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Molecular mechanisms in deformation of cross-linked hydrogel nanocomposite
Molecular mechanisms in deformation of cross-linked hydrogel nanocomposite Santhosh Mathesan, Amrita Rath, Pijush Ghosh PII: DOI: Reference:
S0928-4931(15)30412-4 doi: 10.1016/j.msec.2015.09.087 MSC 5799
To appear in:
Materials Science & Engineering C
Received date: Revised date: Accepted date:
23 April 2015 7 September 2015 23 September 2015
Please cite this article as: Santhosh Mathesan, Amrita Rath, Pijush Ghosh, Molecular mechanisms in deformation of cross-linked hydrogel nanocomposite, Materials Science & Engineering C (2015), doi: 10.1016/j.msec.2015.09.087
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ACCEPTED MANUSCRIPT MOLECULAR MECHANISMS IN DEFORMATION OF CROSS-LINKED
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HYDROGEL NANOCOMPOSITE Santhosh Mathesan a; Amrita Rath b; Pijush Ghosh c* Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai - 600 036, India.
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a,b,c
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ABSTRACT
The self -folding behavior in response to external stimuli observed in hydrogels are potentially
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used in biomedical applications. However, the use of hydrogels is limited because of its reduced mechanical properties. These properties are enhanced when the hydrogels are cross linked and
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reinforced with nanoparticles. In this work, Molecular dynamics (MD) simulation is applied to
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perform uniaxial tension and pull out tests to understand the mechanism contributing towards the
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enhanced mechanical properties. Also, nanomechanical characterization is performed using quasi static nanoindentation experiments to determine the Young’s modulus of hydrogels in the presence of nanoparticles. The stress strain responses for Chitosan (CS), chitosan reinforced with Hydroxyapatite (HAP) and cross linked chitosan are obtained from uniaxial tension test. It is observed that the Young’s Modulus and maximum stress increases as the HAP content increases and also with cross-linking process. Load displacement plot from pullout test is compared for uncross-linked and cross-linked chitosan chains on hydroxyapatite surface. MD simulation reveals that the variation in the dihedral conformation of chitosan chains and the evolution of internal structural variables are associated with mechanical properties. Additional results reveal that the formation of hydrogen bonds and electrostatic interactions are responsible for the above variations in different systems.
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ACCEPTED MANUSCRIPT Keywords: Hydrogel, Nanocomposite, Cross-linked hydrogel, Deformation mechanism, Molecular Dynamics.
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Abbreviations: CS - Chitosan, HAP - Hydroxyapatite, GA - Glutaraldehyde, DOC - Degree of
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cross-linking
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* Corresponding author address:
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Pijush Ghosh Assistant Professor Department of Applied Mechanics Room: MSB 224A Indian Institute of Technology Madras Chennai - 600 036 India Email: [email protected] ; [email protected] Phone : +91-44-2257-4060 (office) : +91-44-2257-5082 (Lab) http://apm.iitm.ac.in/smlab/pijush/Pijush_index.html
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ACCEPTED MANUSCRIPT 1. INTRODUCTION Stimuli responsive hydrogel is a promising material in the biomedical industry as sensors and
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drug encapsulation. These materials are mostly in the form of hydrogels, a three-dimensional polymer networks holding large amounts of water. The rapid change in its physical properties
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when exposed to pH, temperature, magnetic field, UV or electric field can be utilized
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autonomously in different applications [1–5]. Self-folding is used to obtain complex shapes
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suitable for drug encapsulation and micro grippers for surgery. Self-folding is achieved with tethered connections or tether less external medium [4]. The folding behavior is dependent on the
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swelling characteristics of hydrogels [6] , porosity [1], attachment of functional groups to the hydrogel backbone, the degree of cross-linking and filler loading. Most importantly, the folding
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is a function of mechanical properties observed in the material.
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Chitosan (CS) is natural bio adhesive polymer and it is biocompatible, biodegradable and anti-
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infective. CS is widely used in various fields such as biomedical industry in drug delivery, tissue engineering, wound healing [7,8] and food industry in the form of edible films and food packaging [9]. However, their application in the biomedical industry gets limited because of its poor mechanical properties. The mechanical properties of CS can be enhanced by cross-linking, reinforcing with nanoparticles and by blending with other polymers. Addition of nano sized fillers into the polymer can alter the mechanical, thermal, barrier properties of polymer material [10–12]. Recent studies have revealed that most of the biopolymers, proteins and tissues interact with filler materials mainly through electrostatic interactions and hydrogen bond formation at the interface [13,14]. Here, hydroxyapatite (HAP) nanoparticle, a biocompatible ceramic material is applied as nanofillers to reinforce chitosan. Though, the mechanical properties of chitosan and interactions between CS/HAP are available in
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ACCEPTED MANUSCRIPT the literature, the absence of detail interaction mechanisms like conformational behavior and hydrogen bond analysis (CS/HAP) during the deformation process have motivated us to perform This work will be helpful in engineering the mechanical properties of
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this work [14,15]. CS/HAP system.
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Apart from reinforcing hydrogels with filler material, the presence of cross-linking improves
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the mechanical properties of hydrogels. The mechanical properties of CS and its stability in the
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different pH medium can be enhanced either by ionic or covalent cross-linking [15,16]. In this work, glutaraldehyde (GA) is used as a cross-linking agent. The formation of three dimensional
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network structure improves the mechanical properties and their stability in solvent medium. Though different techniques are used to improve the mechanical properties, we have to
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compromise with properties like elasticity and swelling behavior. As the filler loading increases,
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the tensile strength of nanocomposites shows an increasing trend. With further increase of filler
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loading beyond a critical percentage of nanoparticles, the tensile strength is found to be decreased [17]. At higher cross linker content, the hydrogels turn into a brittle material, which shows reduced swelling behavior [18]. Incorporating nanoparticle into cross-linked hydrogels is a suitable technique to have a material with improved mechanical properties besides efficient swelling behavior. Addition of nanoparticles with hydrophilic groups provides attractive sites for water and modifying the swelling behavior of hydrogels. Therefore, hydrogels reinforced with nanoparticles require a lesser degree of cross-linking. This reduces the effect of cross-linking on water absorption capacity of hydrogels. Therefore, an optimized degree of cross-linking and nanofillers content is required to obtain essential mechanical and swelling properties for selffolding applications.
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ACCEPTED MANUSCRIPT Self-folding observed in hydrogels is primarily a bending phenomenon because of differentially stressed films [1,4,6]. Uniaxial tension test is the most fundamental technique to
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determine the mechanical properties. It is one of the simplest tests which can help modeling the folding behavior of hydrogel in the presence of nanoparticle and cross-linking. Besides
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understanding the deformation behavior, it is extremely important to explore the interaction
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mechanisms between hydrogel matrix, nanoparticles and cross-linking agent at an atomistic
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level. This study can assist in designing hydrogel films with desired folding nature. Molecular dynamics simulation is used to predict mechanical properties as well as the interaction
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mechanisms of various materials like collagen/hydroxyapatite, polyethylene and epoxy [13,19,20]. Therefore, we have applied molecular dynamics (MD) simulations to address the
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environment.
self-folding behavior of hydrogels in trigger based physiological
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in understanding the
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deformation behavior and interaction mechanisms. These interactions studies will also be helpful
In this work, we focus on the interaction mechanisms present in HAP/CS matrix with different HAP loading and glutaraldehyde cross-linked chitosan system. The deformation behavior of particle reinforced hydrogel is dependent on the filler loading and it is evaluated using stress strain characteristics. The evolution of internal structural variables over the deformation is used to relate the microscopic mechanisms and different regimes observed in stress strain curves. To explore the interaction between CS and HAP in the presence of cross-linking agent, uncross linked/cross linked chitosan chains were pulled along an axis in the vicinity of HAP. Experimentally, the enhancement of mechanical properties of CS in the presence of HAP is confirmed with the aid of nanoindentation. To the best of author’s knowledge, this work is the
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ACCEPTED MANUSCRIPT first of its kind to address the deformation mechanism of CS/HAP nanocomposite and cross-
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linked chitosan system based on the conformational and hydrogen bond analysis.
SIMULATION METHODOLOGY
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1.1. Polymer nanocomposite model
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The amorphous chitosan box was generated with 200 chains using PACKMOL [21] and each chain has 50 repeating units. Hydroxyapatite (HAP) crystal has a hexagonal unit cell with space
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group P63/m [22]. HAP unit cell with 44 atoms and chemical formula Ca10 P6 O24 (OH)2 was generated [23]. The lattice parameters of the HAP unit cell are: a = 9.4214 Å, b = 9.4214 Å, c =
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6.8814 Å, α = 90°, β = 90° and γ = 120°.With the aid of above mentioned unit cell, HAP
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particles were created by repeating the unit cell in all three direction ( 3 x 2 x 3) with 792 atoms.
