University of Groningen. Block copolymer self-assembly Klymko, Tetyana Romanivna

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1 Unvesty of Gonngen Bloc copolyme self-assembly Klymo, Tetyana Romanvna IMPORTANT NOTE: You ae advsed to consult the publshe's veson (publshe's PD) f you wsh to cte fom t. Please chec the document veson below. Document Veson Publshe's PD, also nown as Veson of ecod Publcaton date: 008 Ln to publcaton n Unvesty of Gonngen/UMCG eseach database Ctaton fo publshed veson (APA): Klymo, T. R. (008). Bloc copolyme self-assembly: homopolyme addtves and multple length scales. s.n. Copyght Othe than fo stctly pesonal use, t s not pemtted to download o to fowad/dstbute the text o pat of t wthout the consent of the autho(s) and/o copyght holde(s), unless the wo s unde an open content lcense (le Ceatve Commons). Tae-down polcy If you beleve that ths document beaches copyght please contact us povdng detals, and we wll emove access to the wo mmedately and nvestgate you clam. Downloaded fom the Unvesty of Gonngen/UMCG eseach database (Pue): o techncal easons the numbe of authos shown on ths cove page s lmted to 10 maxmum. Download date:

2 CHAPTER 6 Lamella-n-Lamella Self-Assembly n Lnea Tenay Multbloc Copolymes: Alexande-de Gennes Appoach and Dsspatve Patcle Dynamcs Smulatons Abstact. A smple theoetcal analyss of the lamella-n-lamella self-assembled state of tenay C-b-(B-b-A) m -b-b-b-c multbloc copolyme melts n the stong segegaton lmt s pesented usng the Alexande-de Gennes appoxmaton. o a gven value of m, the nfluence of the chan length of the vaous blocs and the loy-huggns χ and χ nteacton paametes on the numbe of ntenal domans s dscussed n detal. The theoetcal esults ae cooboated by compute smulatons usng the dsspatve patcle dynamcs technque.

3 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes 6.1 Intoducton In ths Chapte we consde once moe C-b-(B-b-A) m -b-b-b-c multbloc copolymes. Such systems ae the smplest epesentatves of heachcally odeed bloc copolyme-based systems. Due to the possblty to fom stuctues that combne dffeent length scales ths class of systems has been the subject of many expemental [1-15] and theoetcal [16-] nvestgatons. Compaed to the pevous chapte, we wll ntoduce a fa moe smple theoetcal modelng of the lamella-n-lamella self-assembled state usng the so-called Alexandede Gennes appoach. We show that ths smplfed appoach povdes esults that ae vtually dentcal to those obtaned by the fa moe elaboated teatment. It allows us to analyze and dscuss the doman fomaton n C-b-(B-b-A) m -b-b-b-c multbloc copolymes n much moe detal as a functon of the chan length of the blocs and the loy-huggns χ and χ nteacton paametes. To cooboate the theoetcal pedctons, we pefomed compute smulatons usng the well-nown dsspatve patcle dynamcs technque [3-31]. 6. The model Consdeng the tenay C-b-(B-b-A) m -b-b-b-c multbloc copolyme melt n the Alexande-de Gennes appoxmaton mples that we assume all m +1 mddle A- and B- blocs as well as the oute C-blocs to be stetched unfomly nsde the espectve layes. We assume that the m +1shot mddle blocs self-assemble nto ntenal layes confned between elatvely thc C oute layes. In geneal, a global multbloc confomaton can be ethe a bdge o a loop as llustated n gue 6.1. Both global bdges and global loops consst n tun of local loops and bdges. Due to assumed stong ncompatblty between the thee chemcally dffeent speces, the fst and the last B-bloc of the mddle multbloc wll be pesent n the fom of a local bdge confomaton n the fst and the last bounday B-layes (gue 6.1). Let x be the facton of global bdges and 1 x the facton of global loops. The aveage fee enegy pe multbloc copolyme chan s then gven by = x + ( 1 x) + x ln x + (1 x)ln(1 x) (6.1) bdge loop whee and ae the fee eneges of a global bdge and a global loop bdge loop confomaton. The last two tems n (6.1) epesent the entopy of mxng between global loops and bdges. We wll smply assume as a fst appoxmaton that x 1/, and thus ln. Hence, fom now on we wll estct ouselves to bdge loop bdge 7

