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Bhardwaj S, Kumar A. Analytical Model to Deduce the Conformational and Dynamical Behavior in Dendrimers: A Review. Polymers (Basel) 2024; 16:1918. [PMID: 39000773 PMCID: PMC11244006 DOI: 10.3390/polym16131918] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2024] [Revised: 06/27/2024] [Accepted: 07/01/2024] [Indexed: 07/17/2024] Open
Abstract
This review utilizes an optimized Rouse-Zimm discrete hydrodynamic model and the preaveraged Oseen tensor, which accurately consider hydrodynamic interactions to study model dendrimers. We report the analytical theories that have been previously developed for the creation of generalized analytical models for dendrimers. These generalized theories were used to assess the conformational and dynamical behavior of the dendrimers. By including stiffness in the bonds, the neglect of excluded volume interactions may be somewhat offset. This is true at least in the case of short spacers. While the topological limitations on the directions and orientations of the individual bond vectors in dendrimers implement semiflexibility, the intensity of these contacts was determined by the potential geometric orientations of the bonds, and later on the excluded volume interactions in dendrimers, which were described in terms of the effective co-volume between nearest non-bonded monomers and modeled using the delta function pseudopotential. With the aid of the models developed, the authors condensed various conformational and dynamic properties of dendrimers that depend on their degree of semiflexibility and the strength of the excluded volume. These analyses came to the conclusion that the flexible dendrimer in one limit and the earlier described freely rotating model of dendrimers in the other constitute a highly generalized way of capturing a wide range of conformations in the developed mathematical model in dendrimers.
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Affiliation(s)
| | - Amit Kumar
- Theory & Simulation Laboratory, Department of Chemistry, Jamia Millia Islamia (A Central University), New Delhi 110025, India
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2
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Polanowski P, Hałagan K, Sikorski A. Star Polymers vs. Dendrimers: Studies of the Synthesis Based on Computer Simulations. Polymers (Basel) 2022; 14:polym14132522. [PMID: 35808567 PMCID: PMC9269100 DOI: 10.3390/polym14132522] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Revised: 06/18/2022] [Accepted: 06/19/2022] [Indexed: 01/24/2023] Open
Abstract
A generic model was developed for studies of the polymerization process of regular branched macromolecules. Monte Carlo simulations were performed employing the Dynamic Lattice Liquid algorithm to study this process. A core-first methodology was used in a living polymerization of stars with up to 32 arms, and dendrimers consisted of 4-functional segments. The kinetics of the synthesis process for stars with different numbers of branches and dendrimers was compared. The size and structure of star-branched polymers and dendrimers during the synthesis were studied. The influence of the functionality of well-defined cores on the structure and on the dispersity of the system was also examined. The differences in the kinetics in the formation of both architectures, as well as changes to their structures, were described and discussed.
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Affiliation(s)
- Piotr Polanowski
- Department of Molecular Physics, Lodz University of Technology, 90-924 Lodz, Poland; (P.P.); (K.H.)
| | - Krzysztof Hałagan
- Department of Molecular Physics, Lodz University of Technology, 90-924 Lodz, Poland; (P.P.); (K.H.)