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The nanocomposite generated with PACKMOL is shown in Figure.1. 1.2. Cross linked model
The initial structure consists of chitosan chains and the cross-linking agent (glutaraldehyde molecules). Glutaraldehyde (GA) has two reactive sites and chitosan has one reactive site per repeating unit (nitrogen in the amine group). Based on the number of reactive sites present in the chitosan chains, the number of GA was calculated. Degree of cross-linking is defined as the ratio of number of reacted sites to total number of possible reactive sites. The cross-linking is carried out to obtain a structure with the required degree of cross-linking. The cross linking procedure is as follows: GA molecules and 200 chitosan chains were filled in a box using PACKMOL. Chitosan chains with length of 50 repeating units were used for cross-linking. The number of GA molecules was
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ACCEPTED MANUSCRIPT calculated assuming 100% degree of cross linking. Initially, the structure was minimized using Conjugate gradient minimization algorithm. Covalent bond was formed, when the distance
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between two reactive atoms were within the cutoff (5A° to 8A°). Once the covalent bonds were formed, again the structure was minimized and equilibrated using NVT dynamics at 300 K. The
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NVT dynamics was carried out in order increase the kinetic energy of atoms, which enhances the
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possibility of reactive atoms to fall within the cut off range. The process of bond formation,
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minimization and equilibration (NVT) were continued until the required degree of cross-linking was reached. Based on the number of reactive sites reacted during the cross-linking process, the
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degree of cross-linking was determined. Here, the system studied has a degree of cross-linking of
1.3. Simulation details
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structure is shown in Figure 1.
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73 %. The density of the cross-linked system is 0.37 g/cm3. The equilibrated cross-linked
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All simulations were performed by using LAMMPS, a molecular dynamics package developed by Sandia National Laboratories [24]. The CHARMM forcefield was used for atomistic simulation of organic and inorganic materials to predict the mechanical properties. The bonded and non bonded forcefield parameters for HAP were adopted from earlier works [25]. The simulation box was replicated in all the three directions by implementing appropriate periodic boundary conditions. The system was minimized using conjugate gradient minimization algorithm. After minimization, the system was subjected to the annealing process to ensure the minimum energy level. The temperature and pressure were controlled by a Nose/Hoover thermostat and barostat respectively. Following this, the system was relaxed at 300 K before starting of deformation process. The glass transition temperature of the system (404 K) was calculated to ensure our system represents the bulk system [26].
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ACCEPTED MANUSCRIPT 1.4. Uniaxial deformation procedure The box was deformed along x direction under a constant strain rate of 5x1011/s over every
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timestep using NPT dynamics at 300K. During the deformation, zero stress condition was imposed on the planes perpendicular to the loading direction. The component of stress along x-
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direction was calculated from the pressure in x-direction at every timestep using LAMMPS. The
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above procedure was followed for CS, CS/HAP and cross-linked CS system. Also, this model
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can be extended to other deformation studies under different conditions. 1.5. Visualization
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The initial configuration and the trajectory were visualized using VMD and VESTA [27,28].
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2.1. Materials
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2. EXPERIMENTAL DETAILS
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Chitosan powder (Degree of deacetylation > 90%, viscosity: 100-200 cps, medium molecular weight: 105-200 kDa), was supplied by SRL Pvt. Ltd. (India). Hydroxyapatite nanopowder, < 200
nm particle size (BET) was procured from Aldrich and used as received. Chitosan solution (1.5% w/v) was prepared by adding 300 mg of CS powder in 20 mL acetic acid (1% v/v) solution. This mixture was stirred homogeneously by keeping it over a hot plate magnetic stirrer for 2 hours. CS/HAP film was prepared by adding HAP powder to the above formed CS solution and stirred it again for 24-48 hours for homogeneous mixing. The solution formed will be different in color on uniform mixing of HAP powder with CS solution. This solution was poured into a clean petri dish and kept inside oven at 60°C for 24 hours to dry completely. Film of ~ 100 μm thicknesses in the dish was peeled slowly using a twisor and stored in desiccators for further use.
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ACCEPTED MANUSCRIPT 2.2. Nanoindentation tests The depth sensing indentation experiments were carried out on CS/HAP film by using
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Nanoindenter (Hysitron TI 950 TriboIndenterTM). Nanoindentation was performed by using Berkovich diamond tip having Young’s modulus, Etip=1140 GPa and Poisson’s ratio, ʋ tip=0.07.
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A trapezoidal load function having three segments of loading, holding and unloading was
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considered where, each segment was allowed to stand for 10s. All the CS/HAP film was
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subjected to a maximum load of 500 μN. The nanomechanical properties of these films were
3.1. Stress strain behavior
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3. RESULTS AND DISCUSSION
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calculated from unloading portion of the load displacement curve obtained from nanoindentation.
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The stress strain behavior of a pure chitosan system, CS/HAP (10%) and cross-linked chitosan
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system (DOC - 73%) which are deformed at 300 K under constant strain rate is shown in Figure 2 (a). The stress values are observed to increase linearly with strain up to 3.5% in all the three cases. This is denoted as elastic region and considered for the determination of Young’s modulus of the system. Following this, upto 6.5% of strain (approximate displacement of 15 Å) in the chitosan system, no significant increase in stress with respect to strain is observed. This is due to the phenomenon of strain softening following the yield point. The existing experimental and simulation studies indicate the enhancement of mechanical properties in the presence of nanoparticles [10, 13, 15]. Similar results were obtained in our work during the deformation test on CS/HAP system. Increase in Young’s modulus as well as the maximum stress is observed in the cross-linked system compared to the uncross-linked chitosan system and CS/HAP nanocomposites. The stress strain behavior of chitosan system and a system with different
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ACCEPTED MANUSCRIPT percentages of HAP (10%, 20% & 30%) are shown in Figure 2 (b). The values of Young’s modulus and maximum stress for different systems are mentioned in Table 1.
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Young’s modulus and the maximum stress obtained from simulation tend to increase with increase in HAP content. The physical interactions at the interface between nanoparticles and
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chitosan chains are responsible for load sharing phenomenon [29]. The E values obtained from
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MD simulations are compared with nanoindentation results. Nanoindentation results suggest no
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significant improvement in E value between CS with 20% and 30% HAP. This can be attributed to some of the experimental phenomenon such as agglomeration, which reduces the effect of
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nanoparticles on the load transfer mechanism.
In a cross-linked system, the orientation of the polymer backbone towards the direction of
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stress offers more resistance to deformation. This regime observed in stress strain characteristics
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is said to be strain hardening. It is the consequence of GA connecting the chains and allowing the
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polymer matrix to take more stress over the yielding process (three dimensional network structure). Strain hardening region is observed in cross-linked system deformed at 5x1011/s. However, this behavior is absent in cross-linked system when they are deformed at a strain rate of 10^10/s. The regimes observed in stress strain plot are addressed at microscopic level using internal structural variables and at the atomic level using conformational analysis. 3.2. Internal Structural Variables An amorphous polymer system is composed of polymer chains, which are randomly coiled and entangled. The polymer chains are held together by entanglement and inter molecular forces. The response of these forces towards the external deformation determines the mechanical properties of the system. Over the deformation process, the polymer chains are characterized through internal structural variables such as end to end distance, chain orientation parameter and
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ACCEPTED MANUSCRIPT conformational analysis. The study of internal structural variables provides an insight into load transfer or stress transfer mechanism during external deformation.
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3.2.1. End to end distance End to end distance is measured to determine the dimension of a polymer chain. Variation of
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end to end distance provides information about the conformation changes, polymer entropy and
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free energy. The schematic of end to end distance is shown in Figure. 3 (a).
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The force required to stretch the chains is determined from the stiffness of the polymer chain, which in turn is dependent on the end to end distance. Low end to end distance causes the
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polymer to have high local conformational freedom, which increases the polymer entropy and reduces the available free energy [30]. The number of conformations a polymer chain can adopt
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decreases at the higher end to end distance, which occur at larger strains. The end to end distance
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is averaged over all the chains present in the system. At a particular strain, average end to end
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distance is determined over a different percentage of strain. To understand the behavior of polymer chains at different percentage of filler (HAP), the variation of end to end distance over strain is measured for the pristine chitosan and chitosan with 10% HAP and 30% HAP as shown in Figure 3 (b). The end to end distance is not a suitable parameter to be characterized for crosslinked system as the chains no longer remain in linear fashion [31]. At larger strain, the decrease in resistance to deformation is addressed by understanding the evolution of non bonded interactions which is discussed in the later sections. During the initial stages of deformation process (region ‘A’ in Figure.3 (b)), the polymer chains extend at the expense of inter chain non bonded interactions. The regions ‘A’ and ‘B’ in Figure 3 (b) corresponds to the region before and after attaining maximum stress in the stress strain plot (refer Figure 2(b)). As the strain increases, the decrease in the extent of entanglements
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ACCEPTED MANUSCRIPT within the polymer chains results in the reorganization of the network structure. These phenomenons are responsible for the increase in end to end distance of polymer chains at larger
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strains (region ‘B’ in Figure 3(b)). In addition, it is observed that the presence of nanoparticles have a significant effect on end to end distance of chitosan polymer chains as shown in Figure
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3(b). The HAP nanoparticle restricts the extension of chitosan chains around it, modifying the
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conformational behavior of chitosan chains. Also, the end to end distance of chitosan chains is
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dependent on the possible conformations it can attain. The conformational behavior of chitosan chains is determined by the variation of dihedral angles and it is the outcome of non bonded
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interactions with HAP nanoparticles. The conformation behavior of chitosan chains is restricted in the vicinity of HAP surface due to interactions which reduces the end to end distance. The
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conformational behavior is analyzed in later sections.