4 Theoetcal analyss: Alexande-de Gennes appoach a global bdge confomaton and dscuss ts fee enegy n the Alexande-de Gennes appoxmaton. global bdge confomaton global loop confomatons gue 6.1. Schematc epesentaton of a global bdge (top) and a global loop (bottom) confomaton fo a C-b-(B-b-A) 4 -b-b-b-c multbloc copolyme. A, B and C blocs ae denoted by ed, yellow and geen colos, espectvely. 6.3 Theoetcal analyss Let n denote the degee of polymezaton of the ntenal A- and B-blocs ale and N denote the degee of polymezaton of the oute C-blocs, wth N >> n. The statstcal segment length and monome volume ae denoted as a and υ, espectvely, and ae assumed to be equal fo all chemcally dffeent components. The thcness of the ntenal layes and the oute laye ae denoted as h and H (gue 6.). uthemoe Σ s used to denote the ntefacal aea pe multbloc copolyme chan. The loy-huggns nteacton paametes ae χ, χ and χ AC and ae taen postve mplyng unfavoable nteactons between all the chemcally dffeent speces. H h gue 6.. Schematc epesentaton of a global bdge confomaton of a C-b-(B-b-A) m -b-b-b-c copolyme fo m = 6. h and H denote the thcness of the ntenal layes and half of the oute layes, espectvely. 73

5 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes Incompessblty mples Nυ = HΣ (6.) ( m + 1) nυ = hσ (6.3) The total fee enegy pe multbloc copolyme bdge can be wtten as bdge + ( 1) + m0 A + ( m + 1) 0 B + C conf (6.4) = + Hee and ae the ntefacal fee eneges elated to the ntefacal tensons and the aveage ntefacal aea Σ pe multbloc copolyme by γ Σ γ Σ (6.5) = = wth ntefacal tensons gven by a χ γ = and υ 6 a χ γ =. υ 6 The elastc fee eneges of unfomly stetched shot A- and B-blocs 0 A and 0B ae the same and ae gven by 0 3h = 0 A = 0 B = (6.6) na Lewse, the elastc fee enegy 0C fo the oute C-blocs s gven by 3H C = (6.7) Na The confomatonal contbuton conf taes nto account the numbe of dffeent possbltes to ceate multbloc confomatons and, as n ou pevous wo [1], wll be consdeed n a smplfed way by epesentng the mddle multbloc by a chan of 1 blobs popagatng n one decton. The coespondng pobablty s esultng n an ncease n fee enegy (n B T enegetc unts) gven by conf = ( )ln (6.8) 74

6 Theoetcal analyss: Alexande-de Gennes appoach Tang nto account Eqs. (6.), (6.3) and Eqs. (6.5)-(6.8), the fee enegy expesson (6.1) tansfoms nto * Q = γ Σ + + ( 3)ln, (6.9) Σ 3 = and Q * wth γ γ + ( 1) γ 3(m + 1) nυ 3Nυ = +. a a Mnmzaton of the fee enegy (6.9) wth espect to Σ yelds the equlbum nteface aea Σ 0 Q = * γ 1/ 3 (6.10) whch esults n the fnal expesson fo the total fee enegy: * / 3 1/ ( ) ( Q) + ( 3)ln 3 3 = γ (6.11) 6.4 Results and dscussons We consde fst the only system nvestgated expementally so fa,.e., PVP-b- (PI-b-PS) 4 -b-pi-b-pvp. It coesponds to χ = 0. 4, χ = 0. 1, χ N = 340, χ n = 17, m = 4 and n / N = 0.. The fee enegy (eq. 6.11) as a functon of the numbe of ntenal layes s pesented n gue 6.3a. The mnmum occus fo = 5, pecsely as found expementally [4]. Results fo dffeent values m = 3, 5 and 6 ae pesented n gue 6.3b, c and d. The values of found ae 5, 5 and 7. Note, that fo m = 5 the fee eneges fo = 5 and = 7 ae vey close. These esults ae n good ageement wth the ones obtaned fom a much moe elaboated mean-feld calculaton usng the same set of paametes, whee the mnma fo m = 3, 4, 5 and 6 occued fo = 5, 5, 7 and 7 [1]. 75