| | - Andrzej Sikorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
- Correspondence:
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3
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Affiliation(s)
- Manisha Handa
- Department of Chemistry, University of Delhi, Delhi-110007, India
| | - Parbati Biswas
- Department of Chemistry, University of Delhi, Delhi-110007, India
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4
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Neha, Kant R. Static Structure Factor and Viscoelastic Properties of Dendrimer Grafted Nanoparticles in Solution. J Phys Chem B 2021; 125:1951-1959. [PMID: 33566606 DOI: 10.1021/acs.jpcb.0c10458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The theory for the dynamics of multiscale branched polymeric structures is applied to understand the dendrimer-grafted nanoparticles in a dilute solution. The multiscale nature of dendrimer-grafted nanoparticles arises due to larger beads for the nanoparticles and the smaller beads for the polymeric structure connected through the harmonic springs. The multiscale generalized Gaussian structure approach allows us to study several viscoelastic properties: (i) storage and loss moduli and (ii) intrinsic viscosity. The influence of nanoparticles in the dendrimer structure is reflected in low and intermediate frequency regimes of the viscoelastic relaxation moduli. The increase in the size and the number fraction of nanoparticle shows an anomalous enhancement in the relaxation moduli. The increase in number fraction of nanoparticle in dendrimer-grafted nanoparticles decreases the transition frequency between solid- and liquid-like viscoelastic region. The intrinsic viscosity of dendrimer-grafted nanoparticles increases with increasing the size of nanoparticle. The inclusion of hydrodynamic interactions facilitates the dynamics of dendrimer-grafted nanoparticles. The Kratky plot of the static structure factor of all conformation of dendrimer-grafted nanoparticles is also analyzed as a function of number fraction and the size of the nanoparticles. At low wavenumbers, all conformations of dendrimer-grafted nanoparticles show a universal behavior. The compactness of dendrimer-grafted nanoparticles increases with the increase in number fraction and the size of the nanoparticles.
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Affiliation(s)
- Neha
- Complex Systems Group, Department of Chemistry, University of Delhi, Delhi 110007, India
| | - Rama Kant
- Complex Systems Group, Department of Chemistry, University of Delhi, Delhi 110007, India
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5
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Gupta S, Biswas P. Conformations of poly(propylene imine) dendrimers in an ionic liquid at different pH. SOFT MATTER 2020; 16:8400-8411. [PMID: 32808623 DOI: 10.1039/d0sm01026j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The conformational behavior of poly(propylene imine) (PPI) dendrimers at three different solution pH is studied in an ionic liquid (IL) solvent, 1-butyl-3-methylimidazolium chloride ([BMIM]Cl), through molecular dynamics (MD) simulations. The size, shape, density distribution, structure factor, and the scattering intensity are evaluated to probe the conformational transition of dendrimers as a function of pH. The results of the radial atomic and terminal amine group density distribution at low pH indicate a shift in the density towards the periphery of the dendrimers due to the electrostatic repulsion between the charged tertiary amine groups within the dendrimers. The [BMIM] cations are not encapsulated within dendrimers and predominantly reside near the periphery. The extensive back-folding of the outer branches due to the electrostatic repulsion between the solvent cations and the peripheral charged amine groups at neutral and low pH results in a dense compact structure in [BMIM]Cl as compared to that in water, as evident from the results of the structure factor and scattering intensity. The structural analysis in terms of the fractal dimension reveals that the lower generation dendrimers exhibit conformational transition as a function of pH, while the higher generations exhibit a highly compact structure at all solution pH. However, PPI dendrimers at low pH exhibit more free volume as compared to that at high pH, which may be utilized to accommodate specific guest molecules.
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Affiliation(s)
- Shilpa Gupta
- Department of Chemistry, University of Delhi, Delhi-110007, India.
| | - Parbati Biswas
- Department of Chemistry, University of Delhi, Delhi-110007, India.
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6
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Ganazzoli F, Raffaini G. Dendrimer Dynamics: A Review of Analytical Theories and Molecular Simulation Methods. Polymers (Basel) 2020; 12:polym12061387. [PMID: 32575767 PMCID: PMC7361973 DOI: 10.3390/polym12061387] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Revised: 06/06/2020] [Accepted: 06/12/2020] [Indexed: 11/16/2022] Open
Abstract
The theoretical study of dendrimers is reviewed, considering both analytical approaches and molecular simulation methods. We discuss the effect of molecular symmetry on the degeneracy of the relaxation times, and then the calculation of observable quantities, in particular the intrinsic viscosity, and then the viscoelastic complex modulus and the dynamic structure factor, in comparison with the available experimental data. In particular, the maximum intrinsic viscosity with increasing molar mass is analyzed in some detail. The approximations and/or assumptions of the adopted methods are also described in connection with analogous results for polymer of a different topology, in particular linear and star polymers.
