%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%This is the article LaTeX template for RSC journals
%Copyright The Royal Society of Chemistry 2010
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\documentclass[8.5pt,twoside,twocolumn]{article}
\oddsidemargin -1.2cm
\evensidemargin -1.2cm
\textwidth 18cm
\headheight 1.0in
\topmargin -3.5cm
\textheight 22cm
\usepackage[super,sort&compress,comma]{natbib} 
\usepackage{mhchem}
\usepackage{times,mathptmx}
% \usepackage{times}
% feel free not to use mathptmx if it causes difficulties
\usepackage{sectsty}
\usepackage{balance} 

\usepackage{graphicx} %eps figures can be used instead
\usepackage{lastpage}
\usepackage[format=plain,justification=raggedright,singlelinecheck=false,font=small,labelfont=bf,labelsep=space]{caption} 
\usepackage{fancyhdr}
%\pagestyle{fancy}
\usepackage{upgreek}

\begin{document}

%\thispagestyle{plain}
%\fancypagestyle{plain}{
%\fancyhead[L]{\includegraphics[height=8pt]{headers/LH}}
%\fancyhead[C]{\hspace{-1cm}\includegraphics[height=20pt]{headers/CH}}
%\fancyhead[R]{\includegraphics[height=10pt]{headers/RH}\vspace{-0.2cm}}
%\renewcommand{\headrulewidth}{1pt}}
%\renewcommand{\thefootnote}{\fnsymbol{footnote}}
%\renewcommand\footnoterule{\vspace*{1pt}% 
%\hrule width 3.4in height 0.4pt \vspace*{5pt}} 
%\setcounter{secnumdepth}{5}
%
%
%
%\makeatletter 
%\def\subsubsection{\@startsection{subsubsection}{3}{10pt}{-1.25ex plus -1ex minus -.1ex}{0ex plus 0ex}{\normalsize\bf}} 
%\def\paragraph{\@startsection{paragraph}{4}{10pt}{-1.25ex plus -1ex minus -.1ex}{0ex plus 0ex}{\normalsize\textit}} 
%\renewcommand\@biblabel[1]{#1}            
%\renewcommand\@makefntext[1]% 
%{\noindent\makebox[0pt][r]{\@thefnmark\,}#1}
%\makeatother 
%\renewcommand{\figurename}{\small{Fig.}~}
%\sectionfont{\large}
%\subsectionfont{\normalsize} 
%
%\fancyfoot{}
%\fancyfoot[LO,RE]{\vspace{-7pt}\includegraphics[height=9pt]{headers/LF}}
%\fancyfoot[CO]{\vspace{-7.2pt}\hspace{12.2cm}\includegraphics{headers/RF}}
%\fancyfoot[CE]{\vspace{-7.5pt}\hspace{-13.5cm}\includegraphics{headers/RF}}
%\fancyfoot[RO]{\footnotesize{\sffamily{1--\pageref{LastPage} ~\textbar  \hspace{2pt}\thepage}}}
%\fancyfoot[LE]{\footnotesize{\sffamily{\thepage~\textbar\hspace{3.45cm} 1--\pageref{LastPage}}}}
%\fancyhead{}
%\renewcommand{\headrulewidth}{1pt} 
%\renewcommand{\footrulewidth}{1pt}
%\setlength{\arrayrulewidth}{1pt}
%\setlength{\columnsep}{6.5mm}
%\setlength\bibsep{1pt}

\twocolumn[
  \begin{@twocolumnfalse}
\noindent\LARGE{\textbf{Electronic Supplementary Information (ESI): \textit{Variable stiffness material based on rigid low-melting-point-alloy-microstructures embedded in soft poly(dimethylsiloxane) (PDMS)}}}
\vspace{0.6cm}

\noindent\large{\textbf{Bryan E. Schubert,$^{\ast}$\textit{$^{a}$} Dario Floreano \textit{$^{a}$}}}\vspace{0.5cm}
%Please note that \ast indicates the corresponding author(s) but no footnote text is required. 


%\noindent\textit{\small{\textbf{Received Xth XXXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX\newline
%First published on the web Xth XXXXXXXXXX 200X}}}
%
%\noindent \textbf{\small{DOI: 10.1039/b000000x}}
\vspace{0.6cm}
%Please do not change this text.
 \end{@twocolumnfalse}]

%Footnotes
%%%% FILL THIS OUT %%%%%

\makeatletter{\renewcommand*{\@makefnmark}{}
\footnotetext{\textit{$^{\ast}$~Corresponding author: bryan.schubert@epfl.ch}}
\footnotetext{\textit{$^{a}$~Laboratory of Intelligent Systems, Ecole Polytechnique F\'{e}d\'{e}rale de Lausanne, 1015 Lausanne, Switzerland.}}

%additional addresses can be cited as above using the lower-case letters, c, d, e... If all authors are from the same address, no letter is required

