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diff --git a/support/biblio/EXAMPLES/2sorts/2sorts_formats.tex b/support/biblio/EXAMPLES/2sorts/2sorts_formats.tex new file mode 100644 index 0000000000..d95505135d --- /dev/null +++ b/support/biblio/EXAMPLES/2sorts/2sorts_formats.tex @@ -0,0 +1,217 @@ +%% This is an example of a TeX file with formats +%% included into the header of the document. +%% To run it you have to do something like: +%% biblio.pl -o 2sorts_formats.1.tex -d refers.db 2sorts_formats.tex +%% or +%% biblio.pl -o 2sorts_formats.1.tex -d refers.db --nobibitem --uselist 2sorts_formats.tex +%% if you want a really well formatted citation list +%% and then +%% latex 2sorts_formats.1.tex +%% to get 2sorts_formats.1.dvi + +%%------------------------------------------------------ + +%% this is copyed from the template for Macromolecules +%% no ordering of the references is needed. Otherwise add line +%% '%ordering= AUTHORL' + +%begin{biblio} + +%cite_format={(%s)} +%ref_format=${^{%s}}$ + +%% normal article: +% ARTICLE [$AUTHOR0P~L,~F~M; $ {\it $JOURNAL$} {\bf $YEAR$}, {\it $VOL$}, $PAGE$.] + +%% article which is submitted or accepted +% ARTICLE0[$AUTHOR0P~L,~F~M; $ {\it $JOURNAL$} $STATE$.] + +%% normal book +% BOOK [$AUTHOR0P~L,~F~M; $ {\it $TITLE$}; $PUBL$: $PLACE$, $YEAR$.] + +%% article in a book AUTHORE, AUTHORG and AUTHORH - last, first +%% and middle names of the editor +% EDBOOK [$AUTHOR0P~L,~F~M; $ in {\it $BOOKTITLE$}, edited by $AUTHOR0I~E,~G~H;$; $PUBL$: $PLACE$, $YEAR$.] + +%% article in a book without editor +% INBOOK [$AUTHOR0P~L,~F~M; $ in {\it $BOOKTITLE$}, p.$PAGE$ $PUBL$: $PLACE$, $YEAR$.] + +% EPRINT [$AUTHOR0P~L,~F~M; $ in {\it $BOOKTITLE$} $INFO$, $YEAR$.] + +%% Thesis +% THESIS [$AUTHOR0P~L,~F~M; $ {\it $SORT$}; $UNIV$: $PLACE$, $YEAR$.] + +%end{biblio} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%REAL DOCUMENT STARTS HERE!!!! + +\documentstyle[aps,manuscript]{revtex} + +\title{Comb copolymer brush with chemically different side chains} +\date{\today} +%----------------------------------------------- + +\newcommand{\vA}{v_{AA}} +\newcommand{\vB}{v_{BB}} +\newcommand{\vAB}{v_{AB}} +\newcommand{\vx}{v} +\newcommand{\mnu}{\nu} +\newcommand{\khi}{\chi} +\newcommand{\dd}{\partial} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{document} + +\maketitle +%-------------------------------------------------- + +\begin{abstract} +An investigation of side chain microphase separation +within a single comb copolymer molecule containing chemically different +$A$ and $B$ side chains has been carried out. Expressions for the +transition point $\chi_{AB}^*$ in a +good ($\chi_{AB}^* \sim N^{-3/8}$), +marginal ($\chi_{AB}^* \sim N^{-1/2}$), +$\theta$ ($\chi_{AB}^* \sim N^{-2/3}$), +and poor ($\chi_{AB}^* \sim N^{-1}$) +solvent are derived +both by a mean field calculation and by scaling arguments. +Properties of the system below and above the transition point are +described. +Some unusual ``bow-like'' conformations are predicted for a single +molecule in the microphase separated state in a good solvent. +\end{abstract} +%-------------------------------------------------- +\section{Introduction} + +The conformational characteristics of individual comb copolymers with a +high grafting density of side chains in solution has been addressed in a +series of theoretical papers +\cite{Birshtein,WangSafran,Fredrickson,Rouault1,3dFlex,3dRigid,Potemkin,2dComb} +to begin with the original work of +Birshtein et al \cite{Birshtein}. +Irrespective of the solvent quality, be it a good +solvent or a $\theta$-solvent, all theories predict a cylindrical +brush-like structure for sufficiently long side chains. The pertinent +parameters are the side chain grafting density, the side chain length, +the intrinsic stiffness of the backbone and the side chains (the +respective Kuhn segments) and the solvent quality with respect to the +side chains and the backbone. The conformation is characterized by a +number of quantities, the persistence length of the comb copolymer brush +being most important. For sufficiently long side chains the persistence +length is predicted to exceed the backbone length, thus resulting in a +characteristic cylindrical "bottle-brush" structure. Subsequent computer +simulations using a freely jointed hard sphere model essentially +confirmed this picture +\cite{Mika4,BrinkeIkkala,Rouault2,Mika1,Mika3,Mika2}. + +The experimental investigation of comb copolymers with a high grafting +density has assumed large proportions after the successful +polymerization of macromonomers, yielding degrees of polymerization +significantly exceeding the length of the macromonomer itself, by +Tsukahara and coworkers +\cite{Tsukahara2,Tsukahara3,Schmidt,Tsukahara0}. +Besides polymerization of macromonomers +alternative routes have been developed recently using grafting from a +macroinitiator