matt_papers/original_proposal/original_proposal.tex

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\begin{document}

\title{Elucidation of Structural Changes in Osmotically Swollen Polymer Hydrogels}

\author{Matthew A. Meineke\\
Department of Chemistry and Biochemistry\\ 
University of Notre Dame\\
Notre Dame, Indiana 46556}

\date{\today}
\maketitle

\section{Background}

In the past twenty years, research on polymer gel networks has
revealed interesting information about their osmotically swollen
states and their physiological\cite{Tasaki92,Tasaki94} and mechanical
properties. Of particular interest is the observance of a reversible
gel collapse in polyelectrolyte\cite{Horkay2000} and non-ionic
gels.\cite{Tanaka78} The gel collapse has been linked to many
different environment variables including temperature, solvent
polarity, and in the case of polyelectrolyte gels, salt composition.

\begin{figure}
\begin{center}
\epsfxsize=3in
\epsfbox{all_poly.eps}
\end{center}
\caption{Shown here, are the three polymers discussed within this proposal.}
\label{fig:poly}
\end{figure}

Shibayama \emph{et al.}\cite{Shibayama92} have investigated a weakly
charged polyelectrolyte gel with small angle neutron scattering in the
phase region near the volume change. The gel composition was a
copolymer of N-isopropylacrylamide-\emph{co}-acrylic acid (NIPA/AAc)
(structures shown in figure \ref{fig:poly}). In their study the
collapse was studied by varying either the temperature or the
solvent's acetone:water ratio. In their work they found evidence of
microphase separation in the collapsed gel with phase regions on the
order of $300 \mbox{\AA}$. This would imply that there are regions of
aggregates formed from the combination of electrostatic repulsions of
AAc segments and the attractive interactions of the hydrophobic NIPA
segments. However they were unable to reconcile the length scale of
the microphase separation with the theoretical composition of the
polymer strands.

In a system investigated by Horkay \emph{et al.},\cite{Horkay2000} the
gel studied was a neutralized polyelectrolyte network, sodium
polyacrylate, shown in figure \ref{fig:poly}. The system was studied
near the volume collapse by varying the monovalent:divalent salt
cation ratio in solution. Measurements of the shear modulus and the
osmotic pressure were compared against the volume fraction of the
gel. It was found that the  shear modulus was unaffected by the increase in
the divalent cation concentration near the volume change. This implies
that the cross-linking density is unaffected by the increase in the
divalent:monovalent cation ratio in the gel, suggesting the method of
collapse is based only on an increase in the interaction between
polymer strands facilitated by the divalent cations. What remains to
be known, however, is the exact structural nature of these
interactions.

\section{Research Goals}

It is the goal of this research to elucidate the nature of the gel
collapse in the two systems investigated by Shibayama \emph{et al.} and
Horkay \emph{et al.} Through Gibbs Monte Carlo techniques, this
research will simulate the two systems at state points surrounding
their respective gel collapses. Information gained from the
equilibrium configurations will be used to give structural
insight into the nature of the sudden volume changes in the gels.

The first system to be investigated will be the NIPA/AAc system of
Shibayama \emph{et al.} Their system is ideal to begin with because it
will allow the development of Gibbs techniques without the difficulty
of inserting and deleting charged particles into the gel system (here
the solvent is simply a water-acetone mixture). This system will allow
the investigation to answer such questions as the following: How
atomistic does the model have to be to correctly predict the
microphase separation? Does the distribution of AAc monomers affect
the size of the cavities formed? If so, in what way? How do aggregates
form? Do the gel strands collapse laterally together, or longitudinally
along the polymerization axis? 

After simulating the NIPA/AAc system, the investigation will turn to
the system of Horkay \emph{et al.} Here the system is a neutralized
sodium polyacrylate gel. The first question to answer is then, will
the atomistic detail from the first simulation be sufficient for the
more highly charged gel, or will the system require more detail in the
model. Upon completion of the simulation the following questions will
be addressed: Is a microphase separation observed in the
polyelectrolyte gel collapse? If so, what is the distribution and size
of these cavities? Is the collapse longitudinal or lateral with
respect to the gel structure?  How would the system be affected by the
introduction of a trivalent cation? Would the system collapse in the
same way or would a different type of polymer strand interaction be
observed.

