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| author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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| committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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diff --git a/support/biblio/EXAMPLES/hairy/hairy.tex b/support/biblio/EXAMPLES/hairy/hairy.tex new file mode 100644 index 0000000000..0c3a89d23c --- /dev/null +++ b/support/biblio/EXAMPLES/hairy/hairy.tex @@ -0,0 +1,895 @@ +\documentstyle[aps,preprint]{revtex} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newcommand{\lbl}[1]{\label{#1}} +\newcommand{\reff}[1]{eq~\ref{#1}} + + +\newcommand{\be}[1]{ \begin{equation} \lbl{#1} } +\newcommand{\ee}{\end{equation}} + +\newcommand{\bea}[1]{ \begin{eqnarray} \lbl{#1} } +\newcommand{\eea}{\end{eqnarray}} + +\newcommand{\dd}{\partial} + +\newcommand{\vk}{\bf k} +\newcommand{\vb}{\bf b} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\title{Phase equilibria in associating rodlike and flexible chains} + +\date{\today} + +\author{R. Stepanyan$^{\dagger}$, + A. Subbotin$^{\dagger ,\sharp}$, + O. Ikkala$^{\ddagger}$, + G. ten Brinke$^{\dagger}$} + +\address{$^{\dagger }$ +Department of Polymer Science and Material Science Center,\\ +University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands;} + +\address{$^{\sharp }$ +Institute of Petrochemical Synthesis, Russian Academy of\\ +Sciences, Moscow 119991, Russia;} + +\address{$^{\ddagger }$ +Department of Engineering Physics and Mathematics, \\ +Helsinki University of Technology, P.O. Box 2200,\\ +FIN-02015 HUT, Espoo, Finland} + +\date{\today} + +\maketitle + +\begin{abstract} +Abstract goes here +\end{abstract} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newpage + +\section{Introduction} + +Introduction...... + +\cite{MB1091,BF525,bookdeGennesScalingConcepts,Leibler}. +%----------------------------------------------------------------- + +\section{The model and the free energy of the reference system} + +Let us consider a melt consisting of rigid rods of length $L$ and diameter +$d$ and flexible coils consisting of $N$ beads of volume $\nu$ and statistical +segment of length $a$. The coil size is $R_c = a \sqrt{N}$. We will assume that +each rod contains $M$ associating groups (an average distance between two +succesive groups is $b=L/M \ll R_c$) which can form bonds with the +associating end of the coil (FIGURE). It is assumed that each coil has only one +associating end. The energy of association between rod and coil equals +to $-\epsilon $. The concentration of rods in the melt is $c$ and their volume +fraction is $f=(\pi /4)Ld^2c$. + +The interactions between rods and coils can be introduced in the +following way. It is well known that rods and polymer coils in the +molten state are practically incompartible and separate on the nematic phase +consisting of rods and isotropic phase consisting of the flexible +polymers \cite{Flory:MML:11:1138,AbeBallauff}. +Let us consider the interface between the nematic and isotropic phases +(FIGURE fig.1) +which is assumed to be sharp so that the polymer segments can not +penetrate into the nematic phase, and introduce the interfacial tension +$\gamma$ corresponding to planar orientation of rods at the interface +($k_B \equiv 1$) +% +\be{eq0} +\gamma =(w+sT)/d^2 +\ee +% +where $w$ is the energetic part of the surface energy and $s$ is the +entropic part +(here $T$ is temperature, ??we will also assume that $s \sim 1$??). +According to the defenition \reff{eq0} if a rod penetrates into the polymer +melt its energy loss approximatly equals +% +\be{eq01} +\mu _r\simeq 2Ld\gamma =\frac{2L}d\left( w+sT\right) +\ee +The free energy of the isotropic phase with small amount of rigid rods +therefore is given by + +\be{eq02} +{\cal F}_I^{*} = +T V c +\ln \left( \frac{f}{e} \right) + +T V \frac{1-f}{N\nu} +\ln \left( \frac{1-f}{e} \right) + +V c \frac{2L}{d} \left( w+sT \right) +\ee +% +Here we omitted interaction between the rods. $V$ is the volume of the +system. In \reff{eq02} the first two terms imply the translational +energy of the rods and coils correspondingly and the last term is the energy of +rods. + +The coils can also penetrate into the nematic phase where they become +stretched. In order to write the free energy of the nematic phase with small +amount of coils we introduce a chemical potential of the coil in the +nematic phase $\mu _c$ which includes both energetic and entropic +parts and limits to infinity, + +\be{eq05} +\mu _c/T\rightarrow \infty +\ee +for arbitrary $T$. As we will see below it means that the coils +practically