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7
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Handa M, Biswas P. Orientational relaxation of ring polymers in dilute solutions. SOFT MATTER 2019; 15:5896-5907. [PMID: 31271404 DOI: 10.1039/c9sm00640k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The segmental relaxation dynamics of ring polymers in dilute solutions is investigated via optimized Rouse-Zimm theory. To the best of our knowledge, this is the first study that characterizes the orientational relaxation dynamics of ring polymers in dilute solutions. The orientational time autocorrelation functions are governed by two major processes that span a broad range of timescales: (i) local segmental motion at short times, independent of the ring size, and (ii) overall motion of the ring at long times that depends on the limiting ring size. Smaller rings relax faster than larger rings and their respective linear analogues. The hydrodynamic interactions decrease the higher relaxation rates corresponding to the local relaxation modes and increase the smaller relaxation rates which correspond to the collective relaxation modes. The spectral density is independent of frequency in the low frequency regime while it decreases with increasing frequency. Regardless of the ring size, the spin-lattice relaxation rate exhibits a single characteristic maximum as a function of frequency that shifts to a lower value with increasing strength of hydrodynamic interactions.
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Affiliation(s)
- Manisha Handa
- Department of Chemistry, University of Delhi, Delhi-110007, India.
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8
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Gupta S, Biswas P. Effect of pH on Size and Internal Structure of Poly(propylene imine) Dendrimers: A Molecular Dynamics Simulation Study. J Phys Chem B 2018; 122:9250-9263. [PMID: 30199254 DOI: 10.1021/acs.jpcb.8b04653] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
The behavior of poly(propylene imine) dendrimers at three different solution pH is investigated through molecular dynamics (MD) simulations in explicit solvent. MD simulations provide an insight into the conformational properties of dendrimers via the evaluation of their size, shape, radial density distribution, static structure factor, and scattering intensity. The size of the dendrimer increases from high solution pH to low pH. The internal structure of the dendrimer is quantified in terms of the radial atomic density profile and the terminal amine group density distribution. While the radial atomic density distribution shifts away from the core of the dendrimer with decreasing pH, a significant degree of back-folding of the outer generations is observed at high pH for higher generations of growth. Results from the structure factor and scattering intensity indicate two types of conformational transitions: (i) as a function of the solution pH, where the dendrimer evolves from an expanded structure at low pH to a highly compact one at high pH (except for higher generations), and (ii) with increasing generations, where the open structure of the dendrimer at lower generations transforms to a compact structure at higher generations at both high and low pH, characterized by a change in the fractal dimension.
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Affiliation(s)
- Shilpa Gupta
- Department of Chemistry , University of Delhi , Delhi 110007 , India
| | - Parbati Biswas
- Department of Chemistry , University of Delhi , Delhi 110007 , India
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9
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Jurjiu A, Galiceanu M. Dynamics of a Polymer Network Modeled by a Fractal Cactus. Polymers (Basel) 2018; 10:E787. [PMID: 30960712 PMCID: PMC6403701 DOI: 10.3390/polym10070787] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2018] [Revised: 07/14/2018] [Accepted: 07/16/2018] [Indexed: 01/16/2023] Open
Abstract
In this paper, we focus on the relaxation dynamics of a polymer network modeled by a fractal cactus. We perform our study in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. By performing real-space renormalization transformations, we determine analytically the whole eigenvalue spectrum of the connectivity matrix, thereby rendering possible the analysis of the Rouse-dynamics at very large generations of the structure. The evaluation of the structural and dynamical properties of the fractal network in the Rouse type-approach reveals that they obey scaling and the dynamics is governed by the value of spectral dimension. In the Zimm-type approach, the relaxation quantities show a strong dependence on the strength of the hydrodynamic interaction. For low and medium hydrodynamic interactions, the relaxation quantities do not obey power law behavior, while for slightly larger interactions they do. Under strong hydrodynamic interactions, the storage modulus does not follow power law behavior and the average displacement of the monomer is very low. Remarkably, the theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results from the literature.
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Affiliation(s)
- Aurel Jurjiu
- National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj-Napoca 400293, Romania.