7 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes C-b-(B-b-A) 4 -b-b-b-c 39 C-b-(B-b-A) 3 -b-b-b-c a b 54 C-b-(B-b-A) 5 -b-b-b-c 64 6 C-b-(B-b-A) 6 -b-b-b-c = 0.0 B T c d gue 6.3. ee enegy of lamella-n-lamella self-assembled C-b-(B-b-A) m -b-b-b-c multbloc copolyme melt as a functon of the numbe of ntenal layes fo χ = 340, χ = 17, n/n = 0.. (a) m = 4, (b) m = 3, (c) m = 5, (d) m = 6. N n Influence of nteacton stength In ode to nvestgate the effect of ntefacal tenson, numecal calculatons wee pefomed fo dffeent values of the loy-huggns χ -paamete fo m = 3,4,5 and 6, χ = 0.1 and fxed length of the ntenal blocs n = 00. Thoughout the est of ths secton the length N of the oute blocs s assumed to satsfy ( m + 1)n = N, thus assung an equlbum lamella stuctue. The esults ae summazed n Table 6.1. gue 6.4a-d shows the fee enegy as functon of fo m = 4 and loy-huggns 76

8 Theoetcal analyss: Alexande-de Gennes appoach paamete values χ = 0.1, 0.4, 1. 5 and 5, whee the mnma ae found at = 3, 5, 7 and 9, espectvely. Table 6.1. Equlbum numbe of ntenal domans 00. opt as a functon of χ fo χ = 0. 1 and n = χ opt m = 3 N = 700 m = 4 N = 900 m = 5 N = 1100 m = 6 N = 1300 m = 7 N = < > Lage χ values foce a educton n the ntefacal aea whch n tun foces the ntenal shot blocs to become moe stetched. To elefe ths stetchng the system stats to ceate moe ntefaces,.e. lage values of. Of couse, n ealty the values of the loy-huggns nteacton paametes hadly eve exceed unty. The calculatons fo lage values ae nevetheless useful to tac and undestand the tendences n the laye fomaton n tenay C-b-(B-b-A) m -b-b-b-c multbloc copolymes. 77

9 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes 44 4 C-(BA) 4 -B-C χ =0.1 χ = C-(BA) 4 -B-C χ =0.1 χ = opt =3 47 opt = a b C-(BA) 4 -B-C χ =0.1 χ =1.5 opt = C-(BA) 4 -B-C χ =0.1 χ =5 opt = c d gue 6.4. ee enegy of lamella-n-lamella self-assembled C-b-(B-b-A) 4 -b-b-b-c multbloc copolyme melt as a functon of the numbe of ntenal layes fo n = 00, N = 900, χ = 0. 1 and (a) χ = 0.1, (b) χ = 0. 4, (c) χ =1. 5, (d) χ = Chan length nfluence To see how these esults depend on the elastc stetchng of the blocs, the length of the ntenal blocs was deceased to n = 100 wth the oute bloc length N stll satsfyng ( m + 1) n = N. We fst consde fxed χ = The equlbum numbe of ntenal domans opt as a functon of m and χ ae gven n Table 6.. A compason wth Table 6.1 shows that the deceased length of the blocs, mplyng stffe spngs, ndeed eques lage values of χ to obtan the same numbe of ntenal layes. 78

10 Theoetcal analyss: Alexande-de Gennes appoach Table 6.. Equlbum numbe of domans opt as a functon of χ fo n = 100 and χ = χ opt m = 3 N = 350 m = 4 N = 450 m = 5 N = 550 m = 6 N = 650 m = 7 N = Numecal calculatons wee also pefomed fo a constant χ = 0. 1 as a functon of χ wth ntenal bloc lengths of n = 00 and n = 100. The esults ae collected n Table 6.3 and 6.4. gue 6.5 pesents fee enegy gaphs as a functon of fo m = 4, n = 00, N = 900, χ = 0. 1 and χ = (a), χ = (b). Table 6.3. Equlbum numbe of domans opt as a functon of χ fo n = 00 and χ = opt χ n χ m = 3 m = 4 m = 5 m = 6 m = 7 N = 700 N = 900 N = 1100 N = 1300 N = Table 6.4. Equlbum numbe of domans opt as a functon of χ fo n = 100 and χ = opt χ n χ m = 3 m = 4 m = 5 m = 6 m = 7 N = 350 N = 450 N = 550 N = 650 N =