do not penetrate in the nematic phase. + +The free energy of the nematic phase contains also a term connected with +orientational ordering of rods. The last one can be estimated as +\cite{KhokhlovTBOA,SemenovKhokhlov} +$T \ln ( 4 \pi /\Omega )$, +where $\Omega$ is the characteristic fluctuation angle, +$\Omega \simeq 2\pi (d/L)^2$. Thus the free energy is given by +% +\be{eq03} +{\cal F}_N^{*}= +T V c \ln \left( \frac{f}{e} \right) + +T V \frac{1-f}{N\nu} +\ln \left( \frac{1-f}e \right) + +2 T V c \ln \left( \frac{L}{d} \right) + +V \frac{1-f}{N\nu} \mu _c +\ee +The phase equilibrium between the nematic and isotropic phases can be found +in a usuall way by equating the chemical potentials and osmotic pressures in +both phases. +% +\begin{eqnarray} +\mu_I^{*} & = & \mu _N^{*}; \quad +\mu _{I,N}^{*} = \frac{1}{V} \frac{\dd {\cal F}_{I,N}^{*}}{\dd c} + \nonumber\\ +% +P_I &=&P_N; \quad +P_{I,N}=\frac{1}{V} +\left( + c \, \frac{\dd {\cal F}_{I,N}^{*}}{\dd c} - {\cal F}_{I,N}^{*} +\right) +\lbl{eq04} +\end{eqnarray} +Considering limit \reff{eq05}, solution of these equations is given by +% +\be{eq06} +f_N \simeq 1,\quad +f_I \simeq + \left( \frac{L}{d} \right) ^2 + \exp \left( -\frac{2L}{d}\left( \frac wT+s \right) + \right) \ll 1 +\ee + +\section{Nematic-isotropic liquid phase coexistence: effect of association} +% +In this section we study the influence of association between rods and +coils on the macrophase separation described above. +We start from the free energy of association between +rods and coils, ${\cal F}_{bond}$, assuming that they are +ideal (without excluded volume). Let us introduce the probability of bond +$p$. The total number of bonds in the system is $VMcp$ and +equals to the number of associated coils. +Therefore the number of free coils in the system is +$(V/N\nu)(1-f-f\kappa pN)$, where $\kappa \equiv \nu/(\pi b d^2/4)$. The free +energy of bonds can be written through the partition function $Z_{bond}$ as +\cite{SemenovRubinstein1,Erukhimovich:Gel} +% +\be{eq3} +{\cal F}_{bond}=-T\ln Z_{bond} +\ee +where +% +\be{eq4} +Z_{bond} = + P_{comb} + \left( \frac{v_b}V \right)^{V M c p} + \exp \left( \frac{\epsilon \, V M c p}{T} \right) +\ee +and $P_{comb}$ is the number of different ways to bond rods and coils +for a fixed probability of bond $p$; $v_b$ is a bond volume. If we denote +the number of rods in the system as ${\cal N}_r=Vc$, and the number of coils +as ${\cal N}_c=V(1-f)/N\nu$ then the number of ways to choose ${\cal N}_rMp$ +coils for bonds formation is a binomial coefficient +% +\be{eq5} +C_{{\cal N}_c}^{{\cal N}_rMp}=\frac{{\cal N}_c!}{({\cal N}_rMp)!({\cal N}_c-% +{\cal N}_rMp)!} +\ee +% +On the other hand there are +% +\be{eq6} +\frac{({\cal N}_rM)!}{({\cal N}_rM(1-p))!} +\ee +different ways to select ${\cal N}_rMp$ bonds from ${\cal N}_rM$ +associating groups. Therefore + +\be{eq7} +P_{comb} = C_{{\cal N}_c}^{{\cal N}_rMp} + \frac{ ({\cal N}_rM)! }{ ({\cal N}_rM(1-p))! } +\ee +and the free energy of bonds is given by +% +\begin{eqnarray} +{\cal F}_{bond} & = & +VMcp +\left[ + T \ln \left( \frac{N\nu}{v_b} \right) - \epsilon +\right] + +TVcM +\left[ + p\ln p + (1-p) \ln (1-p) +\right] \nonumber\\ +% + & & + +TV \frac{\left( 1-f-f\kappa Np\right) }{N\nu} + \ln \left( \frac{1-f-f\kappa Np}{e} \right) - +TV \frac{(1-f)}{N\nu} + \ln \left( \frac{1-f}{e} \right) +\lbl{eq8} +\end{eqnarray} + +Thus the free energy of the isotropic phase can be presented as the following +% +\be{eq9} +{\cal F}_I = {\cal F}_I^{*} + {\cal F}_{bond} + {\cal F}_{el} +\ee +% +where ${\cal F}_{el}$ is the elastic free energy of the side chains +of the hairy +rod when the density of association is high enough. We approximate it +by \cite{3dFlex,2sorts} + +\be{eq10} +{ \cal F}_{el}= +\left[ + \begin{array}{cl} + TVc\frac{3\kappa d^2}{32a^2}Mp^2\ln \left( \kappa Np\right) ,\quad & + p>\frac{1}{\kappa N} \\ + 0, \quad & + \textrm{otherwise} + \end{array} +\right. +\ee +Hence the final expression for the free energy of the isotropic phase is +given by (per volume of one rod $(\pi /4)Ld^2)$ +% +\begin{eqnarray} +\frac{F_I(f,p)}T &=& + f\frac{2L}{d} \left( \frac wT+s \right) + +Mfp\left[ \ln \left( \frac{N\nu}{v_b}\right) -\frac \epsilon T \right] + +fM\left[ p\ln p+(1-p)\ln (1-p)\right] \nonumber\\ +&& + +f\ln \left( \frac fe \right) + +M \frac{\left( 1-f-f \kappa Np \right) }{N\kappa } + \ln \left( \frac{1-f-f\kappa Np}{e} \right) \nonumber\\ +&& + +f\frac{3\kappa d^2}{32a^2} Mp^2 + \ln \left( \kappa Np \right) H\left( p-\frac 1{\kappa N}\right) +\lbl{eq11} +\end{eqnarray} +% +where +% +$$ +H(x)= +\left[ + \begin{array}{cl} + 1,\quad & x \geq 0 \\ + 0,\quad & x < 0 + \end{array} +\right. +$$ +is the Heavyside's function. +Similarly, the free energy of the nematic phase is +% +\begin{eqnarray} +\frac{F_N(f,p)}T &=& + 2 f \ln \left( \frac Ld \right) + +M\frac{1-f}{N\kappa }\frac{\mu _c}T + +Mfp\left[ \ln \left( \frac{N\nu}{v_b}\right) + -\frac \epsilon T\right] + +fM\left[ p\ln p+(1-p)\ln (1-p)\right] \nonumber\\ +&& + +f\ln \left( \frac fe\right) + +M\frac{\left( 1-f-f\kappa Np\right) }{ N\kappa } + \ln \left( \frac{1-f-f\kappa Np}e\right) +\lbl{eq12} +\end{eqnarray} +% +% +The probability of bonding in both phases can be found from the minimization +of the corresponding free energies +% +\be{eq13} +\frac{\dd F_I}{\dd p}=0; +\quad +\frac{\dd F_N}{\dd p}=0 +\ee +% +and is given by ($N^* \equiv N \nu / v_b$) +% +\be{eq14} +p= \frac{1}{2\kappa Nf} +\left[ + 1-f+\kappa Nf-\epsilon /(TN^{*})- + \sqrt{ + \left(1-f+\kappa Nf-\epsilon /(TN^{*}) \right) ^2 + -4\kappa Nf(1-f) + } +\right] +\ee +for the nematic phase and for the isotropic phase when $p<\frac 1{\kappa N}$. +%Here $N^{*}\equiv N\nu/v_b.$ +For $p>\frac 1{\kappa N}$ the probability of +bonding in the isotropic phase obeys +% +\be{eq15} + \ln + \left[ + \frac{ pN^{*}e^{-\epsilon /T} } + { \left( 1-p\right) \left(1-f_I-f_I\kappa Np\right) } + \right] + +\frac{3\kappa d^2p}{16a^2}\ln \left( \kappa Npe\right) + = 0 +\ee +% +and for a small volume fraction of rods, $f_I \ll 1$, is approximately given by +% +\be{eq24} +p \simeq \frac 1{ 1 + N^{*} e^{-\epsilon^{*}/T}}, +\quad +\epsilon ^{*} = \epsilon - + \frac{3\kappa d^2T}{32a^2} \, + \frac{1}{1+N^{*}e^{-\epsilon /T}} + \ln \left( \frac{\kappa N}{1+N^{*} e^{-\epsilon /T}} \right) +\ee +% +Phase equilibrium between the isotropic and nematic phases can be found in a +standard way from the equilibrium equations +% +\begin{eqnarray} +\frac{\dd F_I}{\dd f_I} &=& \frac{\dd F_N}{\dd f_N} +\nonumber \\ +f_I\frac{\dd F_I}{\dd f_I}-F_I &=& f_N\frac{\dd F_N}{\dd f_N}-F_N +\lbl{eq16} +\end{eqnarray} +using eqs.~\ref{eq11},\ref{eq12} together with \reff{eq14} and \reff{eq24}. +When the probability of bonding in the +isotropic phase $p_I<\frac 1{\kappa N}$ +(or equivalently $\frac{\epsilon}{T} < \ln \frac{\nu}{\kappa v_b}$), +expression \reff{eq14} can be used giving the volume fraction of rods +% +\begin{eqnarray} +f_N & \simeq & 1, + \nonumber\\ +f_I & \simeq & + \left( \frac Ld \right) ^2 + \exp + \left( + -\frac{2L}{d} + \left( \frac wT+s\right) + +\frac M{1+N^{*}e^{-\epsilon /T}} + \left( \frac \epsilon T-\ln N^{*}\right) + \right) \ll 1 +\lbl{eq17} +\end{eqnarray} +% +However, if +$p_I>\frac 1{\kappa N}$ +(or $\frac \epsilon T>\ln \frac \nu{\kappa v_b}$), +the volume fraction of rods in the nematic phase +is still close to the unity whereas $f_I$ obeys the equation +% +\be{eq18} +\ln f_I +- Mp_I \ln \left( 1-f_I-f_I\kappa Np_I \right) +\simeq +2 \ln \left( \frac L d\right) ++ \frac M{N\kappa} - \frac{2Ls}{d} +-Mp_I\ln N^{*} ++\frac{1}{T} \left( Mp_I\epsilon -\frac{2Lw}d \right) +\ee +where $p_I$ has to be determined from \reff{eq15}. +Obviously, for $T \to 0$ $p_I \to 1$ and therefore the last term +in eq.\ref{eq17} becomes dominant. Depending on its sign two +characteristical assymptotics can be distinguished +% +\begin{eqnarray} +f_I \to 0 \qquad\qquad\textrm{if }\quad M\epsilon <\frac{2Lw}d +\nonumber\\ +f_I \to \frac 1{1+N\kappa } \quad\textrm{if }\quad M\epsilon >\frac{2Lw}d +\label{eq19} +\end{eqnarray} +Thus for $\epsilon /w>2b/d$ rods and coils become partially compartible. +This fact has a clear physical meaning. Negative sign of +$-\epsilon + \frac{2Lw}{Md}$ corresponds to the negative ``total'' energy +($\epsilon$-part plus $\gamma$-part) +due to attaching of a coil to a rod, i.e. making it favorable to keep +\emph{all} coils bonded (for $T\to 0$, of course). +Further on we consider only the case $\epsilon /w>2b/d$, +where a region of compatibility of rods and coils exists. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Phase equilibria between nematic, isotropic liquid and microphases} + +There are two mechanisms of attraction between hairy rods, namely due to +incompartibility of the rods and coils and due to nonhomogeneous +distribution of the free polymer coils which is created by the hairy rods. +These mechanisms ultimately result in formation hexagonal and lamellar +structures in the blend. Moreover we can separate two different hexagonal +phases. In one of the phases (we call it H1) the mechanism connected with +nonhomogeneous distribution of the free polymers is dominant and the +''cylinders'' contain only one rod per unit cell $(Q=1)$. In the second +phase (H2) the surface term becomes important