Rheological Modelling of Polymeric Systems for Foods: Experiments and Simulations P.H.S. Santos a, M.A. Carignano b, O.H. Campanella a a Department of Agricultural and Biological Engineering, Purdue University, 225 South University Street, West Lafayette, IN 47907, USA (psantos@purdue.edu;campa@purdue.edu) b Department of Biomedical Engineering and Chemistry of Life Processes Institute, Northwestern University, 245 Sheridan Rd., Evanston, IL 60208, USA (cari@northwestern.edu) ABSTRACT Many experimental studies have focused on the characterization of a number of polymeric systems involving macromolecules such as proteins and polysaccharides; however it is still a challenge to link macroscopic properties of materials with their structural conformation and types of linkages. The present paper presents a computational study of polymeric chains that form an entangled network by physical interactions. Using molecular dynamics simulations we investigate how the stiffness of the chains affects the formation of a percolated space-filling network. Experimental measurements were carried out using polymers with different persistence length (Xanthan Gum and Hydroxypropyl cellulose), i. e. with different stiffness, in order to determine their viscoelastic properties and to compare with theoretical results. Keywords: viscoelasticity; biopolymer; hydrocolloids; molecular dynamics; relaxation time. INTRODUCTION Macromolecules, such as proteins and polysaccharides, are commonly used as ingredients in several food product formulations. Their use has increased in the recent years and their applications in the food technology area can be considered countless. Their ability of building up viscosity and consequently changing the flow properties of systems containing water as solvent make them unique ingredients with distinct functional properties to provide desirable texture and sensorial characteristics[]. In the pharmaceutical and biological areas, hydrocolloids play an important role in microencapsulation of bioactive compounds[2] and in controlling drug delivery[3]. Therefore, knowing the relation between the individual components of these systems, the resulting microscopic structure and ultimately their rheological properties can determine their functional activity and better address their applications. Most foods contain one or more biopolymers. Since they are commonly used as thickener, emulsifier, stabilizer and gelling ingredients, knowing their rheology is of great importance in developing and designing food formulations. The rheological behaviour of these polymeric systems results from the combination of individual components with additional interaction effects[4]. All characteristics and properties of the solution or gel may depend on the nature of the solvent, nature and type of polymer, concentration, temperature, presence of ions and other minor components[5]. In addition, in oder to increase viscosity of water solutions, some of these macromolecules have the ability to self-organize and induce gelation, forming a 3D network with solid-like structure and elastic properties. Yoghurt and other dairy products are examples of colloidal food gels formed by protein aggregates when milk suspension is destabilized by the addition of lactic bacteria (slow acidification), enzymes or both[5]. Other polymeric molecules, such as polysaccharides, are also used as gelling agents in food product formulations. Starch, pectin, agar, carrageenans and others are key ingredients in gelled dessert and confectionary formulations[6]. Several works studied long chain polymers in foods; however most of them have only focused on experimental characterization. In addition to that, it is still a challenge to link macroscopic properties of materials with their structural conformation and types of linkages. Molecular modeling offers the opportunity to bridge this gap and allow the exploration of new applications for food polymeric systems. The