- Faculty of Physics, Babes-Bolyai University, Street Mihail Kogalniceanu 1, Cluj-Napoca 400084, Romania.
| | - Mircea Galiceanu
- Department of Physics, Federal University of Amazonas, Manaus 69077-000, Brazil.
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10
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Jurjiu A, Turcu F, Galiceanu M. Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer. Polymers (Basel) 2018; 10:E164. [PMID: 30966200 PMCID: PMC6415159 DOI: 10.3390/polym10020164] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2017] [Revised: 02/04/2018] [Accepted: 02/06/2018] [Indexed: 01/12/2023] Open
Abstract
In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model. We develop a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multilayer network can be determined iteratively, thereby rendering possible the analysis of the dynamics of networks consisting of a large number of layers. This fact allows us to study in detail the crossover from layer-like behavior to chain-like behavior. Remarkably, we highlight the existence of two bulk-like behaviors. The theoretical findings with respect to the decomposition of the intermediate domain of the relaxation quantities, as well as the chain-like behavior, are well supported by experimental results.
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Affiliation(s)
- Aurel Jurjiu
- Faculty of Physics, Babes-Bolyai University, Street Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania.
| | - Flaviu Turcu
- Faculty of Physics, Babes-Bolyai University, Street Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania.
| | - Mircea Galiceanu
- Department of Physics, Federal University of Amazonas, 69077-000 Manaus, Brazil.
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11
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Liu G, Feng X, Lang K, Zhang R, Guo D, Yang S, Cheng SZD. Dynamics of Shape-Persistent Giant Molecules: Zimm-like Melt, Elastic Plateau, and Cooperative Glass-like. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01058] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- GengXin Liu
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
| | - Xueyan Feng
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
| | - Kening Lang
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
| | - Ruimeng Zhang
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
| | - Dong Guo
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
| | - Shuguang Yang
- Center
for Advanced Low-Dimension Materials, Donghua University, Shanghai 201620, China
| | - Stephen Z. D. Cheng
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
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12
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Jurjiu A, Biter TL, Turcu F. Dynamics of a Polymer Network Based on Dual Sierpinski Gasket and Dendrimer: A Theoretical Approach. Polymers (Basel) 2017; 9:E245. [PMID: 30970922 PMCID: PMC6432022 DOI: 10.3390/polym9070245] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2017] [Revised: 06/17/2017] [Accepted: 06/21/2017] [Indexed: 11/16/2022] Open
Abstract
In this paper we focus on the relaxation dynamics of a multihierarchical polymer network built through the replication of the dual Sierpinski gasket in the form of a regular dendrimer. The relaxation dynamics of this multihierarchical structure is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, we show a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multihierarchical structure can be determined iteratively, thereby rendering possible the analysis of the Rouse-dynamics at very large generations. Remarkably, the general picture that emerges from both approaches, even though we have a mixed growth algorithm and the monomers interactions are taken into account specifically to the adopted approach, is that the multihierarchical structure preserves the individual relaxation behaviors of its constituent components. The theoretical findings with respect to the splitting of the intermediate domain of the relaxation quantities are well supported by experimental results.
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Affiliation(s)
- Aurel Jurjiu
- Faculty of Physics, Babes-Bolyai University, Street Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania.
| | - Teodor-Lucian Biter
- Faculty of Physics, Babes-Bolyai University, Street Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania.
| | - Flaviu Turcu
- Faculty of Physics, Babes-Bolyai University, Street Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania.
