Austen)Brooks)Casey1,)Benjamin)Beach2,)Taylor)Tarlton2...
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Hydrogel is generated Polymer strands are allowed to move and energy compared Par5cles are allowed to move and the energy compared un5l 10% of the total par5cles in the hydrogel are released The process starts all over. The simula5on con5nues 5ll 60% of all molecules are released or a predetermined volume frac5on of the hydrogel is achieved. Simula5ng the Diffusion of Nanopar5cles through Hydrogels Austen Brooks Casey 1 , Benjamin Beach 2 , Taylor Tarlton 2 , Divya Elumalai 2 , and Pedro Derosa 2,3 1 Department of Chemistry and Physics, Warren Wilson College 2 Ins<tute for Micromanufacturing , Louisiana Tech University 3 Department of Mathema<cs and Physics, Grambling State University Acknowledgements This material is based upon work supported by the Na5onal Science Founda5on under the NSF EPSCoR Coopera5ve Agreement No. EPS1003897 with addi5onal support from the Louisiana Board of Regents. Mo<va<on To create a code that tracks the diffusion of nanopar5cles (NPs) through a computa5onal model of a physical hydrogel Understand the contribu5on of various interac5ons to the diffusion of NP through a polymer network Introduc<on Physical hydrogels have many uses ranging from cell encapsula5on and 5ssue scaffolding, to drug delivery. These are transient polymer networks that rely on physical entanglements, ionic interac5ons, and hydrogenbonding as a means to resist dissolu5on. The degree and method of swelling is dependent upon the polymers that make up the hydrogel; that is, whether thermoresponsive or pH sensi5ve polymers are present. Methodology A random walk Monte Carlo algorithm is used to determine the most energe5cally favorable movements for the NP and polymer chains as the hydrogel swells or contracts. The model was executed using MATLAB to simulate the diffusion through a 1 μm 3 par55oned box containing a physical hydrogel. Van der Waal and Columbic interac5ons play in this process. A Java code was used to visualize the diffusion process through the polymer network. We consider the hydrodynamic radius of the solute/NPs diffusing out of the hydrogels The hydrogel considered is a generic physical hydrogel. Future Work Validate simula5ons with experimental data Build a model for crosslinked hydrogels Extend model for pH, temperature, and electromagne5c fields responsive hydrogels. Derive coefficients such as the molecular weight between crosslinks (M c ) and determine a predic5ve model to es5mate these coefficients Calculate how a change in coefficients, such as M c , influences diffusion through a hydrogel Conclusions A 3D coarse grain Monte Carlo model based on the Boltzmann transport was used to simulate the release profiles and diffusion of molecules into and out of physical hydrogels. In the case studied 20% of total NPs were released. The NPs undergo molecular diffusion in the system considered. The model developed is a promising alterna5ve to the computa5onally intensive molecular dynamics approach to simula5ng diffusion. References 1. Hoffman, Allan S. "Hydrogels for biomedical applica5ons." Advanced drug delivery reviews, 64 (2012): 1823. 2. Chang, Chunyu., Ang, Lue., and Lina, Zhang., "Effects of crosslinking methods on structure and proper5es of cellulose/PVA hydrogels." Macromolecular Chemistry and Physics, 209.12 (2008): 12661273. Figure 5: Flowchart detailing the methodology of the model used in this study ()=↓ +↓ >0 ||<,>0||< >0||< Figure 9: Visualiza5on of both solute and solvent molecules Figure 1: Schema5c representa5on of polymer orienta5on in physical and chemical hydrogels. Reproduced from ref [1]. Results Figure 2: SEM of chemical and physical PVA/cellulose hydrogel cross sec5ons Reproduced from ref [2]. Figure 8: Visualiza5on of NPs diffusing out of the hydrogel Figure 7: Visualiza5on of NPs diffusing into of the hydrogel For each new configura5on NPs are moved as follows: Par5cles are allowed to move in any random direc5on if the total energy of the system aier the move is less than or equal to the energy of the system before the move. If the total energy increases, the move is accepted with Boltzmann probability. Any move is rejected if the par5cle overlaps with any other par5cle or with any polymer strand. A new posi5on for the polymer strand is tested, using the force on it as a bias. Polymer strands are allowed to move if the total energy of the system aier the move is less than or equal to the energy of the system before the move. (including the energy associated with bending and stretching). If the total energy increases, the move is accepted with Boltzmann probability. Mo<on of Polymer Mo<on of Par<cles Total Energy of the System PolymerNP Interac5ons have contribu5ons from Coulombic and Van Der Waals interac=ons NP –NP interac=ons are accounted for by shielded Coulombic and Van Der Waals interac=ons Energy contribu5on due to temperature and other are considered using a Boltzmann probability Total Energy of the System Polymer – Polymer Interac5ons have contribu5ons from Coulombic and Van Der Waals interac=ons Energy associated with bending and stretching is also accounted for. Energy contribu5on due to temperature and other are considered using a Boltzmann probability Figure 3: Contribu5on of the polymer strands to the total energy of the system Figure 4: Contribu5on of the diffusing NPs to the total energy of the system Figure 6: Visualiza5on of the hydrogel model Figure 10: Release profile for the first 20% of NPs from a generic physical hydrogel. 0 5 10 15 20 25 0 10000 20000 30000 40000 % Released Timestep Figure 9: Visualiza5on of a hydrogel sample
Transcript of Austen)Brooks)Casey1,)Benjamin)Beach2,)Taylor)Tarlton2...
Hydrogel is generated
Polymer strands are allowed to move and energy
compared
Par5cles are allowed to move and the energy
compared un5l 10% of the total par5cles in the hydrogel
are released
The process starts all over.