objective of the present work was to perform computational and experimental studies of polymeric chains that would form an entangled network with enhanced rheological properties caused by physical interactions among the chains. Using molecular dynamics simulations we investigate how the stiffness of the chains affects the formation of a percolated space-filling network. We also provide experimental rheological data for two polymeric solutions with different persistence length, which in practice describes the polymer flexibility. MATERIALS & METHODS Experimental Characterization To study how the stiffness of large chain molecules affects the rheology of polymeric systems, food grade Xantan Gum (XG) (Keltrol, CPKelco) and Hydroxypropyl cellulose (HPC) (Klucel HF Pharma, Hercules Inc) were used to prepare, 2 and (w/w) water solutions of these polymers. They both are high molecular weight polysaccharides (XG~ 2.5x0 6 [7], HPC~.5x0 6 [8]) with cellulosic backbones and build up viscosity at low concentrations in water. However, the persistence length of XG is 20nm whereas the persistence length of HPC is 5-0nm, which makes XG a much stiffer polymeric chain. The polymeric solutions were characterized by using a rotational AR-G2 Rheometer with Smart Swap TM Geometry (TA Instruments, Delaware, USA). A cone and plate geometry was used and all measurements were carried out at constant temperature of 25ºC. The viscoelastic properties of the solutions were determined by strain sweep, frequency sweep and step strain tests. Simulation Details Molecular dynamics (MD) simulations were performed to study the aggregation process of large polymeric chains. This simulation technique is based on the numerical integration of Newton s equation of motion. The force on each particle of the model polymer is calculated by adding bonding and non-bonding contributions. The polymer chains are modeled as a string of N beads, connected via a FENE potential. The chain flexibility is controlled by an angular harmonic potential acting on the angle defined by three neighboring beads: 0.5 () where θ 0 =80 defines the equilibirum conformation and k is the rigidity constant. Finally, the non bonded interaction is accounted for by a R-shifted Lennard-Jones potential. There are many variables in the problem: the length of the polymer chains (N), the range of the the non-bonded interactions, the polymer concentratin, temperature, and the chain's rigidity (k).. In the present work, only the effect of the angular potential, i.e. the stiffness of the polymer, was investigated. The simulations were performed in a cubic box with periodic boundary conditions. In all cases, N=400, and a system 64 polymer chains is simulated. RESULTS & DISCUSSION Experimental Characterization Small amplitude oscillatory shear (SAOS) tests were carried out to experimentally investigate the viscoelastic characteristics of HPC and Xanthan Gum solutions. The storage (G ) and loss (G ) moduli were determined for, 2 and (w/w) polymer concentrations. Figure presents the strain dependence of G and G at 25 C and frequency of Hz. For both polymers and for all concentrations the storage (G ) and loss (G ) moduli remained constant at most of strain amplitude applied. In addition, higher magnitudes were observed for higher polymer concentrations.
00 00 (Pa) 0 0. % 0 00 Strain (%) Strain (%) Figure Strain sweep tests at Hz and 25 C for, 2 and (w/w) HPC and Xanthan Gum systems. (Pa) 0 00 Frequency sweep tests were also carried out in the linear viscoelastic region applying % strain at a temperature of 25 C (Figure 2). Different behavior is observed for Xanthan Gum and HPC systems. For Xanthan Gum, independent on the concentration, the storage modulus G is higher than the loss modulus G. This indicates that this system may exhibit a solid-like behavior in the investigated frequency range. In addition, it also shows that both storage and loss moduli are not significantly affected by frequency. On the other hand, HPC solutions did exhibit a typical behavior of viscoelastic liquids, except for % HPC system. The loss modulus (G ) is the dominant response at low frequencies whereas the storage modulus becomes the dominant response as frequency increase. For % HPC solutions, G is the dominant response all over the frequency range. A typical behavior of viscoelastic liquid for HPC solutions can also observed in Figure 3. The stress relaxation curves reach small values at short times. No effect of concentration is observed. In contrast, Xanthan Gum solutions seem to behave more like a viscoelastic solid. Typical viscoelastic solids exhibit residual stress when a step strain test is carried out. Among all parameters that influence the rheological behavior of these two biopolymer, chain flexibility could be also used to get a better understanding about how polymer properties affect the viscoelastic characteristics of solutions and gels. 0 0. % 00 00 (Pa) 0 % (Pa) 0 % 0. 0. 0.0 0. 0 Frequency (Hz) 0.0 0. 0 Frequency (Hz) Figure 2 Frequency sweep tests at % strain and 25 C for, 2 and (w/w) HPC and Xanthan Gum systems.