so that rods attract each +other and the cylinders contain $Q>1$ rods per unit cell (fig.2FIGURE). With +decreasing temperature the cylinders first adopts elipsoidal form and +finally transform to the lamellar phase. + +\subsection{Separation of the hexagonal phase H1} + +Let us start with calculation of the interaction energy between the +cylinders in the hexoganal phases (H1, H2). It is connected with +nonhomogeneous distribution of the free polymer coils and is given by (per +cylinder of unit length) + +\be{eq20} +U_H(Q)= +\frac{N\nu(Qp)^2}{2b} +\left[ + \frac 2{\sqrt{3} \, \ell ^2} + \sum_{\{ \vb \}} + \frac{h^2(\frac{a^2N{\vk}^2}6)}{g(\frac{a^2N{\vk}^2}6)} + -\frac 1{4\pi ^2} + \int d{\vk}\frac{h^2(\frac{a^2N{\vk}^2}6)}{g(\frac{a^2N{\vk}^2}6)} +\right] +\ee +where $\ell $ is the period of the structure, $\{ \vb \}$ are the vectors +of the reciprocal lattice, +$$h(u) =\frac 1u\left( 1-e^{-u}\right) $$ +$$g(u) =\frac 2{u^2}\left( u-1+e^{-u}\right)$$ + +After calculation of the sum and integral in eq.\ref{eq20} we find the +interaction energy per volume $(\pi /4)Ld^2$ + +\be{eq21} +U_H(Q)=-\frac 3{32}\frac{\kappa MQp^2fd^2}{a^2N} + \left[ + 3.457 + +\ln \left( \frac{a^2Nf}{Qd^2}\right) + \right] +\ee +Thus the free energy of H1 phase is given by +% +\begin{eqnarray} +\frac{F_{H1}}T &=& + f\frac{2L}{d} \left( \frac wT+s\right) +- Mfp\left[ \frac \epsilon T - \ln N^{*} \right] ++ fM\left[ p\ln p+(1-p)\ln (1-p) \right] ++ 2f\ln \left( \frac Ld \right) +\nonumber \\ +&& ++ M\frac{\left( 1-f-f\kappa Np\right) }{N\kappa } + \ln \left( \frac{1-f-f\kappa Np}e\right) ++ f\frac{3\kappa d^2}{32a^2}Mp^2\ln \left( \kappa Np\right) +\nonumber \\ +&& +- \frac{3}{32} \frac{\kappa Mp^2fd^2}{a^2N} + \left[ 3.457+\ln \left( \frac{a^2Nf}{d^2}\right) \right] +\lbl{eq22} +\end{eqnarray} +Here we approximated the loss of the orientational energy of rod by the term +$2Tf\ln \left( \frac Ld\right) $, and omitted the loss of it translational +entropy because it is relatively small. Phase equilibrium between isotropic +phase and H1 phase can be found from the equilibrium equations +% +\begin{eqnarray} + \frac{\dd F_I}{\dd f_I} =\frac{\dd F_{H1}}{\dd f_{H1}}, + &\quad& + \frac{\dd F_I}{\dd p_I}=\frac{\dd F_{H1}}{\dd p_{H1}}=0 +\nonumber\\ + f_I\frac{\dd F_I}{\dd f_I}-F_I + &=& + f_{H1}\frac{\dd F_{H1}}{\dd f_{H1}}-F_{H1} +\lbl{eq23} +\end{eqnarray} +and the probability of bonding and the binodal lines are +% +\begin{eqnarray} + & p_1 \simeq & p_{H1}\simeq 1, +\nonumber \\ + & f_{H1}^{(1)} \simeq & \frac 3{16}\frac{d^2}{a^2 N}, +\nonumber \\ + & f_I \simeq & + \left( \frac Ld\right) ^2 + \exp \left( -\frac 3{16}\frac{d^2p^2\kappa M}{a^2}\right) \simeq 0 +\lbl{eq26} +\end{eqnarray} + +Similarly the phase equilibrium between the nematic and H1 phases follow +from equations +% +\begin{eqnarray} + \frac{\dd F_N}{\dd f_N} =\frac{\dd F_{H1}}{\dd f_{H1}}, + &\quad& + \frac{\dd F_N}{\dd p_N}=\frac{\dd F_{H1}}{\dd p_{H1}}=0 +\nonumber\\ + f_N\frac{\dd F_N}{\dd f_N}-F_N + &=& + f_{H1}\frac{\dd F_{H1}}{\dd f_{H1}}-F_{H1} +\lbl{eq25} +\end{eqnarray} +% +and solution is given by +% +\begin{eqnarray} +& p_N \simeq &0, \quad p_{H1}\simeq 1, \nonumber \\ +& f_N \simeq &1, \nonumber\\ +& f_{H1}^{(2)} \simeq &\frac 1{1+\kappa N} + \left[ + 1-\exp + \left( + -\frac{\epsilon}{T} + +\frac{2bw}{Td} + +\frac{2bs}d+\ln N^{*} + +\frac{3\kappa d^2}{32a^2}\ln \left( \kappa N\right) + \right) + \right] +\lbl{eq251} +\end{eqnarray} +The critical temperature $(\epsilon /T)_c$ can be obtained from the +intersection of the curves $f_{H1}^{(1)}$ and $f_{H1}^{(2)}$, and obeys the +following equation +% +\be{eq27} +(\epsilon /T)_c = + \frac{1}{1-\frac{2bw}{\epsilon d}} + \left( \frac{2bs}d+\ln + N^{*}+\frac{3\kappa d^2}{32a^2} \ln \left( \kappa N \right) + \right) +\ee +where the probability of bonding $p_c\simeq 1.$ Thus the hexagonal H1 phase +is stable for $f_{H1}^{(1)}<f<f_{H1}^{(2)}$; for $f_I<f<f_{H1}^{(1)}$ the +system separates on the isotropic and H1 phase and for $f_{H1}^{(1)}<f<f_N$ +it separates on the H1 and nematic phase. + +\subsection{Separation of the hexagonal phase H2} + +Let us follow along the binodal line $f_{H1}^{(1)}(T)$ decreasing the +temperature. At some temperature H1 phase becomes unstable with respect to +separation of the isotropic phase and the hexagonal H2 phase. The +corresponding triple point can be obtained from the system of equations + +\begin{eqnarray} +\frac{\dd F_I}{\dd f_I} +=\frac{\dd F_{H1}}{\dd f_{H1}} +=\frac{\dd F_{H2}}{\dd f_{H2}} \, , +\qquad +\frac{\dd F_I}{\dd p_I} +=\frac{\dd F_{H1}}{\dd p_{H1}} +=\frac{\dd F_{H2}}{\dd p_{H2}} +=0 +\nonumber \\ +f_I\frac{\dd