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3.2.2. Chain orientation parameter
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Randomly oriented polymer chains in an amorphous polymer system tend to align in the direction of the load. This orientation of polymer chains incorporates anisotropy in the mechanical properties of the polymers. The intensity of their orientation is studied by determining the fraction of chains aligned along the loading direction at different percentages of strain. The orientation of polymer chains is influenced by the interface in the presence of nanoparticles and loading rate coupled with end to end distance. The extent to which the polymer chains are oriented is related to the magnitude of stress shared by the polymer chains. The angle made by monomer i with the direction of strain is calculated by finding the angle between the vector joining the (i+1)th monomer and (i-1)th monomer and the direction of application of strain. The calculation of chain orientation parameter is described in the schematic shown in Figure 4 (a).
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ACCEPTED MANUSCRIPT The chain segment is said to be aligned with the direction of strain if the angle is less than 20° and greater than 160° with the direction of strain. The effect of nanoparticle on the orientation of
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polymer chains is determined for a chitosan system with 10% HAP and 30% HAP loading as shown in Figure 4 (b). The orientation parameter is observed to increase over the deformation
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process, confirming the alignment of chains along the direction of stress. Furthermore, the
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orientation of chitosan chains in the presence of nanoparticles (10%) is more, compared to the
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pristine chitosan system. At larger strain, the increased orientation behavior is responsible for enhanced mechanical properties of CS/HAP (10%) system as observed in Figure 2(b).
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The orientation of chitosan chains with 30% HAP is similar to pristine chitosan system. The high filler loading in CS/HAP (30%) system allows the nanoparticles come closer to each other.
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The above system represents agglomeration situation in the experiment. This reduces the
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available area for the chitosan chains to interact with HAP nanoparticles. Thus, the CS/HAP
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(30%) shows reduced orientation compared to CS/HAP (10%) and reduced load carrying capacity at larger strain.
The number of conformations available for the chains decreases when the chains are oriented along the loading direction. The chitosan chains present in the cross-linked system shows a reduced orientation parameter compared to pure chitosan system. In a cross-linked system, the GA molecules (in addition to chitosan chains) orient in the direction of stress and hold the chains together as shown in Figure 5 (two chains were selected for clarity in VMD). The distribution of chain segments at one particular strain with different chain orientation parameter was analyzed from a histogram. For a pure chitosan system, the histogram indicating the number of chain segments oriented toward the loading direction at zero percent and 100 percent strain is shown in Figure 6 (a) and (b) respectively. It is observed that most of the chain
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ACCEPTED MANUSCRIPT segments are perpendicular to the loading direction during the initial deformation process. At the end of the deformation process, most of the chain segments are at angles less than 20° or greater
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than 160° as shown in Figure 4 (a). Intermediate histogram gives an idea about the degree of orientation of polymer chains present in a system. The same procedure is applied to chitosan
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system with different percentage of HAP. The number of chain segments oriented towards the
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direction of stress varies with filler loadings. Thus, a major contribution in terms of response of a
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polymer to external tensile load comes in the form of orientation of polymer chain. 3.3. Conformational behavior
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3.3.1. CS/HAP system
The stiffness of polymer chains depends on the conformational freedom available for the
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chains. The conformation of the polymer chain is altered in the presence of nanoparticles, which,
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has significant influence on the self-folding behavior. The dihedral angles φ, ψ, and χ determine
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the structure of chitosan chains. Characterizing the dihedral angle, which involves the glycosidic linkages is adequate to comment on the conformations of monomers as shown in Figure 7 (a) [32]. Here, we have selected a chitosan chain from CS/HAP nanocomposite system, which is in the vicinity of HAP as shown in Figure 7 (b). The dihedral angle, φ is selected for two monomers, which are farther and nearer to HAP. The dihedral angle of monomers far away from HAP with a maximum and minimum of 179.73° and -179.85° respectively as shown in Figure 8 (a) & (b). This indicates the free rotation of monomers with respect to each other. Moving closer to HAP, results in the maximum and minimum value of 171.56° and 102.86° respectively as shown in Figure 8 (c) & (d). The reduced variation in dihedral angle for the monomers closer to HAP shows the influence of HAP on chitosan chains. The stiffness of chitosan chains are expected to be altered because of reduced
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ACCEPTED MANUSCRIPT conformational freedom available due to the presence of HAP. The variations observed in conformational behavior are the outcome of non bonded interactions within the system, which is
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discussed in later sections. 3.3.2. Cross-linked CS/HAP system
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The behavior of chitosan chains in the vicinity of HAP signifies the influence of HAP on
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dihedral conformation of chitosan chains. To have a better insight on the dihedral conformation
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of uncross-linked/cross-linked CS chains in the vicinity of HAP, the following analysis is performed. We are interested in the behavior of chitosan chains in the presence of nanoparticles
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(HAP) as well as cross linking agent (GA). GA cross-linked chitosan chains in the proximity of HAP surface are shown in Figure 9. The behavior of monomers attached to GA is analyzed by
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pulling one chitosan chain along x direction in the vicinity of HAP. Similar analysis is performed
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on uncross-linked CS chains on HAP surface and the load versus displacement curve is obtained
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for both systems as shown in Figure 10. Here, the dihedral analysis is performed in the region encircled in Figure 9, showing the interactions between CS, GA and HAP. For a displacement of 47 Å, no significant difference in the slope between cross-linked and uncross-linked chitosan system is observed due to physical interactions.
In uncross-linked
system, the drop in physical interactions is responsible for reduced load carrying capacity after 47 Å. In a cross-linked/HAP system, the initial stage of deformation is mainly affected by the influence of nanoparticles on chitosan chains (non bonded interactions) similar to uncross linked system. At larger deformations, the GA molecules have a significant effect, thereby overcoming the interactions with HAP and allowing the chitosan chains to take more load (covalent bond with GA).
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ACCEPTED MANUSCRIPT The improved load carrying capacity in cross-linked system is attributed to the presence of GA. The behavior of GA molecules at larger displacement is shown in Figure 11 (a). The
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dihedral variation of angle phi, φ (C2-C1-O1-C4) of monomers connected to GA is shown in Figure 11 (b). As long as the GA molecules posses high conformational freedom, the monomers
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connected to GA have freedom to exhibit the conformational changes. But in the vicinity of
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HAP, the conformation freedom gets arrested and it corresponds to region ‘A’ in Figure 11 (b).
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As the chains slide over the HAP, the GA molecules are completely stretched. The GA molecules become stiffer, thereby reducing the conformational freedom available for the
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connected monomers as shown in Figure 11 (a). Though, the monomer connected to GA is arrested, the nearby monomers are free to rotate. This is due to the restriction from HAP
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dominated by the GA molecules, which corresponds to region B in Figure. 11 (b).
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4. Radial Distribution Function
Radial Distribution Function (RDF) gives the probability of finding a particle at a distance ‘r’ from the reference particle. The observed variation in dihedral conformation and internal structural variables are the results of the dynamics of non bonded interactions like hydrogen bonding, electrostatic interactions and νan der Waal's interaction.
The existence of these
interactions is confirmed in a system by plotting RDF between pairs of atoms. The presence of amine group and hydroxyl groups present in chitosan are the potential reactive sites for the formation of hydrogen bonds as previously reported in the literature. Similarly, Ca2+ and OH- are the reactive sites available for interaction in the HAP crystal. During the deformation process, the RDF is determined between different pairs of atoms in a CS/HAP system at 5% strain as shown in Figure 12. It is observed that the position of the peak (1.785 Å) from Figure 12(a) is greater than the equilibrium bond length (1.04 Å) between
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ACCEPTED MANUSCRIPT nitrogen and hydrogen. Therefore, it confirms the existence of hydrogen bonds between N in amine group (CS) and H in OH group (CS). In all the cases, a prominent peak is observed in the
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range of 2 Å to 4 Å, indicating the formation of hydrogen bond within the chitosan chains. The HAP interacts with chitosan chains primarily through electrostatic interactions, van der
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Waals's interactions or hydrogen bond formation [33]. Electrostatic interactions are observed
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between Ca2+ in HAP & nitrogen in an amine group of chitosan (Figure 12(c)) and Ca2+ in HAP
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& oxygen in CH2OH of chitosan. The peaks observed beyond 5 Å in Figure 12(c) & 12(d)
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corresponds to long range interactions like van der Waal’s interactions [22].