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13
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Yang Y, Qiu F, Zhang H, Yang Y. The Rouse Dynamic Properties of Dendritic Chains: A Graph Theoretical Method. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00040] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yingzi Yang
- The State Key Laboratory
of Molecular Engineering of Polymers, Department of Macromolecular
Science, Fudan University, Shanghai 200433, China
| | - Feng Qiu
- The State Key Laboratory
of Molecular Engineering of Polymers, Department of Macromolecular
Science, Fudan University, Shanghai 200433, China
| | - Hongdong Zhang
- The State Key Laboratory
of Molecular Engineering of Polymers, Department of Macromolecular
Science, Fudan University, Shanghai 200433, China
| | - Yuliang Yang
- The State Key Laboratory
of Molecular Engineering of Polymers, Department of Macromolecular
Science, Fudan University, Shanghai 200433, China
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14
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Katyal D, Kant R. Dynamics of Branched Polymers in Random Layered Flows with Intramolecular Hydrodynamic Coupling: Star and Dendrimer. MACROMOL THEOR SIMUL 2017. [DOI: 10.1002/mats.201700009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Divya Katyal
- Complex Systems Group; Department of Chemistry; University of Delhi; Delhi 110007 India
| | - Rama Kant
- Complex Systems Group; Department of Chemistry; University of Delhi; Delhi 110007 India
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15
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Mielke J, Dolgushev M. Relaxation Dynamics of Semiflexible Fractal Macromolecules. Polymers (Basel) 2016; 8:polym8070263. [PMID: 30974539 PMCID: PMC6432473 DOI: 10.3390/polym8070263] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2016] [Revised: 06/28/2016] [Accepted: 07/01/2016] [Indexed: 11/21/2022] Open
Abstract
We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.
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Affiliation(s)
- Jonas Mielke
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
| | - Maxim Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
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16
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Abstract
The internally functionalized dendrimers are novel polymers that differ from conventional dendrimers by having additional functional units which do not branch out further. We investigate the dynamics of these structures with the inclusion of local semiflexibility and analyze their eigenmodes. The functionalized units clearly manifest themselves leading to a group of eigenvalues which are not present for homogeneous dendrimers. This part of the spectrum reveals itself in the local relaxation, leading to a corresponding process in the imaginary part of the complex dielectric susceptibility.
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Affiliation(s)
- Jonas Grimm
- Institute of Physics, University of Freiburg, Hermann-Herder-Str.3, D-79104 Freiburg, Germany.
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17
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Wawrzyńska E, Sikorski A, Zifferer G. Monte Carlo Simulation Studies of Regular and Irregular Dendritic Polymers. MACROMOL THEOR SIMUL 2015. [DOI: 10.1002/mats.201500036] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Edyta Wawrzyńska
- Department of Physical Chemistry; University of Vienna; Währinger Str. 42 A-1090 Vienna Austria
- Faculty of Chemistry; Warsaw University of Technology; Noakowskiego 3 00-664 Warsaw Poland
- Faculty of Chemistry; University of Warsaw; Pasteura 1 02-093 Warsaw Poland
| | - Andrzej Sikorski
- Faculty of Chemistry; University of Warsaw; Pasteura 1 02-093 Warsaw Poland
| | - Gerhard Zifferer
- Department of Physical Chemistry; University of Vienna; Währinger Str. 42 A-1090 Vienna Austria
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18
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Rai GJ, Kumar A, Biswas P. Effect of excluded volume on the rheology and transport dynamics of randomly hyperbranched polymers. J Chem Phys 2015; 142:174906. [DOI: 10.1063/1.4919643] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gobind Ji Rai
- Department of Chemistry, University of Delhi, Delhi 110007, India
| | - Amit Kumar
- Department of Chemistry, University of Delhi, Delhi 110007, India
| | - Parbati Biswas
- Department of Chemistry, University of Delhi, Delhi 110007, India
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19
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Katyal D, Kant R. Dynamics of generalized Gaussian polymeric structures in random layered flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042602. [PMID: 25974520 DOI: 10.1103/physreve.91.042602] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2014] [Indexed: 06/04/2023]
Abstract
We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α. Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α, the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.