\section{Thermal expansion}
Heating of a material causes dimensional changes due to thermal expansion. For small temperature changes in isotropic materials, the thermal expansion is linear in all directions and can be represented by,
\begin{equation} \epsilon_\text{T} =b_\text{L}  \Delta T, \end{equation}
where $\epsilon_\text{T}$ is the thermal strain, $b_\text{L}$ is the linear coefficient of thermal expansion and $\Delta T$ is the change in temperature.\cite{popovbook} Using this relationship and the equation for resistance, $R = \rho L / A$, and assuming a constant material resistivity, $\rho$, we can determine the change in resistance due to thermal expansion,
\begin{equation} \Delta R / R_0 =(1+b_\text{L}  \Delta T)^{-1}-1. \end{equation}

The thermal coefficient of expansion for the low-melting-point alloy (LMPA) is $b_\text{L} = 25\times10^{-6}$ $^\circ$C$^{-1}$.\cite{bendalloy} For a temperature change of 22 $^\circ$C (25 $^\circ$C to melting at 47 $^\circ$C), the thermal expansion of only the solid LMPA heating (not melting) would result in a resistance change of $-0.55\times10^{-3}$. When the LMPA melts it experiences a linear expansion of at most 0.02\%, which would cause a resistance change of approximately $-0.2 \times 10^{-3}$.\cite{bendalloy}

The volumetric coefficient of thermal expansion for the PDMS (Sylgard 184) is $b_\text{V} = 9.6\times 10^{-4}$ $^\circ$C$^{-1}$.\cite{dowcorning} For small temperature changes we can approximate the linear thermal expansion coefficient as $b_\text{L} = b_\text{V} / 3 = 3.2 \times 10^{-4}$ $^\circ$C$^{-1}$.\cite{mitchellbook} Then, for a 22 $^\circ$C change in temperature, the thermal expansion of only the PDMS channel would result in a change in resistance of $-6.99 \times 10^{-3}$. This is much higher than the resistance change from the thermal expansion of the LMPA only, but it is still much smaller than the resistance change observed from the change in resistivity of the LMPA as it melts ($\Delta R / R_0 = 0.47$) (see Thermal Behavior Section of the main article).

\section{Elastic modulus}
The samples used for elastic modulus tests were fabricated in different ways depending on the material. The PDMS (Sylgard 184) samples were made by laser cutting (40W CO2 Deluxe Hobby Laser, Full Spectrum Laser) pieces of spare PDMS left over from the variable stiffness device fabrication (see Figure \ref{fig:modulus}(a)). The LMPA (Cerrolow 117) samples were fabricated by casting molten alloy in a laser-cut polyester mold on top of a rubber sheet (see Figure \ref{fig:modulus}(b)). The polyester mold was attached to the rubber using double-sided tape. Once cooled, the LMPA could be removed from the mold by peeling off the rubber layer.

\begin{table}[h]
\small
  \caption{\ Data collected for samples of PDMS and LMPA used for testing the modulus of elasticity. Three samples of each type were tested. See Figure \ref{fig:modulus} for sample dimensions. Dimensions were measured by digital calipers.}
  \label{tbl:modulus}
  \begin{tabular*}{0.5\textwidth}{@{\extracolsep{\fill}}lllll}
    \hline
    Material & w/mm & h/mm & L/mm & Elastic modulus \\
     & & & & /MPa \\
    \hline
    PDMS & 2.80$\pm$0.10 & 0.46$\pm$0.08 & 8.30$\pm$0.09 & 1.81$\pm$0.06 \\
    LMPA & 0.58$\pm$0.01 & 0.32$\pm$0.01 & 6.15$\pm$0.18 & 3.00$\pm$0.13 \\
    \hline
  \end{tabular*}
\end{table}

The elastic moduli of the PDMS and LMPA were determined experimentally using the same set-up described for stretching experiments (see Experimental Section of the main article), as shown in Figure \ref{fig:modulus}(d). Samples were clamped by their wide ends, and they were strained at a constant speed of 100 $\upmu$m s$^{-1}$, which corresponds to strain rates of 0.016 s$^{-1}$ and 0.012 s$^{-1}$ for PDMS and LMPA samples, respectively. This speed is the same as was used in the bending and stretching tests performed on the variable stiffness devices. The elastic modulus was extracted from the linear portion of the stress-strain curves ($E = \sigma / \epsilon$). For PDMS samples, the behavior was linear up to approximately 10\% strain, and for LMPA samples linearity stopped near 1\% strain. Table \ref{tbl:modulus} provides a summary of the results from experiments on three samples of each type of material. The modulus of the LMPA is found to be 3 GPa, and that of the PDMS is 1.81 MPa. The modulus of the PDMS is very close to values reported by Schneider \textit{et al.} of 1.82 MPa.\cite{schneider2008jmm} The measured modulus of the LMPA may be lower than the actual modulus as a result of defects in the LMPA samples. This is because, when manufacturing the LMPA test samples, it is very difficult to prevent some air bubbles from getting trapped in the molten alloy.
%