5.1. CS/HAP nanocomposite
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5. Hydrogen bond analysis
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The existence of hydrogen bonds within chitosan chains and between chitosan/HAP is
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confirmed from the RDF plots. The analysis of hydrogen bond formation during the deformation process is performed using VMD [25]. The distance between hydrogen donor and acceptor is 3.5 Å and the angle cutoff between them is taken as 150°. A detailed analysis of evolution of hydrogen bonds is performed to determine the significant donor/acceptor pairs involved in load transfer. The evolution of hydrogen bonds for two donor/acceptor pairs (Figure 13) is discussed in the following sections. The hydrogen bonds are responsible for the strengthening of interface between chitosan matrix and HAP nanoparticles in addition to the electrostatic interactions between them. The increase in Young’s modulus with the addition of HAP content is because of an effective interface and the load transfer mechanism via the interface. The decrease in load carrying capability at larger strains is due to reduced number of hydrogen bonds as shown in Figure 14 (a). At larger strains, the orientation of chain towards the direction of pull is the reason for enhanced interactions
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ACCEPTED MANUSCRIPT between chitosan chains (as shown in Figure.14 (b)) rather than chitosan and HAP nanoparticles. The corresponding increase in hydrogen bonds within chitosan matrix does not assist in
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enhancing the load transfer. From the hydrogen bond analysis, it is observed that the influence of nanoparticle is dominating during the initial stages of deformation via hydrogen bond
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formation. These interactions are accompanied by electrostatic interactions as mentioned in RDF
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analysis. At later stages of deformation, interactions between chitosan and HAP nanoparticles is
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reduced which causes the drop in stress. 5.2. CS/GA system
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The chitosan system has reactive sites which are responsible for the formation of hydrogen bonds. Amine group is one of the major reactive sites which are capable of forming hydrogen
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bond with other groups present in the system. During the cross-linking process, most of the
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hydrogen atoms present in amine group are removed and nitrogen forms imine bond with the
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GA. The number of hydrogen bonds present in the cross-linked system due to amine group over the deformation process is very low compared to uncross-linked system as shown in Figure 15 (a).
Though the number of hydrogen bond present due to amine group decreases, the presence of GA enhances the mechanical properties of the cross-linked system. The oxygen (not participating in cross-linking process) present in GA molecule forms hydrogen bond with OH group of chitosan, the evolution of which over strain is shown in Figure 15 (b). So, in the crosslinked system the number of hydrogen bonds are more compared to that of an uncross-linked system due to the presence of GA molecules. Thus, hydrogen bond formation also contributes to the mechanical properties in cross-linked system.
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ACCEPTED MANUSCRIPT 6. CONCLUSION In summary, we have evaluated the mechanical properties of CS/HAP and cross-linked
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chitosan system using uniaxial deformation process at 300 K upto 100% strain. We determine
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the mechanical properties of CS applying nanoindentation with and without the addition of HAP.
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Chitosan chains interact with HAP mainly through electrostatic interactions and hydrogen bond formation. At lower strain, the deformation behavior is primarily influenced by the presence of
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nanoparticles. At larger strain, the orientation of chitosan chains and their conformational
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behavior determines the mechanical properties. Also, the number of hydrogen bonds, which offers conformational restriction to chitosan chains decreases at larger deformation. As a result,
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the resistance to deformation decreases at the larger strain in the CS/HAP system. Lack of
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conformational freedom to the monomers connected to glutaraldehyde and formation of three-
system.
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dimensional network are also responsible for improved mechanical properties in cross-linked
As a result, the dihedral conformation of hydrogels is modified in the presence of nanoparticles and cross-linking agent. This signifies the relation between structural integrity of hydrogels and their mechanical properties. The fundamental mechanisms will be helpful in understanding the influence of nanoparticle and cross-linking agent on the deformation characteristics of chitosan at atomistic length scale.
ACKNOWLEDGMENT Authors would like to sincerely thank P.G. Senapathy Center for Computing Resources, IIT Madras for providing computational facilities.
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[30] R.M. Statics, Nonlinear elasticity in biological gels, 435 (2005) 0–3. doi:10.1038/nature03497.1. [31] G. F. Carter, D. E. Paul, Materials Science and Engineering, ninth ed., ASM International, U.S.A, 2010. [32] R.A. Cunha, T.A. Soares, V.H. Rusu, F.J.S. Pontes, E.F. Franca, R.D. Lins, The Molecular Structure and Conformational Dynamics of Chitosan Polymers : An Integrated Perspective from Experiments and Computational Simulations, in: D. N. Karunaratne (EDs.), The Complex World of Polysaccharides, Intech, New York, 2012, pp. 232. [33] H.P. Zhang, X. Lu, L.M. Fang, S.X. Qu, B. Feng, J. Weng, Atomic-scale interactions at the interface of biopolymer/hydroxyapatite., Biomed. Mater. 3 (2008) 044110. doi:10.1088/1748-6041/3/4/044110.
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Figure captions
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Figure 1. (a) Chitosan reinforced with HAP (b) chitosan cross-linked with Glutaraldehyde (GA). (Cyan - Carbon; Red - Oxygen; White - Hydrogen; Blue - Nitrogen; Green - Calcium;
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Gold - Phosphorous).
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Figure 2. Stress strain curve for (a) chitosan, chitosan nanocomposite (CS_HAP_10%) and crosslinked chitosan (CS_Cross), (b) chitosan nanocomposite with different percentage of
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HAP.
Figure 3. (a) Schematic representing end to end distance in one polymer chain (b) end to end
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distance of chitosan chains as a function of strain. Figure 4. (a) Schematic showing determination of chain orientation parameter (b) evolution of
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chain orientation parameter during deformation at 300K. Figure 5. The characteristics of cross-linkers (GA molecules) during deformation at (a) 0 % (b)
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50 % (c) 75 % and (d) 100 % strain. (Cyan - Carbon; Red - Oxygen; White - Hydrogen; Blue - Nitrogen).
Figure 6. Histogram representing chain orientation parameter for CS at (a) 0 % and (b) 100 % strain.
Figure 7. (a) Schematic showing different dihedral angles in chitosan molecule (b) dihedrals closer and farther away from HAP is monitored during the deformation process. (Cyan Carbon; Red - Oxygen; White - Hydrogen; Blue - Nitrogen; Green - Calcium; Yellow Phosphorous). Figure 8. The dihedral angle which is farther away from HAP with (a) maximum value and (b) minimum value. The dihedral angle in the proximity of HAP with (c) maximum value and (d) minimum value. (Cyan - Carbon; Red - Oxygen; White - Hydrogen; Blue Nitrogen; Green - Calcium; Gold - Phosphorous). Figure 9. Cross linked chitosan chains in the proximity of HAP surface.
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ACCEPTED MANUSCRIPT Figure 10. Load Displacement plot for uncross linked and cross-linked chitosan chains in the proximity of HAP obtained from single chain pull out test.
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Figure 11. The conformation of monomers when (a) GA molecule in fully extended state (b) variation of dihedral (phi) angle of monomer connected to GA.
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Figure 12. RDF plot for, (a) nitrogen in amine group (CS) and hydrogen in OH group (CS) (b)
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oxygen connecting monomers and hydrogen in OH group (CS) (c) calcium ion in HAP and nitrogen in amine group (d) oxygen in PO43- ion (HAP) and hydrogen in OH group
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(CS).
Figure 13. Schematic representation of possible hydrogen bonds within chitosan chains, between
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chitosan and HAP nanoparticles.
Figure 14. Hydrogen bond evolution over strain between (a) oxygen in PO43- of HAP as acceptor
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and oxygen as donor in OH group of chitosan for CS/HAP system with 10%, 20% and
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30% HAP (b) nitrogen in amine group of chitosan as donor and oxygen as acceptor in
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OH group of chitosan in a CS/HAP (30%) system. Figure 15. Hydrogen bond evolution over strain between (a) nitrogen in amine group and oxygen in OH group of CS (b) oxygen in GA and OH group of CS.