F_I}{\dd f_I}-F_I +=f_{H1}\frac{\dd F_{H1}}{\dd f_{H1}}-F_{H1} +=f_{H2}\frac{\dd F_{H2}}{\dd f_{H2}}-F_{H2} +\lbl{eq23a} +\end{eqnarray} +% +where the free energy of the H2 phase for $Q<\sqrt{N}$ is given by +% +\begin{eqnarray} +\frac{F_{H2}}T +&=& + f\frac Ld\left( \frac wT+s\right) \left( 1+\frac 2Q\right) + +Mfp\left[ \ln N^{*}-\frac \epsilon T\right] + +fM\left[ p\ln p+(1-p)\ln (1-p)\right] +\nonumber \\ +&& + +2f\ln \left( \frac Ld\right) + +M\frac{\left( 1-f-f\kappa Np\right) }{\kappa N} + \ln \left( \frac{1-f-f\kappa Np}e\right) + +f\frac{3d^2\kappa Q}{32a^2}Mp^2\ln \left( \kappa Np\right) +\nonumber \\ +&& + -\frac 3{32}\frac{\kappa MQp^2fd^2}{a^2N} + \left[ 3.457+\ln \left( \frac{a^2Nf}{Qd^2}\right) \right] +\lbl{eq28} +\end{eqnarray} +and the number of rods $Q$ in the cross-section of the cylinder can be +calculated from the minimum condition $\dd F_{H2}/\dd Q=0$, +% +\be{eq28a} +Q \simeq +\sqrt{ + \frac{64ba^2}{3\kappa p^2d^3 \ln \left( \kappa N \right) } + \left( \frac wT+s \right) +} +\ee +Solution of the eqs.~\ref{eq23a} is given by +% +\begin{eqnarray} +&& p_I \simeq p_{H1} \simeq p_{H2}\simeq 1 \nonumber \\ +&& Q_1 \simeq 2+\sqrt{2}, +\quad +f_I\simeq 0, +\quad +f_{H1}^{(1)} \simeq \frac 3{16} \frac{d^2}{a^2N}, +\quad +f_{H2}^{(1)} \simeq \frac 3{16}\frac{Q_1d^2}{a^2N} +\lbl{eq28b} +\end{eqnarray} +and the critical temperature is + +\be{eq23e} +\frac w{T_{c1}} \simeq -s+\frac{3\kappa d^3 Q_1^2}{64 b a^2} + \ln \left( \kappa N \right) +\ee + +Similarly we the binodal line $f_{H1}^{(1)}(T)$ finishes at the triple point +which can be found from the system of equations + +\begin{eqnarray} +&&\frac{\dd F_N}{\dd f_N} = +\frac{\dd F_{H1}}{\dd f_{H1}} = +\frac{\dd F_{H2}}{\dd f_{H2}}, +\quad +\frac{\dd F_N}{\dd p_N} = +\frac{\dd F_{H1}}{\dd p_{H1}} = +\frac{\dd F_{H2}}{\dd p_{H2}} =0 +\nonumber \\ +&&f_N\frac{\dd F_N}{\dd f_N}-F_N = +f_{H1}\frac{\dd F_{H1}}{\dd f_{H1}}-F_{H1}= +f_{H2}\frac{\dd F_{H2}}{\dd f_{H2}}-F_{H2} +\lbl{eq23c} +\end{eqnarray} +% +and is characterized by +% +\begin{eqnarray} +&& +p_N \simeq 0, +\quad +p_{H1} \simeq p_{H2} \simeq 1 +\nonumber\\ +&& +Q_1^{^{\prime }} \simeq Q_1\simeq 2+\sqrt{2}, \quad f_N \simeq 1, +\nonumber \\ +&& +f_{H1}^{(2)}\simeq \frac 1{1+\kappa N}\left[ 1-\exp \left( -\frac \epsilon {% +T_{c1}}+\frac{2bw}{T_{c1}d}+\frac{2bs}d+\ln N^{*}+\frac{3d^2\kappa }{32a^2}% +\ln \left( \kappa N\right) \right) \right] +\nonumber\\ +&& +f_{H2}^{(2)}\simeq \frac 1{1+\kappa N}\left[ 1-\exp \left( -\frac \epsilon {% +T_{c1}}+\left( \frac{2bw}{T_{c1}d}+\frac{2bs}d\right) \left( 1+\frac 2{Q_1}% +\right) +\ln N^{*}+\frac{3d^2\kappa Q_1}{32a^2}\ln \left( \kappa N\right) +\right) \right] +% +\lbl{eq23d} +\end{eqnarray} + +In the first approximation the corresponding critical temperature coinside +with the critical temperature \reff{eq23e}. Note, the small difference +between these critical temperatures, which we do not consider here, result +in a small area of phase separation between H1 and H2 phases. + +The phase equilibrium between the isotropic and the hexagonal H2 phase can +be found based on the equations +% +\begin{eqnarray} +&& + \frac{\dd F_I}{\dd f_I} =\frac{\dd F_{H2}}{\dd f_{H2}}, + \quad + \frac{\dd F_I}{\dd p_I} = \frac{\dd F_{H2}}{\dd p_{H2}} =0 +\nonumber\\ +&& + f_I\frac{\dd F_I}{\dd f_I}-F_I = f_{H2}\frac{\dd F_{H2}}{\dd f_{H2}}-F_{H2} +\lbl{eq231} +\end{eqnarray} +and for $1\ll Q<\sqrt{N\text{ }}$ the probability of bonding and the binodal +lines are given by + +\begin{eqnarray} + && p_I \simeq p_{H2}\simeq 1, +\nonumber\\ + && f_I \simeq 0,\quad +\nonumber \\ + && f_{H2}^{(1)} \simeq + \frac 1{1+\kappa N} + \left[ + 1-\exp \left( -\frac 3{16}\frac{Qd^2}{a^2N}\right) + \right] +\lbl{eq28b1} +\end{eqnarray} +% +where $Q$ defined by \reff{eq28a}. Similarly the equilibrium between the +nematic and the hexagonal H2 phase obeys equations +% +\begin{eqnarray} +&& + \frac{\dd F_N}{\dd f_N} = \frac{\dd F_{H2}}{\dd f_{H2}}, + \quad + \frac{\dd F_N}{\dd p_N} = \frac{\dd F_{H2}}{\dd p_{H2}}=0 +\nonumber \\ +&& + f_N\frac{\dd F_N}{\dd f_N}-F_N = f_{H2}\frac{\dd F_{H2}}{\dd f_{H2}}-F_{H2} +\lbl{eq232} +\end{eqnarray} +and the corresponding probabilities and binodals are +% +\begin{eqnarray} +&& + p_N \simeq 0,\quad p_{H2}\simeq 1, +\nonumber \\ +&& + f_N \simeq 1, +\nonumber \\ +&& + f_{H2}^{(2)} \simeq \frac 1{1+\kappa N} + \left[ + 1-\exp \left( -\frac{\epsilon}{T} + +\left( \frac{2bw}{Td}+\frac{2bs}d \right) \left( 1+\frac{2}{Q} \right) + +\ln N^{*}+\frac{3d^2\kappa Q}{32a^2} \ln \left( \kappa N\right) \right) + \right] +\lbl{eq28b21} +\end{eqnarray} + +With further decreasing temperature the number of rods in the