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Budai L, Budai M, Fülöpné Pápay ZE, Vilimi Z, Antal I. Rheological Considerations of Pharmaceutical Formulations: Focus on Viscoelasticity. Gels 2023; 9:469. [PMID: 37367140 DOI: 10.3390/gels9060469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Revised: 05/26/2023] [Accepted: 06/01/2023] [Indexed: 06/28/2023] Open
Abstract
Controlling rheological properties offers the opportunity to gain insight into the physical characteristics, structure, stability and drug release rate of formulations. To better understand the physical properties of hydrogels, not only rotational but also oscillatory experiments should be performed. Viscoelastic properties, including elastic and viscous properties, are measured using oscillatory rheology. The gel strength and elasticity of hydrogels are of great importance for pharmaceutical development as the application of viscoelastic preparations has considerably expanded in recent decades. Viscosupplementation, ophthalmic surgery and tissue engineering are just a few examples from the wide range of possible applications of viscoelastic hydrogels. Hyaluronic acid, alginate, gellan gum, pectin and chitosan are remarkable representatives of gelling agents that attract great attention applied in biomedical fields. This review provides a brief summary of rheological properties, highlighting the viscoelasticity of hydrogels with great potential in biomedicine.
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Affiliation(s)
- Lívia Budai
- Department of Pharmaceutics, Semmelweis University, 1092 Budapest, Hungary
| | - Marianna Budai
- Department of Pharmaceutics, Semmelweis University, 1092 Budapest, Hungary
| | | | - Zsófia Vilimi
- Department of Pharmaceutics, Semmelweis University, 1092 Budapest, Hungary
| | - István Antal
- Department of Pharmaceutics, Semmelweis University, 1092 Budapest, Hungary
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Affiliation(s)
- Jiuling Wang
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Thomas C. O’Connor
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Gary S. Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Yitong Zheng
- Hongyi Honor School, Wuhan University, Wuhan, Hubei 430072, China
- Department of Physics, School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
| | - Michael Rubinstein
- Thomas Lord Department of Mechanical Engineering and Materials Science, Departments of Biomedical Engineering, Chemistry, and Physics, Duke University, Durham, North Carolina 27708, United States
| | - Ting Ge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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Affiliation(s)
- Li Xi
- Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada
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Abstract
We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G_{GSE}(t) emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G_{GSE}(t) approaches G(t) of the ring melt with no entanglement plateau.
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Affiliation(s)
- Ting Ge
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Michael Rubinstein
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
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Ozaki H, Indei T, Koga T, Narita T. Physical gelation of supramolecular hydrogels cross-linked by metal-ligand interactions: Dynamic light scattering and microrheological studies. POLYMER 2017; 128:363-72. [DOI: 10.1016/j.polymer.2017.01.077] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Affiliation(s)
- Tetsuharu Narita
- Laboratoire
PPMD-SIMM, UPMC-ESPCI ParisTech-CNRS, UMR7615, 10 rue Vauquelin, 75005 Paris, France
| | - Tsutomu Indei
- Department
of Chemical and Biological Engineering, and Center for Molecular Study
of Condensed Soft Matter, Illinois Institute of Technology, 3440 S.
