm f"\,n-VYø m h cݛf"j-n a \bVkø m h cÝc h l h m pu]„\^Û _
ó—fco\ h u h m ]oc„Z m ]„Ûoá å 1 `20 v î 0 v"ä á ƒQä[äKv_
Ó3ð ï-Ô ,˜_ ´ _ éZ l a fá ì_ ´”\^VYÛ Ù j)fu hh \ a V!á üW_ t ì_ Þ Ù ]oj‰á û_ë˜_ ´ h \^j/)] m nõ&á . _:òF_ .uV a Ù á
ó _ ó _ .f a Ý h â,Û^ÝV!á³f"jn û_‰Ø”_ é\ h"a Ù f"Z-Û _˜ò pj)f"uŠVkcoÛ h dOÛ Ù ]of"\f m VYX[j-uŠ]oj a VYjf
f"u] f"\,n-Vkø h cݛc h h pu]„\o` j a ]o\ f'p h dd–\b]oþZ-]ojc„p[á7Û a \ifVkjf"u l-m V a Z-n]"áõfj-n
am ]ou l mk]„m \if a Z-\^] m _ ó~f"co\ lh u m h m ]oc„Z m ]„ÛoÕ á æ ä ùl-ð m 1 ` å 0 vQî/å"å í-á ƒ'ä[ä ô _
Ó3ð ƒo-Ô ,˜_ ´ _ éZ l a fá ì_ ´”\^VYÛ Ù j-f"u hh \ a V!á û_-ëH_ ´ h \^j)] m nõá-f"j-n . _:òF_ .uV a Ùõ_¤ì h m ] h d
Û a \ifVkjVkjc h j a \ h mYm VYj-X m f"u] mkm f"\ h \^Vk]„j a f a V h jn-Z\^VkjX h â·f m VYX[j-uŠ]oj a•h den-VYø m h cÝ
c h l h m pu]„\^Û _ ó—f"co\ h u h m ]„coZ m ]oÛoá æ ä ù í 1 ` ƒ ð v"ä?î:ƒ ð[ôKæ á ƒQä[ä ô _
Ó3ðKæ ÔHüW_ t ì_ Þ Ù ]oj‰á ë˜_ ó _‹Õ ÛbÛif"Vkf"jõá û_7ë˜_ ´ h \^j-] m n‰á . _ òF_ .uV a Ù á û_7ؔ_ é\ h"a Ù f"Z-Ûoá
f"jnó _ ó _ ./f a Ý h â,ÛbÝV _sò p/j-f"uVYcoÛ h d£Û Ù ]of"\§t‡Vkj-n-Zco]onDf m VkX[ju]„j aHh dqf m fu] m t
mó—f"\¬fcon-\ h Vkø u m h h c]oݶc„Z f ]„Ûo\ á Ù ð ] h ù!t æ"h ðl a `2Vk0 cof m áô ] 0 m ]oc a í-\ á h jœuŠ0 Vkco\ h Û^c h l p[á+f"j-n¶ßt‡\if'p=Û^cof a^a ]o\bVkj-X _
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v ƒ 1 `çí ƒ 0 vQî í ƒQåƒ á ƒQä[ä _
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Ó í10 Ôrì_ é _?ú f"\bÛ h j˜f"j-n˜é _?×r_zè \b]on-\bVkcÝÛ h j _E, VkÛbc h uŠ] a \^VYc l \ h l ]o\ a VY]oÛ h d-ø m h cݕc h l h m pt
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å[ä ä21 ` v"å"ä[ï?îv"å"ä 0/á ƒQä[å[å_
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