11 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes C-(BA) 4 -B-C χ =0.05 χ = C-(BA) 4 -B-C χ =0.15 χ = opt = 5 44 opt = a b gue 6.5. ee enegy of lamella-n-lamella self-assembled C-b-(B-b-A) 4 -b-b-b-c multbloc copolyme melt as a functon of the numbe of ntenal layes fo n = 00, N = 900, χ = 0. 1 at (a) χ = 0.05, (b) χ = o the gven value of χ = 0. 1, nealy always the mnmal numbe of = 3 ntenal layes ae found. Only when χ s suffcently small a tanston to a 5-layeed stuctue (moe A/B nteface) s obseved. Of couse, nχ has to be consdeably lage than 10 to eally have a stongly segegated lamella-n-lamella self-assembled state. The ntefacal contbuton to the fee enegy s gven by = + ( 1), nteface (m + 1) nυ γ γ whch can be smply ewtten as nteface = h γ + whee Eqs.6.3 and 6.5 have been used. om ths expesson t follows staghtfowad that when χ > 4χ (( γ > γ ) a 3-layeed has a lowe ntefacal fee enegy than a 5- layeed one. The esults pesented n the vaous tables, howeve, show that n ealty a 3- layeed stuctue s aleady fomed at consdeably smalle values of χ, thus demonstatng n patcula the mpotance of the confomatonal ( 3)ln contbuton (see eq. 6.9) favoung small values of. The tendences obseved ae cooboated by the esults of compute smulatons obtaned by usng dsspatve patcle dynamcs smulaton technque. The esults ae descbed n the next secton, wheeas the computatonal detals ae pesented n the Appendx. 80

12 Theoetcal analyss: Alexande-de Gennes appoach 6.5 Dsspatve patcle dynamc dmulatons of C-b-(B-b-A) m -b-b-b- C multbloc copolymes In the dsspatve patcle dynamcs smulaton technque a lage sees of monomes ae collected nto a few bead-and-spng patcles n ode to smulate the molecula behavo on a longe tme- and length-scale [3-31]. The fst stuaton smulated esembled the expementally studed tenay PVP-b-(PI-b-PS) 4 -b-pi-b-pvp lnea undecabloc copolyme system,.e. m = 4 [5]. gue 6.6 shows the coespondng self-assembled state obseved fo C 4 -(B 1 A 1 ) 4 B 1 -C 4 wth the enegy paametes epesentng the soft epulson (see eq. A) equal to a BA = 85, a = 30. Usng equaton A10 n the appendx fo the elaton between these enegy paametes and the famla loy-huggns paametes ths coesponds to Nχ 338 and nχ 17.. gue 6.6 demonstates that a self-assembled lamella state s fomed wth 5 thn ntenal layes as obseved expementally [4] and calculated theoetcally (gue 6.3a and ef. 1). The same esult s obtaned fo ntenal blocs that ae twce as long C 4 -(B A ) 4 B -C 4 (the subscpts of A, B and C denote the numbe of beads taen fo the calculatons). Subsequently, we addess the ssue of the dependence of the numbe of ntenal layes on the ntefacal tenson. Tables suggest that fo ths pupose t may be best to tae m = 5 because then easonable vaatons n the values of the loy-huggns paametes ae theoetcally pedcted to nduce tanstons between dffeent numbe of ntenal layes. That ths s also the case n the smulatons s shown n gue 6.7, whee 3 snapshots of the same system C 4 -(B 1 A 1 ) 5 B 1 -C 4 ae pesented fo dffeent enegy paametes a, a. gue 6.7 demonstates that when the A-B nteacton becomes less unavouable and the B-C nteacton becomes moe unfavoable, ndeed tanstons ae obseved fom 3 to 5 to 7 ntenal layes. Thee s the obvous tendency to decease the nteface wth a coespondng ncease n the nteface. o the system wth m = 4, C 4 -(B 1 A 1 ) 4 B 1 -C 4, 3 and 5 ntenal layes wee obseved vayng the enegy paametes. To llustate the dependence of the numbe of ntenal layes on the length of the ntenal blocs two systems C 3 -(B 1 A 1 ) 3 B 1 -C 3 and C 3 -(B A ) 3 B -C 3 wee smulated usng the same enegy paamete values. gue 6.8 shows that n the fome case 3 ntenal layes ae fomed and 5 n the latte. Smla smulatons have been pefomed fo m equal to 4, 5 and 6 fo the same a = 75, a = 10 tang n =1 and n =. The numbe of ntenal layes found wee 5, 5 and 7 fo m = 4, 5 and 6, espectvely, ndependently of n. 81