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ACCEPTED MANUSCRIPT Table 1 Young’s modulus (E) and maximum stress values obtained from simulation and Nanoindentation
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tests E (GPa)
Maximum Stress (MPa)
Chitosan(CS)
2.06±0.307
172.1±22.90
CS with 10% HAP
2.83±0.086
212.8±9.70
CS with 20% HAP
3.09±0.082
221.4±3.30
3.39±0.806
CS with 30% HAP
3.92±0.146
245.1±8.10
3.29±0.309
CS with 73% DOC
3.91±0.439
515.5±0.056
E (GPa) Nanoindentation 1.52±0.060 2.61±0.287
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Graphical abstract
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ACCEPTED MANUSCRIPT Highlights
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Molecular dynamics is applied to perform uniaxial deformation tests on cross-linked and nanoparticle reinforced chitosan. Nanoindentation confirms the enhanced mechanical properties of modified chitosan system. Dihedral conformational variations are primarily responsible for altered mechanical characteristics. van der Waals interactions within the modified chitosan system determines the conformational variations. Single chain pull out study of cross-linked and uncross-linked chain reveals different mechanical response.
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S0928-4931(15)30412-4 doi: 10.1016/j.msec.2015.09.087 MSC 5799
To appear in:
Materials Science & Engineering C
Received date: Revised date: Accepted date:
23 April 2015 7 September 2015 23 September 2015
Please cite this article as: Santhosh Mathesan, Amrita Rath, Pijush Ghosh, Molecular mechanisms in deformation of cross-linked hydrogel nanocomposite, Materials Science & Engineering C (2015), doi: 10.1016/j.msec.2015.09.087
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ACCEPTED MANUSCRIPT MOLECULAR MECHANISMS IN DEFORMATION OF CROSS-LINKED
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HYDROGEL NANOCOMPOSITE Santhosh Mathesan a; Amrita Rath b; Pijush Ghosh c* Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai - 600 036, India.
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a,b,c
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ABSTRACT
The self -folding behavior in response to external stimuli observed in hydrogels are potentially
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used in biomedical applications. However, the use of hydrogels is limited because of its reduced mechanical properties. These properties are enhanced when the hydrogels are cross linked and
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reinforced with nanoparticles. In this work, Molecular dynamics (MD) simulation is applied to
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perform uniaxial tension and pull out tests to understand the mechanism contributing towards the
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enhanced mechanical properties. Also, nanomechanical characterization is performed using quasi static nanoindentation experiments to determine the Young’s modulus of hydrogels in the presence of nanoparticles. The stress strain responses for Chitosan (CS), chitosan reinforced with Hydroxyapatite (HAP) and cross linked chitosan are obtained from uniaxial tension test. It is observed that the Young’s Modulus and maximum stress increases as the HAP content increases and also with cross-linking process. Load displacement plot from pullout test is compared for uncross-linked and cross-linked chitosan chains on hydroxyapatite surface. MD simulation reveals that the variation in the dihedral conformation of chitosan chains and the evolution of internal structural variables are associated with mechanical properties. Additional results reveal that the formation of hydrogen bonds and electrostatic interactions are responsible for the above variations in different systems.
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ACCEPTED MANUSCRIPT Keywords: Hydrogel, Nanocomposite, Cross-linked hydrogel, Deformation mechanism, Molecular Dynamics.
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Abbreviations: CS - Chitosan, HAP - Hydroxyapatite, GA - Glutaraldehyde, DOC - Degree of
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cross-linking
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* Corresponding author address:
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Pijush Ghosh Assistant Professor Department of Applied Mechanics Room: MSB 224A Indian Institute of Technology Madras Chennai - 600 036 India Email: [email protected] ; [email protected] Phone : +91-44-2257-4060 (office) : +91-44-2257-5082 (Lab) http://apm.iitm.ac.in/smlab/pijush/Pijush_index.html
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ACCEPTED MANUSCRIPT 1. INTRODUCTION Stimuli responsive hydrogel is a promising material in the biomedical industry as sensors and
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drug encapsulation. These materials are mostly in the form of hydrogels, a three-dimensional polymer networks holding large amounts of water. The rapid change in its physical properties
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when exposed to pH, temperature, magnetic field, UV or electric field can be utilized
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autonomously in different applications [1–5]. Self-folding is used to obtain complex shapes
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suitable for drug encapsulation and micro grippers for surgery. Self-folding is achieved with tethered connections or tether less external medium [4]. The folding behavior is dependent on the
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swelling characteristics of hydrogels [6] , porosity [1], attachment of functional groups to the hydrogel backbone, the degree of cross-linking and filler loading. Most importantly, the folding
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is a function of mechanical properties observed in the material.
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Chitosan (CS) is natural bio adhesive polymer and it is biocompatible, biodegradable and anti-
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infective. CS is widely used in various fields such as biomedical industry in drug delivery, tissue engineering, wound healing [7,8] and food industry in the form of edible films and food packaging [9]. However, their application in the biomedical industry gets limited because of its poor mechanical properties. The mechanical properties of CS can be enhanced by cross-linking, reinforcing with nanoparticles and by blending with other polymers. Addition of nano sized fillers into the polymer can alter the mechanical, thermal, barrier properties of polymer material [10–12]. Recent studies have revealed that most of the biopolymers, proteins and tissues interact with filler materials mainly through electrostatic interactions and hydrogen bond formation at the interface [13,14]. Here, hydroxyapatite (HAP) nanoparticle, a biocompatible ceramic material is applied as nanofillers to reinforce chitosan. Though, the mechanical properties of chitosan and interactions between CS/HAP are available in
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ACCEPTED MANUSCRIPT the literature, the absence of detail interaction mechanisms like conformational behavior and hydrogen bond analysis (CS/HAP) during the deformation process have motivated us to perform This work will be helpful in engineering the mechanical properties of
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this work [14,15]. CS/HAP system.
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Apart from reinforcing hydrogels with filler material, the presence of cross-linking improves
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the mechanical properties of hydrogels. The mechanical properties of CS and its stability in the
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different pH medium can be enhanced either by ionic or covalent cross-linking [15,16]. In this work, glutaraldehyde (GA) is used as a cross-linking agent. The formation of three dimensional
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network structure improves the mechanical properties and their stability in solvent medium. Though different techniques are used to improve the mechanical properties, we have to
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compromise with properties like elasticity and swelling behavior. As the filler loading increases,
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the tensile strength of nanocomposites shows an increasing trend. With further increase of filler
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loading beyond a critical percentage of nanoparticles, the tensile strength is found to be decreased [17]. At higher cross linker content, the hydrogels turn into a brittle material, which shows reduced swelling behavior [18]. Incorporating nanoparticle into cross-linked hydrogels is a suitable technique to have a material with improved mechanical properties besides efficient swelling behavior. Addition of nanoparticles with hydrophilic groups provides attractive sites for water and modifying the swelling behavior of hydrogels. Therefore, hydrogels reinforced with nanoparticles require a lesser degree of cross-linking. This reduces the effect of cross-linking on water absorption capacity of hydrogels. Therefore, an optimized degree of cross-linking and nanofillers content is required to obtain essential mechanical and swelling properties for selffolding applications.
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ACCEPTED MANUSCRIPT Self-folding observed in hydrogels is primarily a bending phenomenon because of differentially stressed films [1,4,6]. Uniaxial tension test is the most fundamental technique to
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determine the mechanical properties. It is one of the simplest tests which can help modeling the folding behavior of hydrogel in the presence of nanoparticle and cross-linking. Besides
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understanding the deformation behavior, it is extremely important to explore the interaction
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mechanisms between hydrogel matrix, nanoparticles and cross-linking agent at an atomistic
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level. This study can assist in designing hydrogel films with desired folding nature. Molecular dynamics simulation is used to predict mechanical properties as well as the interaction
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mechanisms of various materials like collagen/hydroxyapatite, polyethylene and epoxy [13,19,20]. Therefore, we have applied molecular dynamics (MD) simulations to address the
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self-folding behavior of hydrogels in trigger based physiological
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in understanding the
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deformation behavior and interaction mechanisms. These interactions studies will also be helpful
In this work, we focus on the interaction mechanisms present in HAP/CS matrix with different HAP loading and glutaraldehyde cross-linked chitosan system. The deformation behavior of particle reinforced hydrogel is dependent on the filler loading and it is evaluated using stress strain characteristics. The evolution of internal structural variables over the deformation is used to relate the microscopic mechanisms and different regimes observed in stress strain curves. To explore the interaction between CS and HAP in the presence of cross-linking agent, uncross linked/cross linked chitosan chains were pulled along an axis in the vicinity of HAP. Experimentally, the enhancement of mechanical properties of CS in the presence of HAP is confirmed with the aid of nanoindentation. To the best of author’s knowledge, this work is the
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ACCEPTED MANUSCRIPT first of its kind to address the deformation mechanism of CS/HAP nanocomposite and cross-
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linked chitosan system based on the conformational and hydrogen bond analysis.