cross-section $% +Q$ becomes larger than $\sqrt{N}$ and the cylinders become elongated in one +direction. + +\subsection{Separation of the lamellar phase} + +The free energy of the lamellar phase is +% +\begin{eqnarray} +\frac{F_L}T &=& + f\frac Ld\left( \frac wT+s\right) + +Mfp\left[ \ln N^{*}-\frac \epsilon T\right] + +fM\left[ p\ln p+(1-p)\ln (1-p)\right] +\nonumber \\ +&& + +2f\ln \left( \frac Ld\right) + +M\frac{\left( 1-f-f\kappa Np\right) }{\kappa N} + \ln \left( \frac{2h^{*}}\xi \frac{1-f-f\kappa Np}e\right) + +f\frac{ 3\pi ^2d^2\kappa ^2}{32a^2}NMp^3 +\nonumber \\ +&& + -0.227f^{*}M \left( \frac{p^2a^2}{\kappa ^2d^2N}\right) ^{1/3} + -1.312M \frac{(f-f^{*})}{f^{*}} + \left( \frac{p^2d^2}{\kappa a^2N^2}\right) ^{1/3} +% +\lbl{eq29} +\end{eqnarray} +where +% +$$ +h^{*}=\frac{\pi d}2\left( 1+\kappa Np \right) ; +\quad +\xi =\frac a{6\pi } \left( \frac{aN}{\kappa pd}\right) ^{1/3} +$$ +% +The phase equilibrium between the isotropic and the lamellar phase can be +found from the equations +% +\begin{eqnarray} +&& + \frac{\dd F_I}{\dd f_I} =\frac{\dd F_L}{\dd f_L}, + \quad + \frac{\dd F_I}{\dd p_I}=\frac{\dd F_L}{\dd p_L} +\nonumber \\ +&& + f_I\frac{\dd F_I}{\dd f_I}-F_I = f_L\frac{\dd F_L}{\dd f_L}-F_L +\lbl{eq2311} +\end{eqnarray} +and the probability of bonding and the binodals are given by +% +\begin{eqnarray} +&& + p_I \simeq p_L\simeq 1, +\nonumber\\ +&& + f_I \simeq 0, +\nonumber \\ +&& + f_L^{(1)} \simeq \frac{1}{1+\kappa N} + \left[ + 1-\frac \xi {2h^{*}} + \exp \left( -1.312\left( \frac{\kappa ^2d^2N}{a^2}\right) ^{1/3}\right) + \right] +\label{eq28b2} +\end{eqnarray} +Similarly the equilibrium between the nematic and the lamellar phase obeys +equations +% +\begin{eqnarray} +&& + \frac{\dd F_N}{\dd f_N} = \frac{\dd F_L}{\dd f_L}, + \quad + \frac{\dd F_N}{\dd p_N} = \frac{\dd F_L}{\dd p_L} +\nonumber \\ +&& + f_N \frac{\dd F_N}{\dd f_N}-F_N = f_L\frac{\dd F_L}{\dd f_L}-F_L +\lbl{eq2321} +\end{eqnarray} +and the corresponding probabilities and binodals are +% +\begin{eqnarray} +&& + p_N \simeq 0, + \quad + p_L\simeq 1, +\nonumber\\ +&& + f_N \simeq 1, + \quad +\nonumber \\ +&& + f_L^{(2)} \simeq \frac{1}{1+\kappa N} + \left[ + 1-\exp \left( -\frac \epsilon T + +\frac{2bw}{Td}+\frac{2bs}d+\ln N^{*} + +\frac{3\pi ^2d^2\kappa ^2N}{32a^2}\right) + \right] +\lbl{eq28b3} +\end{eqnarray} + +\section{Discussion} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newpage +{\bf Literature} + + +Relevant literature + +\cite{SemenovKhokhlov,SemenovRubinstein1,Erukhimovich:Gel} + +\cite{AndrikopoulosVlassopoulosVoyiatzis,Benmouna} + +\cite{KhalaturKhokhlov1,KhalaturKhokhlov2} + +\cite{SemenovNyrkovaKhokhlov,3dFlex} + +\cite{Angerman:PhaseAssocDiblock,Dormidontova:PhaseHbondBrush} + +Theory: + +\cite{Ballauff:CompatHairyRodsCoils,Ballauff:PhaseHairyRodsCoils} + +Lattice: + +\cite{SemenovBlockHomo,Leibler,bookChaikinLubensky,bookKorn} + + +Hairy rods: + +Experiment: + +\cite{SteuerRehahnBallauff,AdamSpiess,SteuerHorthBallauff} + +\cite{GaldaKistnerMartinBallauff,PetekidisVlassopoulosFytas2} + +\cite{PetekidisVlassopoulosFytas1} + + +\begin{references} + +\end{references} + +\end{document} diff --git a/support/biblio/EXAMPLES/hairy/libtex b/support/biblio/EXAMPLES/hairy/libtex new file mode 100755 index 0000000000..54db38c841 --- /dev/null +++ b/support/biblio/EXAMPLES/hairy/libtex @@ -0,0 +1,51 @@ +PREFIX="../../" +VLEVEL="1" #verbosity level +PROJECT="hairy" +REFS=refers.db +# FORMATS=$PREFIX"formats/physreve_with_title" +FORMATS=$PREFIX"formats/macromolecules" +ABBR=$PREFIX"formats/abbr.tex" + +SUFFIX=".1" + +BIBLIO=$PREFIX"biblio.pl" +LATEX="latex" +DVIPS="dvips" +PSTOPS="pstops" + +RM="rm -f" + +OUTTEX="$PROJECT$SUFFIX.tex" +OUTDVI="$PROJECT$SUFFIX.dvi" +TEXFILE="$PROJECT.tex" +DVIFILE="$PROJECT.dvi" +PSFILE="$PROJECT.ps" +PS2FILE="$PROJECT.2.ps" + +echo $OUTTEX + +$RM $PSFILE $PS2FILE $OUTDVI $PROJECT$SUFFIX.aux 2> /dev/null + +$BIBLIO -v $VLEVEL -o $OUTTEX -d $REFS -f $FORMATS -a $ABBR --movepoint --nobibitem --uselist $TEXFILE +# $BIBLIO -v $VLEVEL -o $OUTTEX -d $REFS -f $FORMATS -a $ABBR $TEXFILE +$LATEX $OUTTEX +$LATEX $OUTTEX + +if [ -e $OUTDVI ] +then + mv $OUTDVI $DVIFILE +else + echo File $OUTDVI not found!!! +fi + +if [ -e $DVIFILE ] +then + echo MAKING POSTSCRIPT + touch $DVIFILE + $DVIPS -o $PSFILE $DVIFILE + $PSTOPS "2:0L@.7(21cm,0)+1L@.7(21cm,14.85cm)" $PSFILE $PS2FILE +else + echo NO DVI FILE FOUND +fi + +$RM *.log *~ 2> /dev/null diff --git a/support/biblio/EXAMPLES/hairy/refers.db b/support/biblio/EXAMPLES/hairy/refers.db new file mode 100644 index 0000000000..509a339644 --- /dev/null +++ b/support/biblio/EXAMPLES/hairy/refers.db @@ -0,0 +1,1948 @@ +%LABEL = SuccesvolSolliciteren +%TYPE = book +%AUTHORP = +%AUTHORL = Wams +%AUTHORF = Bert +%TITLE = Succesvol Solliciteren! (Het sollicitatiestandaardwerk voor Nederland. Alles over het gehele sollicitatieproces.) +%PAGES = 240 +%PUBL = SIWU +%PLACE = Enschede +%YEAR = 2001 +%---------- +LABEL = bookKorn +TYPE = book +AUTHORL = Korn|Korn +AUTHORF = G. |Th. +AUTHORM = A. |M. +TITLE = Mathematical handbook for scientists and engineers : definitions, theorems, and formulas for reference and review +PAGES = 1130 +PUBL = McGraw-Hill Book Co +PLACE = New York +YEAR = 1968 +---------- +LABEL = bookChaikinLubensky +TYPE = book +AUTHORP = +AUTHORL = Chaikin|Lubensky +AUTHORF = P.