Having simulated both systems, it will then be of interest to compare
the results of the two systems. Here, such questions as the following
can be investigated: Do both systems show similar structural features
when collapsed? Is there a simple model to account for and predict
those features in one or both systems? 

\section{Methodology}

In the research, I will be employing Gibbs ensemble Monte Carlo
techniques.\cite{Panag2000,Frenkel_Smit} The Gibbs ensemble allows
the simulation of two phases in equilibrium, by simulating two
separate systems, one for each phase, and linking the two systems
through particle and volume exchanges. The total system is then
considered to be at constant $NVT$ where $T$ is the constant
temperature of the system, $N$ is the total number of particles, and
$V$ is the total volume. Each particle and volume exchange must then
be constrained to $N$ and $V$: $N = N_{I} + N_{II}$ and $V = V_{I} +
V_{II}$. The whole system then has the following partition function:

\begin{equation}
Q_{NVT} = \frac{1}{\Lambda^{3N}N!} \sum_{N_{I}=0}^{N} \left( 
        \begin{array}{c} 
        N \\ 
        N_{I}
        \end{array} 
        \right) \int_{0}^{V} dV_{I}\,V_{I}^{N_{I}}V_{II}^{N_{II}} 
        \int d\xi_{I}^{N_{I}} \mbox{exp} \left[ -\beta U_{I}(N_{I}) \right] 
        \int d\xi_{II}^{N_{II}} \mbox{exp} \left[ -\beta U_{II}(N_{II}) \right]
\label{eq:partition_function}
\end{equation}

Where $\Lambda$ is the thermal de Broglie wavelength, $\xi$ is the
scaled coordinates of the particles in the two regions, $\beta =
\frac{1}{k_{B}T}$, here $k_{B}$ is Boltzman's constant, and $U(N)$ is
the total intermolecular potential for the interactions of $N$
particles. An ensemble with this given partition function will have the
following probability density:

\begin{equation}
\rho(N_{I},V_{I}; N, V, T) \propto 
        \frac{N!}{N_{I}! N_{II}!}
        \mbox{exp}
        \left[
        N_{I} \ln V_{I} + N_{II} \ln V_{II} 
        - \beta U_{I}(N_{I}) - \beta U_{II}(N_{II})
        \right]
\label{eq:probability_density}
\end{equation}

With these two equations, one can then specify the probability of
accepting or rejecting any of the Monte Carlo moves in the
simulation. For Gibbs ensemble Monte Carlo, there are three types of
moves at each trial step. The first is a random translational move
within one of the simulation boxes. This has the following acceptance
probability:

\begin{equation}
\mathcal{P}_{\mbox{translation}} = 
        \mbox{min}
        \left[ 1, 
        \mbox{exp} \left( -\beta \Delta U \right)
        \right]
\label{eq:translate_accept}
\end{equation}

Where $\Delta U$ is the change in the total energy of the box due to
the configurational change. The second type of move is a volume
change, where box~I is expanded or contracted by $\Delta V$ and box~II
is contracted or expanded by the same amount to satisfy the
constraint: $V = V_{I} + V_{II}$. this move has the following
acceptance probability:

\begin{equation}
\mathcal{P}_{\mbox{volume}} = 
        \mbox{min}
        \left[ 1,
        \mbox{exp} \left(
        -\beta \Delta U_{I} - \beta \Delta U_{I} 
        + N_{I} \ln \frac{V_{I} + \Delta V}{V_{I}}
        + N_{II} \ln \frac{V_{II} - \Delta V}{V_{II}}
        \right)
        \right]
\label{eq:volume_accept}
\end{equation}

The third possible move is the exchange of particle between boxes. The
following acceptance probability is for the transfer of a particle
from box~II to box~I.

\begin{equation}
\mathcal{P}_{\mbox{transfer}} = 
        \mbox{min} \left[ 1,
        \frac{N_{II} V_{I}}{(N_{I} + 1) V_{II}}
        \mbox{exp} \left(
        -\beta \Delta U_{I} - \beta \Delta U_{II}
        \right)
        \right]
\label{eq:transfer_accept}
\end{equation}
        
For a multicomponent mixture, equation \ref{eq:transfer_accept} is
changed by replacing $N_{I}$ and $N_{II}$ with $N_{I,j}$ and $N_{II,j}$
respectively. Where $j$, is the species of the particle being
transfered.