SIMULATION METHODOLOGY
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1.1. Polymer nanocomposite model
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The amorphous chitosan box was generated with 200 chains using PACKMOL [21] and each chain has 50 repeating units. Hydroxyapatite (HAP) crystal has a hexagonal unit cell with space
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group P63/m [22]. HAP unit cell with 44 atoms and chemical formula Ca10 P6 O24 (OH)2 was generated [23]. The lattice parameters of the HAP unit cell are: a = 9.4214 Å, b = 9.4214 Å, c =
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6.8814 Å, α = 90°, β = 90° and γ = 120°.With the aid of above mentioned unit cell, HAP
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particles were created by repeating the unit cell in all three direction ( 3 x 2 x 3) with 792 atoms.
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The nanocomposite generated with PACKMOL is shown in Figure.1. 1.2. Cross linked model
The initial structure consists of chitosan chains and the cross-linking agent (glutaraldehyde molecules). Glutaraldehyde (GA) has two reactive sites and chitosan has one reactive site per repeating unit (nitrogen in the amine group). Based on the number of reactive sites present in the chitosan chains, the number of GA was calculated. Degree of cross-linking is defined as the ratio of number of reacted sites to total number of possible reactive sites. The cross-linking is carried out to obtain a structure with the required degree of cross-linking. The cross linking procedure is as follows: GA molecules and 200 chitosan chains were filled in a box using PACKMOL. Chitosan chains with length of 50 repeating units were used for cross-linking. The number of GA molecules was
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ACCEPTED MANUSCRIPT calculated assuming 100% degree of cross linking. Initially, the structure was minimized using Conjugate gradient minimization algorithm. Covalent bond was formed, when the distance
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between two reactive atoms were within the cutoff (5A° to 8A°). Once the covalent bonds were formed, again the structure was minimized and equilibrated using NVT dynamics at 300 K. The
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NVT dynamics was carried out in order increase the kinetic energy of atoms, which enhances the
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possibility of reactive atoms to fall within the cut off range. The process of bond formation,
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minimization and equilibration (NVT) were continued until the required degree of cross-linking was reached. Based on the number of reactive sites reacted during the cross-linking process, the
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degree of cross-linking was determined. Here, the system studied has a degree of cross-linking of
1.3. Simulation details
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structure is shown in Figure 1.
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73 %. The density of the cross-linked system is 0.37 g/cm3. The equilibrated cross-linked
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All simulations were performed by using LAMMPS, a molecular dynamics package developed by Sandia National Laboratories [24]. The CHARMM forcefield was used for atomistic simulation of organic and inorganic materials to predict the mechanical properties. The bonded and non bonded forcefield parameters for HAP were adopted from earlier works [25]. The simulation box was replicated in all the three directions by implementing appropriate periodic boundary conditions. The system was minimized using conjugate gradient minimization algorithm. After minimization, the system was subjected to the annealing process to ensure the minimum energy level. The temperature and pressure were controlled by a Nose/Hoover thermostat and barostat respectively. Following this, the system was relaxed at 300 K before starting of deformation process. The glass transition temperature of the system (404 K) was calculated to ensure our system represents the bulk system [26].
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ACCEPTED MANUSCRIPT 1.4. Uniaxial deformation procedure The box was deformed along x direction under a constant strain rate of 5x1011/s over every
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timestep using NPT dynamics at 300K. During the deformation, zero stress condition was imposed on the planes perpendicular to the loading direction. The component of stress along x-
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direction was calculated from the pressure in x-direction at every timestep using LAMMPS. The
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above procedure was followed for CS, CS/HAP and cross-linked CS system. Also, this model
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can be extended to other deformation studies under different conditions. 1.5. Visualization
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The initial configuration and the trajectory were visualized using VMD and VESTA [27,28].
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2.1. Materials
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2. EXPERIMENTAL DETAILS
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Chitosan powder (Degree of deacetylation > 90%, viscosity: 100-200 cps, medium molecular weight: 105-200 kDa), was supplied by SRL Pvt. Ltd. (India). Hydroxyapatite nanopowder, < 200
nm particle size (BET) was procured from Aldrich and used as received. Chitosan solution (1.5% w/v) was prepared by adding 300 mg of CS powder in 20 mL acetic acid (1% v/v) solution. This mixture was stirred homogeneously by keeping it over a hot plate magnetic stirrer for 2 hours. CS/HAP film was prepared by adding HAP powder to the above formed CS solution and stirred it again for 24-48 hours for homogeneous mixing. The solution formed will be different in color on uniform mixing of HAP powder with CS solution. This solution was poured into a clean petri dish and kept inside oven at 60°C for 24 hours to dry completely. Film of ~ 100 μm thicknesses in the dish was peeled slowly using a twisor and stored in desiccators for further use.
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ACCEPTED MANUSCRIPT 2.2. Nanoindentation tests The depth sensing indentation experiments were carried out on CS/HAP film by using
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Nanoindenter (Hysitron TI 950 TriboIndenterTM). Nanoindentation was performed by using Berkovich diamond tip having Young’s modulus, Etip=1140 GPa and Poisson’s ratio, ʋ tip=0.07.
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A trapezoidal load function having three segments of loading, holding and unloading was
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considered where, each segment was allowed to stand for 10s. All the CS/HAP film was
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subjected to a maximum load of 500 μN. The nanomechanical properties of these films were
3.1. Stress strain behavior
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3. RESULTS AND DISCUSSION
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calculated from unloading portion of the load displacement curve obtained from nanoindentation.
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The stress strain behavior of a pure chitosan system, CS/HAP (10%) and cross-linked chitosan
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system (DOC - 73%) which are deformed at 300 K under constant strain rate is shown in Figure 2 (a). The stress values are observed to increase linearly with strain up to 3.5% in all the three cases. This is denoted as elastic region and considered for the determination of Young’s modulus of the system. Following this, upto 6.5% of strain (approximate displacement of 15 Å) in the chitosan system, no significant increase in stress with respect to strain is observed. This is due to the phenomenon of strain softening following the yield point. The existing experimental and simulation studies indicate the enhancement of mechanical properties in the presence of nanoparticles [10, 13, 15]. Similar results were obtained in our work during the deformation test on CS/HAP system. Increase in Young’s modulus as well as the maximum stress is observed in the cross-linked system compared to the uncross-linked chitosan system and CS/HAP nanocomposites. The stress strain behavior of chitosan system and a system with different
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ACCEPTED MANUSCRIPT percentages of HAP (10%, 20% & 30%) are shown in Figure 2 (b). The values of Young’s modulus and maximum stress for different systems are mentioned in Table 1.
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Young’s modulus and the maximum stress obtained from simulation tend to increase with increase in HAP content. The physical interactions at the interface between nanoparticles and
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chitosan chains are responsible for load sharing phenomenon [29]. The E values obtained from
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MD simulations are compared with nanoindentation results. Nanoindentation results suggest no
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significant improvement in E value between CS with 20% and 30% HAP. This can be attributed to some of the experimental phenomenon such as agglomeration, which reduces the effect of
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nanoparticles on the load transfer mechanism.
In a cross-linked system, the orientation of the polymer backbone towards the direction of
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stress offers more resistance to deformation. This regime observed in stress strain characteristics
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is said to be strain hardening. It is the consequence of GA connecting the chains and allowing the
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polymer matrix to take more stress over the yielding process (three dimensional network structure). Strain hardening region is observed in cross-linked system deformed at 5x1011/s. However, this behavior is absent in cross-linked system when they are deformed at a strain rate of 10^10/s. The regimes observed in stress strain plot are addressed at microscopic level using internal structural variables and at the atomic level using conformational analysis. 3.2. Internal Structural Variables An amorphous polymer system is composed of polymer chains, which are randomly coiled and entangled. The polymer chains are held together by entanglement and inter molecular forces. The response of these forces towards the external deformation determines the mechanical properties of the system. Over the deformation process, the polymer chains are characterized through internal structural variables such as end to end distance, chain orientation parameter and
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ACCEPTED MANUSCRIPT conformational analysis. The study of internal structural variables provides an insight into load transfer or stress transfer mechanism during external deformation.
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3.2.1. End to end distance End to end distance is measured to determine the dimension of a polymer chain. Variation of
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end to end distance provides information about the conformation changes, polymer entropy and
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free energy. The schematic of end to end distance is shown in Figure. 3 (a).