prepared by either atom-transfer radical polymerization +\cite{Beers1} +or by living cationic polymerization +\cite{Schappacher}. +Using atom transfer +radical polymerization molecular brushes with block copolymer side +chains have been prepared as well. + +The experimental characterization of the comb copolymer brush +conformation in dilute solution is a highly nontrivial issue. It was +achieved recently by Schmidt and co-workers +\cite{Borner1,Wintermantel1,Wintermantel2,Wintermantel3,DziezokSheiko,Sheiko,GerleRoos,FischerGerleSchmidt} +using a combination +of light scattering experiments and theoretical modeling. Since the high +grafting density is supposed to lead to a stiff molecular structure, the +modeling has been based on the Kratky-Porod worm-like chain model. +For high molar mass polymacromonomers based on methacryloyl +end-functionalized oligo methacrylates ($M_n = 2410~g/mole$) in the good +solvent THF, the Kuhn statistical segment length, which is twice the +persistence length, turned out to be $120~nm$. For polymacromonomers +($M_n = 3624~g/mole$) consisting of polystyrene main and side chains this +value was $190~nm$ in the good solvent toluene and $120~nm$ in the +"$\theta$-solvent" cyclohexane. + +At the same time one of the most challenging problems in +the polymer physics is a description of a microphase +formation in copolymer systems. +Theoretically, self-organization in block copolymer systems has +attracted +a lot of attention during the last decades and a fairly complete picture +has emerged for the +relatively simple diblock copolymers. +\cite{Helfand1,Semenov,Leibler,FredricksonHelfand} +As a consequence, the interest gradually shifts towards more +complicated architectures such as comb or graft copolymers +\cite{Dobrynin1,Cruz1,Foster1,WernerFredrickson,Nap1}. +The discussion of structure formation in comb copolymers using the weak +segregation limit has been presented in some detail. Compared to diblock +copolymers the description is only slightly complicated by the fact that +the single chain correlation functions are more involved. Phase diagrams +of various comb copolymer systems have been published. Although +different in details, the general trends are the same as for diblock +copolymers. Of course, rather than the overall chain length, it is the +length of the "repeat unit" that determines the order-disorder +transition temperature as well as the characteristic length scale of the +ordered structures. + +The application of the weak segregation approach, however, requires a +relatively low +grafting density such that the distance between two +consecutive grafting points along the backbone is at least of the order +of the Flory radius of the side chains. If the grafting density of comb +copolymers is very high, the structure in the melt will usually involve +segregation between individual molecules. Even if the incompatibility +between backbone and side chains is high, the high grafting density may +well prevent segregation of several backbones. Furthermore, a high +grafting density combined with long side chains implies the volume +fraction of the backbone to be of the order of 0.1 or lower, not +necessarily the most interesting part of the melt phase diagram. + +Still, microphase separation may occur provided chemically different +side chains are used. In this case unfavorable interaction between the +side chains may lead to a micro domain +structure within a single molecule. The present paper is devoted to this +subject. +The main objective is to identify conditions for "microphase separation" +of side chains of two +different types within a single comb copolymer molecule under different +solvent conditions. + +The paper is organized as follows. The next section describes the +self-consistent field approach to a molecule with a straight +backbone and chemically different side chains. We show the possibility +of side chain separation +within the molecule and discuss the limits of the theory's +applicability. +The subsequent section is devoted to possible unusual behavior +of comb copolymer molecules with a flexible backbone and +microphase separated side chains. Then all results are summarized and +discussed in the last section. + +%------------------------------------------- +\section{Useful literature (not from the article)} +Very interesting and useful books on this subject (polymers) are +\cite{bookdeGennesScalingConcepts,GrosKhokh,bookCloizeaux} or more specific +books devoted to peculiarities if comb copolymers behavior +\cite{bookPlate,bookMcArdle}. +Still unpublished works, like \cite{FischerSchmidt}, can be very helpful too. + +Thesis \cite{thesisHyvarinen} is a good reading too! +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{references} + + +\end{references} + + + + + +\end{document}
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