|T. +AUTHORM = M.|C. +TITLE = Principles of condensed matter physics +PAGES = 700 +PUBL = Cambridge Univ. Press +PLACE = Cambridge +YEAR = 1995 +---------- +LABEL = bookSpinGlassTheory +TYPE = book +AUTHORP = +AUTHORL = Mezard|Parisi|Virasoro +AUTHORF = M.|G.|M. +AUTHORM = | |A. +TITLE = Spin Glass Theory and Beyond +PAGES = +PUBL = World Scientific Publishing Co Pte Ltd +PLACE = Singapore +YEAR = 1987 +---------- +LABEL = Brinke4 +TYPE = edbook +AUTHORP = |ten +AUTHORL = Ikkala|Brinke +AUTHORF = O.|G. +BOOKTITLE= Handbook of Advanced Electronic and Photonic Materials and Devices, Part 8 Conducting Polymers +AUTHORI = +AUTHORE = Nalwa +AUTHORG = Hari +AUTHORH = Singh +PAGE = 185 +PUBL = Academic Press +PLACE = +YEAR = 2000 +---------- +LABEL = AbeBallauff +TYPE = edbook +AUTHORL = Abe|Ballauff +AUTHORF = A.|M. +BOOKTITLE= Liquid Crystallinity in Polymers, Chapter 4 The Flory Lattice Model +%%%: Principles and Fundamental Properties +AUTHORI = +AUTHORE = Ciferri +AUTHORG = A. +AUTHORH = +PAGE = 131 +EPAGE = 167 +PUBL = VCH Publishers +PLACE = New York +YEAR = 1991 +---------- +LABEL = KhokhlovTBOA +TYPE = edbook +AUTHORL = Khokhlov +AUTHORF = A. +AUTHORM = R. +BOOKTITLE= Liquid Crystallinity in Polymers, Chapter 3 Theories Based on the Onsager Approach +%%%: Principles and Fundamental Properties +AUTHORI = +AUTHORE = Ciferri +AUTHORG = A. +AUTHORH = +PAGE = 97 +EPAGE = 129 +PUBL = VCH Publishers +PLACE = New York +YEAR = 1991 +---------- +LABEL = bookMcArdle +TYPE = edbook +AUTHORL = Warner +AUTHORF = M +AUTHORM = +TITLE = +BOOKTITLE= Side Chain Liquid Crystal Polymers +AUTHORI = +AUTHORE = McArdle +AUTHORG = C. +AUTHORH = B. +PUBL = Blackie +PLACE = Glasgow and London +YEAR = 1989 +---------- +LABEL = bookdeGennesLiqCryst +TYPE = book +AUTHORP = de +AUTHORL = Gennes +AUTHORF = P.-G. +AUTHORM = +TITLE = The Physics of Liquid Crystals +PUBL = Clarendon Press +PLACE = Oxford +YEAR = 1974 +---------- +LABEL = bookdeGennesScalingConcepts +TYPE = book +AUTHORP = de +AUTHORL = Gennes +AUTHORF = P.-G. +AUTHORM = +TITLE = Scaling Concepts in Polymer Physics +PUBL = Cornell University Press +PLACE = Ithaca +YEAR = 1985 +---------- +LABEL = bookPlate +TYPE = book +AUTHORL = Plate|Shibaev +AUTHORF = N. |V. +AUTHORM = A. |P. +TITLE = Comb-Shaped Polymers and Liquid Crystals +PUBL = Plenum Press +PLACE = New York and London +YEAR = 1987 +---------- +LABEL = GrosKhokh +TYPE = book +AUTHORL = Grosberg|Khokhlov +AUTHORF = A. |A. +AUTHORM = Yu. |R. +TITLE = Statistical Physics of \mml +PUBL = American Institute of Physics +PLACE = New York +YEAR = 1994 +---------- +LABEL = Landau +TYPE = book +AUTHORL = Landau|Lifshits +AUTHORF = L |E. +AUTHORM = D. |M. +TITLE = Statistical Physics +PUBL = Pergamon +PLACE = Oxford +YEAR = 1980 +---------- +LABEL = bookLipatovNesterov +TYPE = book +AUTHORL = Lipatov|Nesterov +AUTHORF = Y. |A. +AUTHORM = S. |E. +TITLE = Thermodynamics of Polymer Blends +PUBL = Technomic +PLACE = Lancaster, Basel +YEAR = 1997 +---------- +LABEL = bookCloizeaux +TYPE = book +AUTHORP = des +AUTHORL = Cloizeaux|Jannink +AUTHORF = J. |G. +TITLE = Polymers in Solutions: Their modelling and Structure +PUBL = Clarendon Press +PLACE = Oxford +YEAR = 1990 +---------- +LABEL = LifshitzGrosbergKhokhlov1 +TYPE = article +AUTHORL = Lifshitz|Grosberg|Khokhlov +AUTHORF = I. |A. |A. +AUTHORM = M. |Yu. |R. +JOURNAL = \rmp +VOL = 50 +PAGE = 683 +EPAGE = 713 +YEAR = 1978 +TITLE = Some problems of the statistical physics of polymer chains with volume interaction +URL = RevModPhys_LifshitsGrosbergKhokhlov1978.pdf +---------- +LABEL = Vasilevskaya +TYPE = article +AUTHORP = | | | |ten +AUTHORL = Vasilevskaya|Klochkov|Khalatur|Khokhlov|Brinke +AUTHORF = V. |A. |P. |A. |G. +AUTHORM = V. |A. |G. |R. | +TITLE = Microphase separation within comb-like copolymer with attractive side-chains: computer simulations +JOURNAL = \mts +VOL = 10 +PAGE = 389 +EPAGE = 394 +YEAR = 2001 +URL = vasilevskaya_attractive.pdf +---------- +LABEL = Helfand1 +TYPE = article +AUTHORL = Helfand|Wasserman +AUTHORF = E. |Z. +AUTHORM = |R. +TITLE = +JOURNAL = \mml +VOL = 9 +PAGE = 879 +YEAR = 1976 +---------- +LABEL = Tsukahara0 +TYPE = edbook +AUTHORL = Tsukahara +AUTHORF = Y. +BOOKTITLE=Macromolecular Design: Concept and Practice +AUTHORI = +AUTHORE = Mishra +AUTHORG = M. +AUTHORH = +PAGE = 161 +EPAGE = 227 +PUBL = Polymer Frontiers International Inc. +PLACE = New York +YEAR = 1993 +---------- +LABEL = Schmidt +TYPE = article +AUTHORL = Tsukahara|Tsutsumi|Yamashita|Shimada +AUTHORF = Y. |K. |S. |S. +TITLE = +JOURNAL = \mml +VOL = 23 +PAGE = 5201 +YEAR = 1990 +---------- +LABEL = Tsukahara2 +TYPE = article +AUTHORL = Tsukahara|Mizuno|Segawa|Yamashita +AUTHORF = Y. |K. |A. |Y. +TITLE = +JOURNAL = \mml +VOL = 22 +PAGE = 1546 +EPAGE = 1552 +YEAR = 1989 +---------- +LABEL = Tsukahara3 +TYPE = article +AUTHORL = Tsukahara|Tsutsumi|Yamashita +AUTHORF = Y. |K. |Y. +TITLE = +JOURNAL = \mml +VOL = 22 +PAGE = 2869 +EPAGE = 2871 +YEAR = 1989 +---------- +LABEL = Ballauff +TYPE = article +AUTHORL = Ballauff +AUTHORF = M. +AUTHORM = +TITLE = +JOURNAL = \ang +VOL = 28 +PAGE = 253 +YEAR = 1989 +---------- +LABEL = Antonietti +TYPE = article +AUTHORL = Antonietti|Henke|Th\"unemann +AUTHORF = M. |S. |A. +AUTHORM = | |F. +TITLE = Highly Ordered Materials with Ultra-Low Surface Energies. 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RubinsteinSemenov +TYPE = article +AUTHORL = Rubinstein|Semenov +AUTHORF = M.|A. +AUTHORM = |N. +JOURNAL = \mml +PAGE = 1058 +EPAGE = 1068 +YEAR = 2001 +VOL = 34 +TITLE = Dynamics of Entangled Solutions of Associating Polymers +URL = ma0013049.pdf +---------- +LABEL = Floudas +TYPE = article +AUTHORL = Floudas|Hadjichristidis|Stamm|Likhtman|Semenov +AUTHORF = G. |N. |M. |A. |A. +AUTHORM = | | |E. |N. +JOURNAL = \jcp +PAGE = 3318 +EPAGE = 3328 +YEAR = 1997 +VOL = 106 +TITLE = Microphase separation in block copolymer-homopolymer blends: Theory and experiment +URL = JCP03318.pdf +---------- +LABEL = Leibler +TYPE = article +AUTHORL = Leibler +AUTHORF = L. +TITLE = Theory of Microphase Separation in Blok Copolymers +JOURNAL = \mml +PAGE = 1602 +YEAR = 1980 +VOL = 13 +---------- +LABEL = FredricksonHelfand +TYPE = article +AUTHORL = Fredrickson|Helfand +AUTHORF = G. |E. +AUTHORM = H. | +TITLE = +JOURNAL = \mml +PAGE = 697 +YEAR = 1987 +VOL = 87 +---------- +LABEL = Dobrynin1 +TYPE = article +AUTHORL = Dobrynin|Erukhimovich +AUTHORF = A.|I. +AUTHORM = V.|Y. +TITLE = Computer-aided comparative investigation of architecture influence of block copolymer phase diagrams +JOURNAL = \mml +PAGE = 276 +EPAGE = 281 +YEAR = 1993 +VOL = 26 +---------- +LABEL = Cruz1 +TYPE = article +AUTHORL = Olvera de la Cruz|Sanchez +AUTHORF = M. |I. +TITLE = +JOURNAL = \mml +PAGE = 2501 +YEAR = 1986 +VOL = 19 +---------- +LABEL = Foster1 +TYPE = article +AUTHORL = Foster|Jasnow|Balazs +AUTHORF = D. |D. |A. +AUTHORM = P. | |C. +TITLE = +JOURNAL = \mml +PAGE = 3450 +EPAGE = 3462 +YEAR = 1995 +VOL = 28 +TITLE = Macrophase and Microphase Separation in Random Comb Copolymers +---------- +LABEL = WernerFredrickson +TYPE = article +AUTHORL = Werner|Fredrickson +AUTHORF = A.|G. +AUTHORM = |H. +TITLE = Architectural Effects on the Stability Limits of $ABS$ Block Copolymers +JOURNAL = \jpsb +PAGE = 849 +EPAGE = 864 +YEAR = 1997 +VOL = 35 +URL = JPolimSciB_v35p849y1997.pdf +---------- +LABEL = Nap1 +TYPE = 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Brinke3 +TYPE = article +AUTHORL = Kosonen|Ruokolainen|Knaapila|Torkkeli|Jokela|Serimaa|Brinke|Bras|Monkman|Ikkala +AUTHORP = | | | | | |ten +AUTHORF = H.|J.|M.|M.|K.|R.|G.|W.|A.|O. +TITLE = Nanoscale Conducting Cylinders Based on Self-Organization of Hydrogen-Bonded Polyaniline Supramolecules +JOURNAL = \mml +PAGE = 8671 +EPAGE = 8675 +YEAR = 2000 +VOL = 33 +URL = mika/Brinke3.pdf +---------- +LABEL = 3dFlex +TYPE = article +AUTHORP = | | |ten +AUTHORL = Subbotin|Saariaho|Ikkala|Brinke +AUTHORF = A. |M. |O. |G. +TITLE = Elasticity of comb copolymer cylindrical brushes +JOURNAL = \mml +PAGE = 3447 +EPAGE = 3452 +YEAR = 2000 +VOL = 33 +URL = mika/3dFlex.pdf +---------- +LABEL = Birshtein +TYPE = article +AUTHORL = Birshtein|Borisov|Zhulina|Khokhlov|Yurasova +AUTHORF = T.|O.|Y.|A.|T. +AUTHORM = M.|V.|B.|R.|A. +TITLE = Conformations of comb-like macromolecules +JOURNAL = \polsciussr +PAGE = 1293 +EPAGE = 1300 +YEAR = 1987 +VOL = 29 +---------- +LABEL = Fredrickson +TYPE = article +AUTHORL 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Theory and Simul1. +%YEAR =1995 +%VOL =4 +%---------- +EOF
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