The simula5on con5nues 5ll 60% of all molecules are
released or a predetermined volume frac5on of the hydrogel is achieved.
Simula5ng the Diffusion of Nanopar5cles through Hydrogels Austen Brooks Casey1, Benjamin Beach2, Taylor Tarlton2, Divya Elumalai2, and Pedro Derosa2,3
1Department of Chemistry and Physics, Warren Wilson College 2Ins<tute for Micromanufacturing , Louisiana Tech University
3Department of Mathema<cs and Physics, Grambling State University
Acknowledgements This material is based upon work supported by the Na5onal Science Founda5on under the NSF EPSCoR Coopera5ve Agreement No. EPS-‐1003897 with addi5onal support from the
Louisiana Board of Regents.
Mo<va<on v To create a code that tracks the diffusion of nanopar5cles (NPs) through a computa5onal
model of a physical hydrogel v Understand the contribu5on of various interac5ons to the diffusion of NP through a
polymer network
Introduc<on v Physical hydrogels have many uses ranging from cell encapsula5on and 5ssue-‐
scaffolding, to drug delivery. v These are transient polymer networks that rely on physical entanglements, ionic
interac5ons, and hydrogen-‐bonding as a means to resist dissolu5on. v The degree and method of swelling is dependent upon the polymers that make up the
hydrogel; that is, whether thermo-‐responsive or pH sensi5ve polymers are present.
Methodology v A random walk Monte Carlo algorithm is used to determine the most energe5cally
favorable movements for the NP and polymer chains as the hydrogel swells or contracts.
v The model was executed using MATLAB to simulate the diffusion through a 1 µm3 par55oned box containing a physical hydrogel.
v Van der Waal and Columbic interac5ons play in this process. v A Java code was used to visualize the diffusion process through the polymer network. v We consider the hydrodynamic radius of the solute/NPs diffusing out of the hydrogels v The hydrogel considered is a generic physical hydrogel.
Future Work v Validate simula5ons with experimental data v Build a model for cross-‐linked hydrogels v Extend model for pH, temperature, and electromagne5c fields responsive hydrogels. v Derive coefficients such as the molecular weight between crosslinks (Mc) and
determine a predic5ve model to es5mate these coefficients v Calculate how a change in coefficients, such as Mc, influences diffusion through a
hydrogel
Conclusions v A 3-‐D coarse grain Monte Carlo model based on the Boltzmann transport was used to
simulate the release profiles and diffusion of molecules into and out of physical hydrogels.
v In the case studied 20% of total NPs were released. v The NPs undergo molecular diffusion in the system considered. v The model developed is a promising alterna5ve to the computa5onally intensive
molecular dynamics approach to simula5ng diffusion.
References 1. Hoffman, Allan S. "Hydrogels for biomedical applica5ons." Advanced drug delivery
reviews, 64 (2012): 18-‐23. 2. Chang, Chunyu., Ang, Lue., and Lina, Zhang., "Effects of crosslinking methods on
structure and proper5es of cellulose/PVA hydrogels." Macromolecular Chemistry and Physics, 209.12 (2008): 1266-‐1273.
Figure 5: Flowchart detailing the methodology of the model used in this study
𝑢(𝑟)= 𝑢↓𝑉𝑑𝑊 + 𝑢↓𝐶𝐵 𝑧>0 ||𝑧<𝐿,𝑥>0||𝑥<𝐿 𝑎𝑛𝑑 𝑦>0||𝑦<𝐿
Figure 9: Visualiza5on of both solute and solvent molecules
Figure 1: Schema5c representa5on of polymer orienta5on in physical and chemical hydrogels. Reproduced from ref [1].
Results
Figure 2: SEM of chemical and physical PVA/cellulose hydrogel cross sec5ons Reproduced from ref [2].
Figure 8: Visualiza5on of NPs diffusing out of the hydrogel
Figure 7: Visualiza5on of NPs diffusing into of the hydrogel
For each new configura5on NPs are moved as follows: v Par5cles are allowed to move in any random direc5on if the
total energy of the system aier the move is less than or equal to the energy of the system before the move.
v If the total energy increases, the move is accepted with Boltzmann probability.
v Any move is rejected if the par5cle overlaps with any other par5cle or with any polymer strand.
v A new posi5on for the polymer strand is tested, using the force on it as a bias.
v Polymer strands are allowed to move if the total energy of the system aier the move is less than or equal to the energy of the system before the move. (including the energy associated with bending and stretching).
v If the total energy increases, the move is accepted with Boltzmann probability.
Mo<on of Polymer Mo<on of Par<cles
Total Energy of the System
Polymer-‐NP Interac5ons
have contribu5ons
from Coulombic and Van Der
Waals interac=ons
NP –NP interac=ons are accounted for by shielded Coulombic and Van Der Waals interac=ons
Energy contribu5on
due to temperature and other
are considered using a
Boltzmann probability Total Energy
of the System
Polymer –Polymer
Interac5ons have
contribu5ons from
Coulombic and Van Der Waals interac=ons
Energy associated
with bending and stretching
is also accounted for.
Energy contribu5on
due to temperature and other are considered using a
Boltzmann probability
Figure 3: Contribu5on of the polymer strands to the total energy of the system
Figure 4: Contribu5on of the diffusing NPs to the total energy of the system
Figure 6: Visualiza5on of the hydrogel model
Figure 10: Release profile for the first 20% of NPs from a generic physical hydrogel.
0
5
10
15
20
25
0 10000 20000 30000 40000
% Released
Timestep
Figure 9: Visualiza5on of a hydrogel sample
