142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

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Asymmetric Star Polymers Synthesis and Properties 113 Fig. 8. a Comparison of the spinodal curves cN t (f A ) for diblock and different AB n miktoarm copolymers with n=2, 3, and 4. The experimental results from an AB 2 (l ) and the two AB 3 (o , m ) miktoarm stars are shown together with the investigated temperature range (vertical lines). b Critical values of cN t plotted as a function of the number of arms of the B blocks. The dependence of the optimal composition corresponding to the minima of the spinodal curves are also shown. The line is only a guide to the eye (reproduced with permission from [78])
114 N. Hadjichristidis, S. Pispas, M. Pitsikalis, H. Iatrou, C. Vlahos because of the presence of the core, the arms will be stretched more than the present theory predicts. Floudas et al. have developed [78] a mean field theory to treat the phase stability criteria for the most general case of miktoarm star copolymers, namely, A n B m , with asymmetric number of branches m„n. The case of AB n was treated in detail. The static structure factor in the disordered phase was calculated and the resulting spinodal curves for the series of AB n miktoarms are plotted in Fig. 8a. They found that these copolymers are more difficult to phase separate than linear diblocks since the critical values of cN t (N t =N A +nN B ) are higher than the diblock case at any composition. The spinodal curves are asymmetric due to the inherent asymmetry of miktoarm stars. The critical values corresponding to the minima of the spinodal and the respective compositions are plotted in Fig. 8b for miktoarms with different n. For n up to 3 there is a considerable increase in the value of (cN t) c which indicates an increasing compatibility between A and B blocks. However for n>3 there is a reversal in (cN t) c which, for n>10, differs only slightly from that of the A-b-B diblock copolymers. The maximum value of (cN t) c at n=3 results from a delicate balance between the stretching free energies of the A and B blocks while for higher number of arms the free energy of the system is mainly determined by the B blocks forming the star. These theoretical predictions have been tested experimentally by SAXS measurments. Kosmas [79] studied the behavior of miktoarm stars at the interface of two different phases using a simple mesoscopic model that incorporates the thermodynamic parameters into the size of the Kuhn length. The latter depends on the distance z perpendicular to the interface by the simple discontinuous function l(z)=l + for z‡0, l(z)=l – for z£0. From the discontinuity of the Kuhn length only the P Z component of the probability distribution function P(z 0,z)=P xP yP z of finding the end of an homopolymer chain at z distance from the origin (z 0 ) is affected. The weight of a macrostate W(z 0 ) of finding the one end at z 0 and the other anywhere then is obtained from the entropy S=-kT P(z 0,z)lnP(z 0, z) which connects P(z 0,z) with W(z 0),S=kTlnW(z 0). The density profiles of the chain end as a function of the distance z 0 from the interface in the limit of large available volume is given then by ( ) W( z ) . In the case of miktoarm Wz = 0 0 dz W( z ) stars consisting of i arms (i=1, 2, ..., f) the weight of macrostate W mikto is the product of the weights of the macrostates of the f different arms Wmikto= Wi . The density profile of the star common junctions is given by the relation W 2r erfc( 3z0 / Ri ( z 0) 2) mikto = ri 1+ Pii r [ ] i L -L 0 0 where R i (z 0 )=R i+ for z‡0 and R i (z 0 )=R i+ i
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142 Advances in Polymer Science Edi
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Branched Polymers I Volume Editor:
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Volume Editor Dr. Jacques Roovers I
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Preface While books have been writt
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Contents Synthesis of Branched Poly
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Synthesis of Branched Polymers by C
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Poly(macromonomers), Homo- and Copo
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Dendrimers and Dendrimer-Polymer Hy
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Author Index Volumes 101-142 Author
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Author IndexVolumes 101-142 231 Dun
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Author Index Volumes 101-142 233 Ka
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Author Index Volumes 101-142 235 Og
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Author Index Volumes 101-142 237 Su
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Subject Index Addition-fragmentatio
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Subject Index 241 Microphases 11z,
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142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

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