13 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes gue 6.6. Snapshot of C4-(B1A1)4B1-C4 fo aba = 85, a = 30. a. b. c. gue 6.7. Snapshots of self-assembled C4-(B1A1)5 B1-C4 multbloc copolyme melt fo: (a) a = 50, a = 50; (b) a = 75, a = 10; (c) a = 65, a = 300 a. b. gue 6.8. Snapshots of (a) C3-(B1A1)3 B1-C3 and (b) C3-(BA)3 B-C3 fo a = 75 and a = 10. 8

14 Theoetcal analyss: Alexande-de Gennes appoach 6.6 Summay In ths Chapte, we pesented a smple theoetcal analyss of the stongly segegated lamella-n-lamella self-assembled state of tenay C-b-(B-b-A) m -b-b-b-c multbloc copolymes usng the Alexande-de Gennes appoach. Ths smplfed descpton allowed us to dscuss n detal the nfluence of the petnent paametes on the numbe of ntenal layes fomed. The man obsevaton concens the senstvty of on the ntefacal tenson between the oute C-layes and the adjacent ntenal B-layes. The theoetcally obseved geneal tendences wee cooboated by the esults of compute modelng usng dsspatve patcle dynamcs technque. Appendx. Computatonal detals The dsspatve patcle dynamcs (DPD) smulaton method was ntoduced by Hoogebugge and Koelman [3] and fst successfully appled by Goot and Madden [4] to dbloc copolyme melts. The tme evoluton fo a set of nteactng patcles s found by solvng Newton s equatons of moton. The foce actng on the -th patcle f due to patcle j s the sum of a consevatve foce andom foce R j C D R f = ( j + j + j ) j, a dsspatve foce D, and a C j j (A1) whee the sum s ove all othe patcles wthn a cetan cut-off adus C. Snce C s the only length scale t s used as the unt of length and thus set equal to 1. The consevatve C foce j s a soft epulsve foce gven by j aj (1 ) ej, j < C c j = c (A) 0, j c whee a j s the epulsve nteacton paamete between patcles and j, j = j, j ej =, D j = j. The dsspatve foce j s a hydodynamc dag foce and s defned by j D j = D γω ( 0, j c j )( e j v j ) e, j j < c (A3) whee γ s a fcton paamete, ω D s a -dependent weght functon. The andom foce descbes themal nose D j 83

15 Chapte 6 Lamella-n-Lamella Stuctue of C-(BA)m-B-C Multbloc Copolymes R j R σω ( j ) = 0, j C θj ej, Δt j < C (A4) whee σ s the nose ampltude, ω R s a weght functon, and θ j s a andom vaable wth nomal dstbuton, t s a tme step. The dsspatve foce slows down the patcles by emovng the netc enegy fom them and ths effect s balanced by the andom foce due to themal fluctuatons. cton γ and nose σ ae elated by [5]: σ = γ B T (A5) The assocated weght functons satsfy the fluctuaton-dsspaton theoem f the followng elaton s satsfed [6] The standad choce fo The spng foce D ω s ( ω R ()) D ω = (A6) ( C j ), j < D C ω = (A7) 0, j C S that acts on bead due to ts connecton wth beads j satsfes S = C j (A8) j whee C s a hamonc type spng constant, whch s chosen to be equal to 4 (n tems of B T) [5]. A modfed veson of the velocty-velet algothm s used to solve Newton s equatons of moton [7] ( t + Δt) = ( t) + v ( t) Δt f( t) Δt v~ ( t + Δt) = v ( t) + λf ( t) Δt f ( t + Δt) = f [ ( t + Δt), v ~ ( t + Δt)] v ( t + Δt) = v ( t) + 0.5Δt[ f ( t) + f ( t + Δt)] (A9) Goot and Waen [5] pesented a detaled nvestgaton of the effect of λ on the steady state tempeatue and showed that fo a patcle densty ρ=3 and nose σ =3, the optmum value s gven by λ =0.65 fo whch the tempeatue contol can be mantaned even at lage tme-steps of t =0.06. o ou calculatons we too accodngly λ = 0.65, t = 0.06, ρ = 3 and σ = 3. The DPD smulatons ae pefomed n a cubc box of L 3 gds wth peodc bounday condtons. Snce the patcle densty ρ s set equal to 3, the total numbe of smulated DPD beads equal 3L 3. As epoted n Refs. 8-30, the mophology obtaned by DPD smulatons may depend on the fnte sze of the smulaton box. In ou smulatons we have peodc stuctues wth lage peods and to exclude fnte sze effects we have to tae the smulaton box suffcently lage. The numbe of DPD beads pe chan s n 84