00 00 0 0 Stress (Pa) 0. 0.0 % HPC HPC Stress (Pa) 0. 0.0 % XG XG E-3 E-3 E-4 0 50 00 50 200 250 E-4 0 50 00 50 200 250 time (s) time (s) Figure 3 Relaxation test experiments at large strain (50%) and 25 C for and (w/w) HPC and Xanthan Gum systems. Simulations To study the effect of the angular potential, i.e. the stiffness of the polymer, on the formation of a space filling network, two systems with different rigidity constants (k=0 and k=00) were used. The lowest the constant, the more flexible the chain will be. Conversely, higher constant values provide very stiff polymeric chains. Figure 4 shows a snapshot of the two entangled networks formed by systems with different angular potential. Figure 5 Snapshot of simulated polymeric systems with different angular potential 0 and 00. As can be observed in Figure 5, the network formed by the long chains seems to be affected by the angular potential of the chains. Flexible polymers formed a more entangled network with larger porous (Figure 5a). It is still not clear how the parameters affect the formation of this percolated network. To further investigate how this different networks influence the rheology of the systems, simulated frequency sweep tests were performed. Small amplitude oscillatory shear strain (SAOS) were applied to the simulation box producing a shear stress wave of the same frequency, but not necessarily in phase. Knowing the response of the material (stress) and the phase difference between stress and strain waves, the storage (G ) and loss (G ) muduli can
be calculated. Figure 6 illustrates how the simulation is performed and how the properties are calculated. This methodology was previously used to calculate the rheological properties of transient colloidal gels[9] and gels with irreversible bonds[0] ]. Preliminary simulated results are depicted in Figure 7 and similar trends were observed by comparing them to the experimental data. The system formed by stiff chains was not much affected by frequency as the soft chains network. The phase angle of the stiff polymeric system at the two frequencies is very small, showing the solid-like behavior of it even at the lower frequency. On the other hand, greater frequency dependence was observed for the soft chain network, which is in agreement with the experimental measurements for HPC solutions. strain stress Figure 6 Schematic of application of small amplitude oscillatory shear strain to the simulation box. Simulated sinusoidal strain applied to the box and shear stress response. Figure 7 - Simulated oscillatory strain (black dash) and stress response (red line) for the two simulated systems (k=0 and k=00). The two plots on the top show the obtained data for the soft chains (k=0) and the two at the bottom refer to the stiff chains (k=00). High (right plots) and low (left plots) frequencies were applied to the simulated box to investigate their frequency dependence.
CONCLUSION The rheological properties of Xanthan Gum and HPC water solutions were determined for, 2 and polymer concentrations. Strain sweep, frequency sweep and stress relaxation tests were experimentally performed. The results showed a different behaviour for these two biopolymers. Among the parameters that affect the rheology of them, the polymer chain stiffness could be playing an important role. A first attempt to get a better understanding about how this parameter can influence the macroproperties of polymeric solutions or gels was made by using molecular dynamics simulations. Preliminary results show that the angular potential does affect the structure of the network formed and the viscoelastic properties of the resulting system. Similar trends were observed by experimental and simulated data, showing that Molecular Dynamics simulations can be a useful tool to gain a better understanding on the interactions of macromolecules that result in the mechanical properties of complex foods such as gels. ACKNOWLEDGEMENTS This work was supported by the U.S. Army Research Office under the Multi-University Research Initiative (MURI) grant number W9NF-08--07. REFERENCES. Foegeding, E.A. 2007. Rheology and sensory texture of biopolymer gels. Current Opinion in Colloid & Interface Science. 2(4-5): p. 242-250. 2. Borgogna, M., et al. 200. Food microencapsulation of bioactive compounds: Rheological and thermal characterisation of non-conventional gelling system. Food Chemistry. 22(2): p. 46-423. 3. Wua, W., et al. 200. Chitosan-based responsive hybrid nanogels for integration of optical phsensing, tumor cell imaging and controlled drug delivery. Biomaterials. 3(32): p. 837-838. 4. Fischer, P., et al. 2009. Rheological approaches to food systems. Comptes Rendus Physique. 0(8): p. 740-750. 5. Mezzenga, R., et al. 2005. Understanding foods as soft materials. Nature Materials. 4(0): p. 729-740. 6. Burey, P., et al. 2009. Confectionery Gels: A Review on Formulation, Rheological and Structural Aspects. International Journal of Food Properties. 2(): p. 76-20. 7. Nussinovitch, A. 997. Hydrocolloid applications: gum technology in the food and other industries. London: Chapman & Hall. 8. Hercules Incorporated. 200. KLUCEL Hydroxypropylcellulose:Physical and Chemical Properties. Technical Information. 9. Santos, P.H.S., Campanella, O.H.; Carignano, M.A. 200. Brownian Dynamics Study of Gel- Forming Colloidal Particles. Journal of Physical Chemistry B, 200. 4(4): p. 3052-3058. 0. Whittle, M. & Dickinson E. 997. Brownian dynamics simulation of gelation in soft sphere systems with irreversible bond formation. Molecular Physics. 90(5): p. 739-757.