In addition to the standard Gibbs ensemble trial moves, I will also
make use of a hybrid Monte Carlo\cite{Frenkel_Smit,Mehlig92} move for
the box containing the polymer gel network. This will allow me to run
short molecular dynamic integration paths in order to relax the
polymer structure. In the hybrid Monte Carlo trial move, the system is
given a Boltzmann weighted distribution of velocities and allowed to
evolve through the integration of the equations of motion for a given
number of time steps. The final configuration is then accepted or
rejected with the following probability:

\begin{equation}
\mathcal{P}_{\mbox{dynamics}} = 
        \mbox{min} \left[ 1, 
        \mbox{exp} \left( -\beta \Delta \mathcal{H} \right)
        \right]
\label{eq:hybrid_accept}
\end{equation}
Where $\Delta \mathcal{H}$ is the change in the total Hamiltonian of
the system.

These four moves will form the basis of the simulation, however, there
are still some considerations with which the final form of the
simulation will need to deal. The main point needing development, will
be a method of setting the chemical potential in the solvent reservoir
box. Because of the particle transfer move in the Gibbs ensemble, the
chemical potentials of both boxes will fluctuate as particles are
exchanged between the boxes. The two boxes will then
settle to the same chemical potential once equilibrium is
reached. This poses a problem for the solvent reservoir box, as it
will not truly be a solvent reservoir if it's chemical potential
fluctuates. Meaning, if the solvent concentration in the box
fluctuates, then it is not truly representative of the bulk solvent,
which experimentally would stay at constant concentration. Therefore, a
method will need to be developed that will allow me to regulate the
chemical potential in the solvent box.

One possible method, is that of parallel tempering.\cite{Yamamoto2000}
Normally, parallel tempering is used as a method to more fully sample
the phase space of a simulation by simulating parallel systems at
higher temperatures, and at intervals attempting to swap one of the
configurations of the high temperature runs with that of the low
temperature simulation you are interested in. I propose to modify this
method slightly, and instead of simulating other systems at higher
temperatures, run simulations of duplicates of the solvent boxes at a
set chemical potential, and periodically swap their configurations
with that of the solvent reservoir that is equilibrating with the gel
box. The acceptance probability for such an exchange will then need to
be determined before this method could be implemented within the
simulation.

A second problem arises for the simulation of the ionic salts in
solution. Here the particle insertion and deletion methods run the
possibility of being rejected at every attempt. The reason for this is
due to the immense change in configurational energy associated with
the removal or insertion of a charged species into a solution. One
possible method around this is a method similar to that of Lyubarsev
\emph{et al.}\cite{Lyubarsev98} Whereby particle insertions are
attempted through the slow growth of the particle into the system. In
this case, the simulation would allow the slow growth of a charge onto
an inserted ``neutral'' ion. Therefore allowing time for the solvent
to rearrange itself about the new charge and increase the likelihood
of the insertion being accepted.

\section{Proposal Summary}

Through the use of standard Monte Carlo techniques I propose to
simulate first the system of Shibayama \emph{et al.}, and then second
that of Horkay \emph{et al.} In the first simulation I plan to work
out many of the details concerning the methodology and the atomistic
detail of the model employed. In the second simulation, I will use the
model and methodology from the previous simulation and add to it the
capability of simulating ions within the solution. Results from both
systems will be used to determine the micro-structural details of the
reversible gel collapse observed in both polymer gels.