16 Theoetcal analyss: Alexande-de Gennes appoach the ange The sze of the smulaton box volume used was taen n the ange V = , n such a way that fo each case consdeed L exceded the length of the chans. All smulatons wee stated fom andom postons. ollowng the wo of Goot and Waen [5], the epulsve paametes between the same types of patcles s taen as a = 5. o dffeent types of patcles a j can be chosen fom the elaton between the enegy paamete a j and the loy Huggns nteacton paamete χ j a = χ (A10) j a j REERENCES [1] J. Ruoolanen, R. Mänen, M. Toel, T. Mäelä, R. Semaa, G. ten Bne, O. Iala, Scence 1998, 80, 557. [] O. Iala, G. ten Bne, Scence 00, 95, 407. [3] J. Ruoolanen, G. ten Bne, O. Iala, Adv. Mate. 1999, 11, 777. [4] J. Masuda, A. Taano, Y. Nagata, A. Noo, Y. Matsushta, Phys. Rev. Lett. 006, 97, [5] Y. Nagata, J. Masuda, A. Noo, D. Cho, A. Taano, Y. Matsushta, Macomolecules 005, 38, 100. [6] C.C. Evans,.S. Bates, M.D. Wad, Chem. Mate. 000, 1, 36. [7] A.. Thünemann, S. Geneal, Macomolecules 001, 34, [8] C. Osuj, C.Y. Chao, I. Bta, C.K. Obe, E.L. Thomas, Adv. unct. Mate. 00, 1, 753. [9] I.A. Ansa, V. Castelletto, T. Myhayly, I.W. Hamley, Z.B. Lu, T. Itoh, C.T. Ime, Macomolecules 003, 36, [10] G.O.R. Albeda van Eensten, E. Polushn, H. Njland, O. Iala, G. ten Bne, Macomolecules 003, 36, [11] C.Y. Chao, X. L, C.K. Obe, C. Osuj, E.L. Thomas, Adv. Mate. 004, 14, 364. [1] O. Iala, G. ten Bne, Chem. Com. 004, 131. [13] C.S. Tsao, H.L. Chen, Macomolecules 004, 37, [14] I.W. Hamley, V. Castelletto, P. Paas, Z.B. Lu, C.T. Ime, T. Itoh, Soft Matte 005, 1, 355. [15] B. Nandan, C.H. Lee, H.L. Chen, W.C. Chen, Macomolecules 005, 38, [16] R. Nap, C. Ko, G. ten Bne, S.I. Kuchanov, Euopean Phys. J. E 001, 4, 515. [17] R. Nap, N. Susho, I.Ya. Euhmovch, G. ten Bne, Macomolecules 006, 39, [18] Y. Smnova, G. ten Bne, I.Ya. Euhmovch, J. Chem. Phys. 006, 14, [19] S. I. Kuchanov, V.E. Pchugn, G. ten Bne, E-Polymes 006, 01. [0] S.I. Kuchanov, V.E. Pchugn, G. ten Bne, Euophys. Lett. 006, 76, 959. [1] A. Subbotn, T. Klymo, G. ten Bne, Macomolecules 007, 40, 915. [] T. Klymo, A. Subbotn, G. ten Bne, J. Chem. Phys. submtted. [3] P.J.Hoogebugge, J.M.V.A. Koelman, Euophys. Lett. 199, 19, 155. [4] R.D. Goot, T.J. Madden, J.Chem. Phys. 1998, 108, [5] R.D. Goot, P.B. Waen, J.Chem. Phys. 1997, 107, 443. [6] P. Espanol, P.B.Waen, Euophys.Lett. 1995, 30, 191. [7] M.P.Allen, D.J. Tldesley, Compute Smulaton of Lquds, 1987, Claendon, Oxfod. [8] U.Mca, K.Bnde, Macomol. Theoy Smul. 1995, 4, 419. [9] Y. Bahbot-Ravv, Z.G. Wang, Phys. Rev. Lett. 000, 85, 348. [30] Q. Wang, P..Nealey, J.J. de Pablo, Macomolecules 001, 34, [31] C.-I. Huang, C.-M. Chen, ChemPhysChem, 007, 8,

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