Dearborn Street, Suite 150, Chicago, Illinois 60616, United States
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Karim M, Indei T, Schieber JD, Khare R. Determination of linear viscoelastic properties of an entangled polymer melt by probe rheology simulations. Phys Rev E 2016; 93:012501. [PMID: 26871112 DOI: 10.1103/physreve.93.012501] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Indexed: 11/07/2022]
Abstract
Particle rheology is used to extract the linear viscoelastic properties of an entangled polymer melt from molecular dynamics simulations. The motion of a stiff, approximately spherical particle is tracked in both passive and active modes. We demonstrate that the dynamic modulus of the melt can be extracted under certain limitations using this technique. As shown before for unentangled chains [Karim et al., Phys. Rev. E 86, 051501 (2012)PLEEE81539-375510.1103/PhysRevE.86.051501], the frequency range of applicability is substantially expanded when both particle and medium inertia are properly accounted for by using our inertial version of the generalized Stokes-Einstein relation (IGSER). The system used here introduces an entanglement length d_{T}, in addition to those length scales already relevant: monomer bead size d, probe size R, polymer radius of gyration R_{g}, simulation box size L, shear wave penetration length Δ, and wave period Λ. Previously, we demonstrated a number of restrictions necessary to obtain the relevant fluid properties: continuum approximation breaks down when d≳Λ; medium inertia is important and IGSER is required when R≳Λ; and the probe should not experience hydrodynamic interaction with its periodic images, L≳Δ. These restrictions are also observed here. A simple scaling argument for entangled polymers shows that the simulation box size must scale with polymer molecular weight as M_{w}^{3}. Continuum analysis requires the existence of an added mass to the probe particle from the entrained medium but was not observed in the earlier work for unentangled chains. We confirm here that this added mass is necessary only when the thickness L_{S} of the shell around the particle that contains the added mass, L_{S}>d. We also demonstrate that the IGSER can be used to predict particle displacement over a given timescale from knowledge of medium viscoelasticity; such ability will be of interest for designing nanoparticle-based drug delivery.
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Affiliation(s)
- Mir Karim
- Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, Texas 79409, USA
| | - Tsutomu Indei
- Center for Molecular Study of Condensed Soft Matter, and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616, USA
| | - Jay D Schieber
- Center for Molecular Study of Condensed Soft Matter, and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616, USA.,Department of Physics, Illinois Institute of Technology, 3101 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Street, Chicago, Illinois 60616, USA
| | - Rajesh Khare
- Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, Texas 79409, USA
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Kuhnhold A, Paul W. Active one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:042601. [PMID: 25974519 DOI: 10.1103/physreve.91.042601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Indexed: 06/04/2023]
Abstract
We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.
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Affiliation(s)
- A Kuhnhold
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
| | - W Paul
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
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Abstract
We have developed a fast simulation that generates a random walk of an isolated probe sphere in a generalized linear viscoelastic complex fluid over a highly extended dynamic range. We introduce a coupled harmonically bound Brownian particle (c-HBBP) model, in which the relaxation modes of the viscoelastic medium are treated as harmonic wells. These wells are coupled to the probe sphere and perform Brownian motion in bound harmonic potentials corresponding to the next-longer relaxation mode, according to the relaxation spectrum of the viscoelastic material. We implement this c-HBBP model by generating variable temporal step sizes that have a uniform distribution in logarithmic time. We create and analyze trajectories for several different viscoelastic complex fluids: a polymer system at its gel point, a dense emulsion system, a blend of two monodisperse polystyrene polymers for which the relaxation spectrum has been measured, and a model anisotropic soft system that shows dense emulsion-like and gel-point behaviors along two orthogonal directions. Except for unusual viscoelastic materials, such as the polymer system at its gel point, the generated trajectories are neither self-similar nor self-affine. The resulting mean square displacements predicted by the c-HBBP model are consistent with the single-particle generalized Stokes-Einstein relation of linear passive microrheology.
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Affiliation(s)
- Manas Khan
- Department of Physics and Astronomy, University of California-Los Angeles, Los Angeles, CA 90095, USA.
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Kuhnhold A, Paul W. Temperature dependent micro-rheology of a glass-forming polymer melt studied by molecular dynamics simulation. J Chem Phys 2014; 141:124907. [DOI: 10.1063/1.4896151] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kuhnhold A, Paul W. Passive one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:022602. [PMID: 25215751 DOI: 10.1103/physreve.90.022602] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Indexed: 06/03/2023]
Abstract
We present a molecular dynamics simulation study of the possibility of performing a microrheological analysis of a polymer melt by following the Brownian motion of a dispersed nanoparticle. We study the influence of the size of the nanoparticle, taken to be comparable to the radius of gyration of the chains, and of the strength of the interaction between the nanoparticle and the repeat units of the polymer chains. The influence of the presence of the nanoparticle on the melt mechanical behavior is analyzed, and the importance of effects of different levels of hydrodynamic analysis on the frequency-dependent dynamic shear modulus derived from the particle motion is worked out.
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Affiliation(s)
- A Kuhnhold
- Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, 06099 Halle (Saale), Germany
| | - W Paul
- Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, 06099 Halle (Saale), Germany
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