\bibliographystyle{achemso}
\bibliography{original_proposal} \end{document}
Revision:	58
Committed:	Tue Jul 30 18:57:05 2002 UTC (22 years, 1 month ago) by mmeineke
Content type:	application/x-tex
File size:	13092 byte(s)
Log Message:	This is the original proposal I gave in 2001
#	User	Rev	Content
1	mmeineke	58	\documentclass[11pt]{article}
2			\usepackage{epsf}
3			\usepackage[ref]{overcite}
4			\usepackage{setspace}
5			\usepackage{tabularx}
6			\pagestyle{plain}
7			\pagenumbering{arabic}
8			\oddsidemargin 0.0cm \evensidemargin 0.0cm
9			\topmargin -21pt \headsep 10pt
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13			\renewcommand\citemid{\ } % no comma in optional reference note
14
15
16			\begin{document}
17
18			\title{Elucidation of Structural Changes in Osmotically Swollen Polymer Hydrogels}
19
20			\author{Matthew A. Meineke\\
21			Department of Chemistry and Biochemistry\\
22			University of Notre Dame\\
23			Notre Dame, Indiana 46556}
24
25			\date{\today}
26			\maketitle
27
28			\section{Background}
29
30			In the past twenty years, research on polymer gel networks has
31			revealed interesting information about their osmotically swollen
32			states and their physiological\cite{Tasaki92,Tasaki94} and mechanical
33			properties. Of particular interest is the observance of a reversible
34			gel collapse in polyelectrolyte\cite{Horkay2000} and non-ionic
35			gels.\cite{Tanaka78} The gel collapse has been linked to many
36			different environment variables including temperature, solvent
37			polarity, and in the case of polyelectrolyte gels, salt composition.
38
39			\begin{figure}
40			\begin{center}
41			\epsfxsize=3in
42			\epsfbox{all_poly.eps}
43			\end{center}
44			\caption{Shown here, are the three polymers discussed within this proposal.}
45			\label{fig:poly}
46			\end{figure}
47
48			Shibayama \emph{et al.}\cite{Shibayama92} have investigated a weakly
49			charged polyelectrolyte gel with small angle neutron scattering in the
50			phase region near the volume change. The gel composition was a
51			copolymer of N-isopropylacrylamide-\emph{co}-acrylic acid (NIPA/AAc)
52			(structures shown in figure \ref{fig:poly}). In their study the
53			collapse was studied by varying either the temperature or the
54			solvent's acetone:water ratio. In their work they found evidence of
55			microphase separation in the collapsed gel with phase regions on the
56			order of $300 \mbox{\AA}$. This would imply that there are regions of
57			aggregates formed from the combination of electrostatic repulsions of
58			AAc segments and the attractive interactions of the hydrophobic NIPA
59			segments. However they were unable to reconcile the length scale of
60			the microphase separation with the theoretical composition of the
61			polymer strands.
62
63			In a system investigated by Horkay \emph{et al.},\cite{Horkay2000} the
64			gel studied was a neutralized polyelectrolyte network, sodium
65			polyacrylate, shown in figure \ref{fig:poly}. The system was studied
66			near the volume collapse by varying the monovalent:divalent salt
67			cation ratio in solution. Measurements of the shear modulus and the
68			osmotic pressure were compared against the volume fraction of the
69			gel. It was found that the shear modulus was unaffected by the increase in
70			the divalent cation concentration near the volume change. This implies
71			that the cross-linking density is unaffected by the increase in the
72			divalent:monovalent cation ratio in the gel, suggesting the method of
73			collapse is based only on an increase in the interaction between
74			polymer strands facilitated by the divalent cations. What remains to
75			be known, however, is the exact structural nature of these
76			interactions.
77
78			\section{Research Goals}
79
80			It is the goal of this research to elucidate the nature of the gel
81			collapse in the two systems investigated by Shibayama \emph{et al.} and
82			Horkay \emph{et al.} Through Gibbs Monte Carlo techniques, this
83			research will simulate the two systems at state points surrounding
84			their respective gel collapses. Information gained from the
85			equilibrium configurations will be used to give structural
86			insight into the nature of the sudden volume changes in the gels.
87
88			The first system to be investigated will be the NIPA/AAc system of
89			Shibayama \emph{et al.} Their system is ideal to begin with because it
90			will allow the development of Gibbs techniques without the difficulty
91			of inserting and deleting charged particles into the gel system (here
92			the solvent is simply a water-acetone mixture). This system will allow
93			the investigation to answer such questions as the following: How
94			atomistic does the model have to be to correctly predict the
95			microphase separation? Does the distribution of AAc monomers affect
96			the size of the cavities formed? If so, in what way? How do aggregates