\begin{figure*}
  \centering
  \includegraphics[width=138mm]{Figures/supp_modulus_v2.pdf}
  \caption{(a) Top- and side-view drawings of PDMS samples for modulus testing being created by laser cutting. (b) Top- and side-view drawings of LMPA samples for modulus testing being created by casting of molten LMPA. (c) Photographs of PDMS (top) and LMPA (bottom) samples. The LMPA sample is broken in the middle from modulus testing. (d) Photograph of test setup, showing a LMPA sample clamped between acrylic plates attached to a force sensor and a fixed support. The stage is used to apply strain to the samples.}
  \label{fig:modulus}
\end{figure*}

%\subsection{This is the subsection heading style}
%Section headings can be typeset with and without numbers.\cite{Abernethy2003}
%
%\subsubsection{This is the subsubsection style.~~} These headings should end in a full point.  
%
%\paragraph{This is the next level heading.~~} For this level please use \texttt{\textbackslash paragraph}. These headings should also end in a full point.
%
%\section{Equations}
%
%Equations can be typeset inline \textit{e.g.} $ y = mx + c$ or displayed with and without numbers:
%
% \[ A = \pi r^2 \]
%
%\begin{equation}
%  \frac{\text{\gamma}}{\text{\epsilon}x} r^2 = 2r
%\end{equation}
%
%\section{Graphics and tables}
%\subsection{Graphics}
%Graphics should be inserted on the page where they are first mentioned (unless they are equations, which appear in the flow of the text).\cite{Cotton1999}
%
%\begin{figure}[h]
%\centering
%  \includegraphics[height=3cm]{example}
%  \caption{An example figure caption}
%  \label{fgr:example}
%\end{figure}
%
%% an example of a two-column figure
%%\begin{figure*}
%  %\centering
%  %\includegraphics[height=3cm]{example.jpg}
%  %\caption{An example figure caption, an image from the \textit{Physical Chemistry Chemical Physics} cover gallery.}
%  %\label{fgr:example}
%%\end{figure*}
%
%\subsection{Tables}
%Tables typeset in RSC house style do not include vertical lines. Table footnote symbols are lower-case italic letters and are typeset at the bottom of the table. Table captions do not end in a full point.\cite{Arduengo1992,Eisenstein2005}
%
%
%\begin{table}[h]
%\small
%  \caption{\ An example of a caption to accompany a table}
%  \label{tbl:example}
%  \begin{tabular*}{0.5\textwidth}{@{\extracolsep{\fill}}lll}
%    \hline
%    Header one/units & Header two & Header three \\
%    \hline
%    1 & 2 & 3 \\
%    4 & 5 & 6 \\
%    7 & 8 & 9 \\
%    10 & 11 & 12 \\
%    \hline
%  \end{tabular*}
%\end{table}
%
%Adding notes to tables can be complicated.  Perhaps the easiest
%method is to generate these manually.
%
%% an example of a two-column table
%%\begin{table*}
%%\small
%  %\caption{\ An example of a caption to accompany a table, table captions do not end in a full point}
%  %\label{tbl:example}
%  %\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lllllll}
%    %\hline
%    %Header one & Header two & Header three & Header four & Header five & Header six  & Header seven\\
%    %\hline
%    %1 & 2 & 3 & 4 & 5 & 6  & 7\\
%    %8 & 9 & 10 & 11 & 12 & 13 & 14 \\
%    %15 & 16 & 17 & 18 & 19 & 20 & 21\\
%    %\hline
%  %\end{tabular*}
%%\end{table*}
%
%You can also put lists into the text. You can have bulleted or numbered lists of almost any kind. 
%The \texttt{mhchem} package can also be used so
%that formulae are easy to input: \texttt{\textbackslash ce\{H2SO4\}} gives \ce{H2SO4}. 
%
%

 %For footnotes in the main text of the article please number the footnotes to avoid duplicate symbols. e.g.  \footnote[num]{your text} the corresponding author \ast counts as footnote 1, ESI as footnote 2, e.g. if there is no ESI, please start at [num]=[2], if ESI is cited in the title please start at [num]=[3] etc. Please also cite the ESI within the main body of the text using \dag.

%The \balance command can be used to balance the columns on the final page if desired. It should be placed anywhere within the first column of the last page.

%\balance

%If notes are included in your references you can change the title from 'References' to 'Notes and references' using the following command:
%\renewcommand\refname{Notes and references}

\balance

\footnotesize{
\bibliography{bibtex_database} %your .bib file
\bibliographystyle{rsc} %the RSC's .bst file
}

\end{document}