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The force required to stretch the chains is determined from the stiffness of the polymer chain, which in turn is dependent on the end to end distance. Low end to end distance causes the
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polymer to have high local conformational freedom, which increases the polymer entropy and reduces the available free energy [30]. The number of conformations a polymer chain can adopt
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decreases at the higher end to end distance, which occur at larger strains. The end to end distance
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is averaged over all the chains present in the system. At a particular strain, average end to end
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distance is determined over a different percentage of strain. To understand the behavior of polymer chains at different percentage of filler (HAP), the variation of end to end distance over strain is measured for the pristine chitosan and chitosan with 10% HAP and 30% HAP as shown in Figure 3 (b). The end to end distance is not a suitable parameter to be characterized for crosslinked system as the chains no longer remain in linear fashion [31]. At larger strain, the decrease in resistance to deformation is addressed by understanding the evolution of non bonded interactions which is discussed in the later sections. During the initial stages of deformation process (region ‘A’ in Figure.3 (b)), the polymer chains extend at the expense of inter chain non bonded interactions. The regions ‘A’ and ‘B’ in Figure 3 (b) corresponds to the region before and after attaining maximum stress in the stress strain plot (refer Figure 2(b)). As the strain increases, the decrease in the extent of entanglements
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ACCEPTED MANUSCRIPT within the polymer chains results in the reorganization of the network structure. These phenomenons are responsible for the increase in end to end distance of polymer chains at larger
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strains (region ‘B’ in Figure 3(b)). In addition, it is observed that the presence of nanoparticles have a significant effect on end to end distance of chitosan polymer chains as shown in Figure
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3(b). The HAP nanoparticle restricts the extension of chitosan chains around it, modifying the
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conformational behavior of chitosan chains. Also, the end to end distance of chitosan chains is
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dependent on the possible conformations it can attain. The conformational behavior of chitosan chains is determined by the variation of dihedral angles and it is the outcome of non bonded
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interactions with HAP nanoparticles. The conformation behavior of chitosan chains is restricted in the vicinity of HAP surface due to interactions which reduces the end to end distance. The
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conformational behavior is analyzed in later sections.
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3.2.2. Chain orientation parameter
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Randomly oriented polymer chains in an amorphous polymer system tend to align in the direction of the load. This orientation of polymer chains incorporates anisotropy in the mechanical properties of the polymers. The intensity of their orientation is studied by determining the fraction of chains aligned along the loading direction at different percentages of strain. The orientation of polymer chains is influenced by the interface in the presence of nanoparticles and loading rate coupled with end to end distance. The extent to which the polymer chains are oriented is related to the magnitude of stress shared by the polymer chains. The angle made by monomer i with the direction of strain is calculated by finding the angle between the vector joining the (i+1)th monomer and (i-1)th monomer and the direction of application of strain. The calculation of chain orientation parameter is described in the schematic shown in Figure 4 (a).
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ACCEPTED MANUSCRIPT The chain segment is said to be aligned with the direction of strain if the angle is less than 20° and greater than 160° with the direction of strain. The effect of nanoparticle on the orientation of
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polymer chains is determined for a chitosan system with 10% HAP and 30% HAP loading as shown in Figure 4 (b). The orientation parameter is observed to increase over the deformation
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process, confirming the alignment of chains along the direction of stress. Furthermore, the
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orientation of chitosan chains in the presence of nanoparticles (10%) is more, compared to the
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pristine chitosan system. At larger strain, the increased orientation behavior is responsible for enhanced mechanical properties of CS/HAP (10%) system as observed in Figure 2(b).
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The orientation of chitosan chains with 30% HAP is similar to pristine chitosan system. The high filler loading in CS/HAP (30%) system allows the nanoparticles come closer to each other.
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The above system represents agglomeration situation in the experiment. This reduces the
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available area for the chitosan chains to interact with HAP nanoparticles. Thus, the CS/HAP
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(30%) shows reduced orientation compared to CS/HAP (10%) and reduced load carrying capacity at larger strain.
The number of conformations available for the chains decreases when the chains are oriented along the loading direction. The chitosan chains present in the cross-linked system shows a reduced orientation parameter compared to pure chitosan system. In a cross-linked system, the GA molecules (in addition to chitosan chains) orient in the direction of stress and hold the chains together as shown in Figure 5 (two chains were selected for clarity in VMD). The distribution of chain segments at one particular strain with different chain orientation parameter was analyzed from a histogram. For a pure chitosan system, the histogram indicating the number of chain segments oriented toward the loading direction at zero percent and 100 percent strain is shown in Figure 6 (a) and (b) respectively. It is observed that most of the chain
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ACCEPTED MANUSCRIPT segments are perpendicular to the loading direction during the initial deformation process. At the end of the deformation process, most of the chain segments are at angles less than 20° or greater
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than 160° as shown in Figure 4 (a). Intermediate histogram gives an idea about the degree of orientation of polymer chains present in a system. The same procedure is applied to chitosan
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system with different percentage of HAP. The number of chain segments oriented towards the
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direction of stress varies with filler loadings. Thus, a major contribution in terms of response of a
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polymer to external tensile load comes in the form of orientation of polymer chain. 3.3. Conformational behavior
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3.3.1. CS/HAP system
The stiffness of polymer chains depends on the conformational freedom available for the
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chains. The conformation of the polymer chain is altered in the presence of nanoparticles, which,
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has significant influence on the self-folding behavior. The dihedral angles φ, ψ, and χ determine
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the structure of chitosan chains. Characterizing the dihedral angle, which involves the glycosidic linkages is adequate to comment on the conformations of monomers as shown in Figure 7 (a) [32]. Here, we have selected a chitosan chain from CS/HAP nanocomposite system, which is in the vicinity of HAP as shown in Figure 7 (b). The dihedral angle, φ is selected for two monomers, which are farther and nearer to HAP. The dihedral angle of monomers far away from HAP with a maximum and minimum of 179.73° and -179.85° respectively as shown in Figure 8 (a) & (b). This indicates the free rotation of monomers with respect to each other. Moving closer to HAP, results in the maximum and minimum value of 171.56° and 102.86° respectively as shown in Figure 8 (c) & (d). The reduced variation in dihedral angle for the monomers closer to HAP shows the influence of HAP on chitosan chains. The stiffness of chitosan chains are expected to be altered because of reduced
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ACCEPTED MANUSCRIPT conformational freedom available due to the presence of HAP. The variations observed in conformational behavior are the outcome of non bonded interactions within the system, which is
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discussed in later sections. 3.3.2. Cross-linked CS/HAP system
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The behavior of chitosan chains in the vicinity of HAP signifies the influence of HAP on
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dihedral conformation of chitosan chains. To have a better insight on the dihedral conformation
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of uncross-linked/cross-linked CS chains in the vicinity of HAP, the following analysis is performed. We are interested in the behavior of chitosan chains in the presence of nanoparticles
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(HAP) as well as cross linking agent (GA). GA cross-linked chitosan chains in the proximity of HAP surface are shown in Figure 9. The behavior of monomers attached to GA is analyzed by
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pulling one chitosan chain along x direction in the vicinity of HAP. Similar analysis is performed
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on uncross-linked CS chains on HAP surface and the load versus displacement curve is obtained
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for both systems as shown in Figure 10. Here, the dihedral analysis is performed in the region encircled in Figure 9, showing the interactions between CS, GA and HAP. For a displacement of 47 Å, no significant difference in the slope between cross-linked and uncross-linked chitosan system is observed due to physical interactions.
In uncross-linked
system, the drop in physical interactions is responsible for reduced load carrying capacity after 47 Å. In a cross-linked/HAP system, the initial stage of deformation is mainly affected by the influence of nanoparticles on chitosan chains (non bonded interactions) similar to uncross linked system. At larger deformations, the GA molecules have a significant effect, thereby overcoming the interactions with HAP and allowing the chitosan chains to take more load (covalent bond with GA).
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ACCEPTED MANUSCRIPT The improved load carrying capacity in cross-linked system is attributed to the presence of GA. The behavior of GA molecules at larger displacement is shown in Figure 11 (a). The
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dihedral variation of angle phi, φ (C2-C1-O1-C4) of monomers connected to GA is shown in Figure 11 (b). As long as the GA molecules posses high conformational freedom, the monomers
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connected to GA have freedom to exhibit the conformational changes. But in the vicinity of
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HAP, the conformation freedom gets arrested and it corresponds to region ‘A’ in Figure 11 (b).
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As the chains slide over the HAP, the GA molecules are completely stretched. The GA molecules become stiffer, thereby reducing the conformational freedom available for the
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connected monomers as shown in Figure 11 (a). Though, the monomer connected to GA is arrested, the nearby monomers are free to rotate. This is due to the restriction from HAP
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dominated by the GA molecules, which corresponds to region B in Figure. 11 (b).
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4. Radial Distribution Function
Radial Distribution Function (RDF) gives the probability of finding a particle at a distance ‘r’ from the reference particle. The observed variation in dihedral conformation and internal structural variables are the results of the dynamics of non bonded interactions like hydrogen bonding, electrostatic interactions and νan der Waal's interaction.