97			form? Do the gel strands collapse laterally together, or longitudinally
98			along the polymerization axis?
99
100			After simulating the NIPA/AAc system, the investigation will turn to
101			the system of Horkay \emph{et al.} Here the system is a neutralized
102			sodium polyacrylate gel. The first question to answer is then, will
103			the atomistic detail from the first simulation be sufficient for the
104			more highly charged gel, or will the system require more detail in the
105			model. Upon completion of the simulation the following questions will
106			be addressed: Is a microphase separation observed in the
107			polyelectrolyte gel collapse? If so, what is the distribution and size
108			of these cavities? Is the collapse longitudinal or lateral with
109			respect to the gel structure? How would the system be affected by the
110			introduction of a trivalent cation? Would the system collapse in the
111			same way or would a different type of polymer strand interaction be
112			observed.
113
114			Having simulated both systems, it will then be of interest to compare
115			the results of the two systems. Here, such questions as the following
116			can be investigated: Do both systems show similar structural features
117			when collapsed? Is there a simple model to account for and predict
118			those features in one or both systems?
119
120			\section{Methodology}
121
122			In the research, I will be employing Gibbs ensemble Monte Carlo
123			techniques.\cite{Panag2000,Frenkel_Smit} The Gibbs ensemble allows
124			the simulation of two phases in equilibrium, by simulating two
125			separate systems, one for each phase, and linking the two systems
126			through particle and volume exchanges. The total system is then
127			considered to be at constant $NVT$ where $T$ is the constant
128			temperature of the system, $N$ is the total number of particles, and
129			$V$ is the total volume. Each particle and volume exchange must then
130			be constrained to $N$ and $V$: $N = N_{I} + N_{II}$ and $V = V_{I} +
131			V_{II}$. The whole system then has the following partition function:
132
133			\begin{equation}
134			Q_{NVT} = \frac{1}{\Lambda^{3N}N!} \sum_{N_{I}=0}^{N} \left(
135			\begin{array}{c}
136			N \\
137			N_{I}
138			\end{array}
139			\right) \int_{0}^{V} dV_{I}\,V_{I}^{N_{I}}V_{II}^{N_{II}}
140			\int d\xi_{I}^{N_{I}} \mbox{exp} \left[ -\beta U_{I}(N_{I}) \right]
141			\int d\xi_{II}^{N_{II}} \mbox{exp} \left[ -\beta U_{II}(N_{II}) \right]
142			\label{eq:partition_function}
143			\end{equation}
144
145			Where $\Lambda$ is the thermal de Broglie wavelength, $\xi$ is the
146			scaled coordinates of the particles in the two regions, $\beta =
147			\frac{1}{k_{B}T}$, here $k_{B}$ is Boltzman's constant, and $U(N)$ is
148			the total intermolecular potential for the interactions of $N$
149			particles. An ensemble with this given partition function will have the
150			following probability density:
151
152			\begin{equation}
153			\rho(N_{I},V_{I}; N, V, T) \propto
154			\frac{N!}{N_{I}! N_{II}!}
155			\mbox{exp}
156			\left[
157			N_{I} \ln V_{I} + N_{II} \ln V_{II}
158			- \beta U_{I}(N_{I}) - \beta U_{II}(N_{II})
159			\right]
160			\label{eq:probability_density}
161			\end{equation}
162
163			With these two equations, one can then specify the probability of
164			accepting or rejecting any of the Monte Carlo moves in the
165			simulation. For Gibbs ensemble Monte Carlo, there are three types of
166			moves at each trial step. The first is a random translational move
167			within one of the simulation boxes. This has the following acceptance
168			probability:
169
170			\begin{equation}
171			\mathcal{P}_{\mbox{translation}} =
172			\mbox{min}
173			\left[ 1,
174			\mbox{exp} \left( -\beta \Delta U \right)
175			\right]
176			\label{eq:translate_accept}
177			\end{equation}
178
179			Where $\Delta U$ is the change in the total energy of the box due to
180			the configurational change. The second type of move is a volume
181			change, where box~I is expanded or contracted by $\Delta V$ and box~II
182			is contracted or expanded by the same amount to satisfy the
183			constraint: $V = V_{I} + V_{II}$. this move has the following
184			acceptance probability:
185
186			\begin{equation}
187			\mathcal{P}_{\mbox{volume}} =
188			\mbox{min}
189			\left[ 1,
190			\mbox{exp} \left(
191			-\beta \Delta U_{I} - \beta \Delta U_{I}
192			+ N_{I} \ln \frac{V_{I} + \Delta V}{V_{I}}
193			+ N_{II} \ln \frac{V_{II} - \Delta V}{V_{II}}
194			\right)
195			\right]
196			\label{eq:volume_accept}
197			\end{equation}
198
199			The third possible move is the exchange of particle between boxes. The
200			following acceptance probability is for the transfer of a particle
201			from box~II to box~I.
202
203			\begin{equation}
204			\mathcal{P}_{\mbox{transfer}} =
205			\mbox{min} \left[ 1,
206			\frac{N_{II} V_{I}}{(N_{I} + 1) V_{II}}
207			\mbox{exp} \left(
208			-\beta \Delta U_{I} - \beta \Delta U_{II}
209			\right)
210			\right]
211			\label{eq:transfer_accept}
212			\end{equation}
213
214			For a multicomponent mixture, equation \ref{eq:transfer_accept} is
215			changed by replacing $N_{I}$ and $N_{II}$ with $N_{I,j}$ and $N_{II,j}$
216			respectively. Where $j$, is the species of the particle being
217			transfered.
218
219			In addition to the standard Gibbs ensemble trial moves, I will also
220			make use of a hybrid Monte Carlo\cite{Frenkel_Smit,Mehlig92} move for
221			the box containing the polymer gel network. This will allow me to run
222			short molecular dynamic integration paths in order to relax the
223			polymer structure. In the hybrid Monte Carlo trial move, the system is
224			given a Boltzmann weighted distribution of velocities and allowed to
225			evolve through the integration of the equations of motion for a given
226			number of time steps. The final configuration is then accepted or
227			rejected with the following probability:
228
229			\begin{equation}
230			\mathcal{P}_{\mbox{dynamics}} =
231			\mbox{min} \left[ 1,
232			\mbox{exp} \left( -\beta \Delta \mathcal{H} \right)
233			\right]
234			\label{eq:hybrid_accept}
235			\end{equation}
236			Where $\Delta \mathcal{H}$ is the change in the total Hamiltonian of
237			the system.
238
239			These four moves will form the basis of the simulation, however, there
240			are still some considerations with which the final form of the
241			simulation will need to deal. The main point needing development, will
242			be a method of setting the chemical potential in the solvent reservoir
243			box. Because of the particle transfer move in the Gibbs ensemble, the
244			chemical potentials of both boxes will fluctuate as particles are
245			exchanged between the boxes. The two boxes will then
246			settle to the same chemical potential once equilibrium is
247			reached. This poses a problem for the solvent reservoir box, as it
248			will not truly be a solvent reservoir if it's chemical potential
249			fluctuates. Meaning, if the solvent concentration in the box
250			fluctuates, then it is not truly representative of the bulk solvent,
251			which experimentally would stay at constant concentration. Therefore, a
252			method will need to be developed that will allow me to regulate the
253			chemical potential in the solvent box.
254
255			One possible method, is that of parallel tempering.\cite{Yamamoto2000}
256			Normally, parallel tempering is used as a method to more fully sample
257			the phase space of a simulation by simulating parallel systems at
258			higher temperatures, and at intervals attempting to swap one of the
259			configurations of the high temperature runs with that of the low
260			temperature simulation you are interested in. I propose to modify this
261			method slightly, and instead of simulating other systems at higher
262			temperatures, run simulations of duplicates of the solvent boxes at a
263			set chemical potential, and periodically swap their configurations
264			with that of the solvent reservoir that is equilibrating with the gel
265			box. The acceptance probability for such an exchange will then need to
266			be determined before this method could be implemented within the
267			simulation.
268
269			A second problem arises for the simulation of the ionic salts in
270			solution. Here the particle insertion and deletion methods run the
271			possibility of being rejected at every attempt. The reason for this is
272			due to the immense change in configurational energy associated with
273			the removal or insertion of a charged species into a solution. One
274			possible method around this is a method similar to that of Lyubarsev
275			\emph{et al.}\cite{Lyubarsev98} Whereby particle insertions are
276			attempted through the slow growth of the particle into the system. In
277			this case, the simulation would allow the slow growth of a charge onto
278			an inserted ``neutral'' ion. Therefore allowing time for the solvent
279			to rearrange itself about the new charge and increase the likelihood
280			of the insertion being accepted.
281
282			\section{Proposal Summary}
283
284			Through the use of standard Monte Carlo techniques I propose to
285			simulate first the system of Shibayama \emph{et al.}, and then second
286			that of Horkay \emph{et al.} In the first simulation I plan to work
287			out many of the details concerning the methodology and the atomistic
288			detail of the model employed. In the second simulation, I will use the
289			model and methodology from the previous simulation and add to it the
290			capability of simulating ions within the solution. Results from both
291			systems will be used to determine the micro-structural details of the
292			reversible gel collapse observed in both polymer gels.
293
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