The existence of these
interactions is confirmed in a system by plotting RDF between pairs of atoms. The presence of amine group and hydroxyl groups present in chitosan are the potential reactive sites for the formation of hydrogen bonds as previously reported in the literature. Similarly, Ca2+ and OH- are the reactive sites available for interaction in the HAP crystal. During the deformation process, the RDF is determined between different pairs of atoms in a CS/HAP system at 5% strain as shown in Figure 12. It is observed that the position of the peak (1.785 Å) from Figure 12(a) is greater than the equilibrium bond length (1.04 Å) between
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ACCEPTED MANUSCRIPT nitrogen and hydrogen. Therefore, it confirms the existence of hydrogen bonds between N in amine group (CS) and H in OH group (CS). In all the cases, a prominent peak is observed in the
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range of 2 Å to 4 Å, indicating the formation of hydrogen bond within the chitosan chains. The HAP interacts with chitosan chains primarily through electrostatic interactions, van der
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Waals's interactions or hydrogen bond formation [33]. Electrostatic interactions are observed
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between Ca2+ in HAP & nitrogen in an amine group of chitosan (Figure 12(c)) and Ca2+ in HAP
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& oxygen in CH2OH of chitosan. The peaks observed beyond 5 Å in Figure 12(c) & 12(d)
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corresponds to long range interactions like van der Waal’s interactions [22].
5.1. CS/HAP nanocomposite
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5. Hydrogen bond analysis
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The existence of hydrogen bonds within chitosan chains and between chitosan/HAP is
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confirmed from the RDF plots. The analysis of hydrogen bond formation during the deformation process is performed using VMD [25]. The distance between hydrogen donor and acceptor is 3.5 Å and the angle cutoff between them is taken as 150°. A detailed analysis of evolution of hydrogen bonds is performed to determine the significant donor/acceptor pairs involved in load transfer. The evolution of hydrogen bonds for two donor/acceptor pairs (Figure 13) is discussed in the following sections. The hydrogen bonds are responsible for the strengthening of interface between chitosan matrix and HAP nanoparticles in addition to the electrostatic interactions between them. The increase in Young’s modulus with the addition of HAP content is because of an effective interface and the load transfer mechanism via the interface. The decrease in load carrying capability at larger strains is due to reduced number of hydrogen bonds as shown in Figure 14 (a). At larger strains, the orientation of chain towards the direction of pull is the reason for enhanced interactions
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ACCEPTED MANUSCRIPT between chitosan chains (as shown in Figure.14 (b)) rather than chitosan and HAP nanoparticles. The corresponding increase in hydrogen bonds within chitosan matrix does not assist in
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enhancing the load transfer. From the hydrogen bond analysis, it is observed that the influence of nanoparticle is dominating during the initial stages of deformation via hydrogen bond
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formation. These interactions are accompanied by electrostatic interactions as mentioned in RDF
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analysis. At later stages of deformation, interactions between chitosan and HAP nanoparticles is
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reduced which causes the drop in stress. 5.2. CS/GA system
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The chitosan system has reactive sites which are responsible for the formation of hydrogen bonds. Amine group is one of the major reactive sites which are capable of forming hydrogen
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bond with other groups present in the system. During the cross-linking process, most of the
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hydrogen atoms present in amine group are removed and nitrogen forms imine bond with the
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GA. The number of hydrogen bonds present in the cross-linked system due to amine group over the deformation process is very low compared to uncross-linked system as shown in Figure 15 (a).
Though the number of hydrogen bond present due to amine group decreases, the presence of GA enhances the mechanical properties of the cross-linked system. The oxygen (not participating in cross-linking process) present in GA molecule forms hydrogen bond with OH group of chitosan, the evolution of which over strain is shown in Figure 15 (b). So, in the crosslinked system the number of hydrogen bonds are more compared to that of an uncross-linked system due to the presence of GA molecules. Thus, hydrogen bond formation also contributes to the mechanical properties in cross-linked system.
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ACCEPTED MANUSCRIPT 6. CONCLUSION In summary, we have evaluated the mechanical properties of CS/HAP and cross-linked
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chitosan system using uniaxial deformation process at 300 K upto 100% strain. We determine
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the mechanical properties of CS applying nanoindentation with and without the addition of HAP.
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Chitosan chains interact with HAP mainly through electrostatic interactions and hydrogen bond formation. At lower strain, the deformation behavior is primarily influenced by the presence of
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nanoparticles. At larger strain, the orientation of chitosan chains and their conformational
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behavior determines the mechanical properties. Also, the number of hydrogen bonds, which offers conformational restriction to chitosan chains decreases at larger deformation. As a result,
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the resistance to deformation decreases at the larger strain in the CS/HAP system. Lack of
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conformational freedom to the monomers connected to glutaraldehyde and formation of three-
system.
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dimensional network are also responsible for improved mechanical properties in cross-linked
As a result, the dihedral conformation of hydrogels is modified in the presence of nanoparticles and cross-linking agent. This signifies the relation between structural integrity of hydrogels and their mechanical properties. The fundamental mechanisms will be helpful in understanding the influence of nanoparticle and cross-linking agent on the deformation characteristics of chitosan at atomistic length scale.
ACKNOWLEDGMENT Authors would like to sincerely thank P.G. Senapathy Center for Computing Resources, IIT Madras for providing computational facilities.
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Figure captions
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Figure 1. (a) Chitosan reinforced with HAP (b) chitosan cross-linked with Glutaraldehyde (GA). (Cyan - Carbon; Red - Oxygen; White - Hydrogen; Blue - Nitrogen; Green - Calcium;
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Gold - Phosphorous).
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Figure 2. Stress strain curve for (a) chitosan, chitosan nanocomposite (CS_HAP_10%) and crosslinked chitosan (CS_Cross), (b) chitosan nanocomposite with different percentage of
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HAP.
Figure 3. (a) Schematic representing end to end distance in one polymer chain (b) end to end
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distance of chitosan chains as a function of strain. Figure 4. (a) Schematic showing determination of chain orientation parameter (b) evolution of
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chain orientation parameter during deformation at 300K. Figure 5. The characteristics of cross-linkers (GA molecules) during deformation at (a) 0 % (b)
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50 % (c) 75 % and (d) 100 % strain. (Cyan - Carbon; Red - Oxygen; White - Hydrogen; Blue - Nitrogen).
Figure 6. Histogram representing chain orientation parameter for CS at (a) 0 % and (b) 100 % strain.
Figure 7. (a) Schematic showing different dihedral angles in chitosan molecule (b) dihedrals closer and farther away from HAP is monitored during the deformation process. (Cyan Carbon; Red - Oxygen; White - Hydrogen; Blue - Nitrogen; Green - Calcium; Yellow Phosphorous). Figure 8. The dihedral angle which is farther away from HAP with (a) maximum value and (b) minimum value. The dihedral angle in the proximity of HAP with (c) maximum value and (d) minimum value. (Cyan - Carbon; Red - Oxygen; White - Hydrogen; Blue Nitrogen; Green - Calcium; Gold - Phosphorous). Figure 9. Cross linked chitosan chains in the proximity of HAP surface.
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ACCEPTED MANUSCRIPT Figure 10. Load Displacement plot for uncross linked and cross-linked chitosan chains in the proximity of HAP obtained from single chain pull out test.
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Figure 11. The conformation of monomers when (a) GA molecule in fully extended state (b) variation of dihedral (phi) angle of monomer connected to GA.
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Figure 12. RDF plot for, (a) nitrogen in amine group (CS) and hydrogen in OH group (CS) (b)
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oxygen connecting monomers and hydrogen in OH group (CS) (c) calcium ion in HAP and nitrogen in amine group (d) oxygen in PO43- ion (HAP) and hydrogen in OH group
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(CS).
Figure 13. Schematic representation of possible hydrogen bonds within chitosan chains, between
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chitosan and HAP nanoparticles.
Figure 14. Hydrogen bond evolution over strain between (a) oxygen in PO43- of HAP as acceptor
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and oxygen as donor in OH group of chitosan for CS/HAP system with 10%, 20% and
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30% HAP (b) nitrogen in amine group of chitosan as donor and oxygen as acceptor in
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OH group of chitosan in a CS/HAP (30%) system. Figure 15. Hydrogen bond evolution over strain between (a) nitrogen in amine group and oxygen in OH group of CS (b) oxygen in GA and OH group of CS.
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ACCEPTED MANUSCRIPT Table 1 Young’s modulus (E) and maximum stress values obtained from simulation and Nanoindentation
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tests E (GPa)
Maximum Stress (MPa)
Chitosan(CS)
2.06±0.307
172.1±22.90
CS with 10% HAP
2.83±0.086
212.8±9.70
CS with 20% HAP
3.09±0.082
221.4±3.30
3.39±0.806
CS with 30% HAP
3.92±0.146
245.1±8.10
3.29±0.309
CS with 73% DOC
3.91±0.439
515.5±0.056
E (GPa) Nanoindentation 1.52±0.060 2.61±0.287
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Molecular dynamics is applied to perform uniaxial deformation tests on cross-linked and nanoparticle reinforced chitosan. Nanoindentation confirms the enhanced mechanical properties of modified chitosan system. Dihedral conformational variations are primarily responsible for altered mechanical characteristics. van der Waals interactions within the modified chitosan system determines the conformational variations. Single chain pull out study of cross-linked and uncross-linked chain reveals different mechanical response.
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