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Affiliation(s)
- Divya Katyal
- Department of Chemistry, University of Delhi, Delhi 110007, India
| | - Rama Kant
- Department of Chemistry, University of Delhi, Delhi 110007, India
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20
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Fürstenberg F, Gurtovenko AA, Dolgushev M, Blumen A. Molecular Dynamics Simulations of Hyperbranched PAMAM Vicsek Fractals. MACROMOL THEOR SIMUL 2014. [DOI: 10.1002/mats.201400063] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Florian Fürstenberg
- Theoretical Polymer Physics; University of Freiburg; Hermann-Herder-Str. 3 D-79104 Freiburg Germany
| | - Andrey A. Gurtovenko
- Institute of Macromolecular Compounds; Russian Academy of Sciences; Bolshoi pr. V.O. 31 St.Petersburg 199004 Russia
- Faculty of Physics; St.Petersburg State University; Ul'yanovskaya ul. 1 Petrodvorets St.Petersburg 198504 Russia
| | - Maxim Dolgushev
- Theoretical Polymer Physics; University of Freiburg; Hermann-Herder-Str. 3 D-79104 Freiburg Germany
| | - Alexander Blumen
- Theoretical Polymer Physics; University of Freiburg; Hermann-Herder-Str. 3 D-79104 Freiburg Germany
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21
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Galiceanu M, Reis AS, Dolgushev M. Dynamics of semiflexible scale-free polymer networks. J Chem Phys 2014; 141:144902. [DOI: 10.1063/1.4897563] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Jurjiu A, Dockhorn R, Mironova O, Sommer JU. Two universality classes for random hyperbranched polymers. SOFT MATTER 2014; 10:4935-4946. [PMID: 24882064 DOI: 10.1039/c4sm00711e] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We grow AB2 random hyperbranched polymer structures in different ways and using different simulation methods. In particular we use a method of ad hoc construction of the connectivity matrix and the bond fluctuation model on a 3D lattice. We show that hyperbranched polymers split into two universality classes depending on the growth process. For a "slow growth" (SG) process where monomers are added sequentially to an existing molecule which strictly avoids cluster-cluster aggregation the resulting structures share all characteristic features with regular dendrimers. For a "quick growth" (QG) process which allows for cluster-cluster aggregation we obtain structures which can be identified as random fractals. Without excluded volume interactions the SG model displays a logarithmic growth of the radius of gyration with respect to the degree of polymerization while the QG model displays a power law behavior with an exponent of 1/4. By analyzing the spectral properties of the connectivity matrix we confirm the behavior of dendritic structures for the SG model and the corresponding fractal properties in the QG case. A mean field model is developed which explains the extension of the hyperbranched polymers in an athermal solvent for both cases. While the radius of gyration of the QG model shows a power-law behavior with the exponent value close to 4/5, the corresponding result for the SG model is a mixed logarithmic-power-law behavior. These different behaviors are confirmed by simulations using the bond fluctuation model. Our studies indicate that random sequential growth according to our SG model can be an alternative to the synthesis of perfect dendrimers.
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Affiliation(s)
- A Jurjiu
- Leibniz Institut für Polymerforschung Dresden e.V., Hohe Strasse 6, D-01069, Dresden, Germany.
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Rai GJ, Kumar A, Biswas P. Intramolecular relaxation of flexible dendrimers with excluded volume. J Chem Phys 2014; 141:034902. [DOI: 10.1063/1.4890078] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wawrzyńska E, Eisenhaber S, Parzuchowski P, Sikorski A, Zifferer G. Monte Carlo Simulation Studies of the Size and Shape of Regular Three Generation Dendrimers. MACROMOL THEOR SIMUL 2014. [DOI: 10.1002/mats.201300159] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Edyta Wawrzyńska
- Department of Physical Chemistry; University of Vienna; Währinger Str. 42 A-1090 Vienna Austria
- Department of Chemistry; Warsaw University of Technology; Noakowskiego 3 00-664 Warsaw Poland
- Department of Chemistry; University of Warsaw; Pasteura 1 02-093 Warsaw Poland
| | - Stephan Eisenhaber
- Department of Physical Chemistry; University of Vienna; Währinger Str. 42 A-1090 Vienna Austria
| | - Paweł Parzuchowski
- Department of Chemistry; Warsaw University of Technology; Noakowskiego 3 00-664 Warsaw Poland
| | - Andrzej Sikorski
- Department of Chemistry; University of Warsaw; Pasteura 1 02-093 Warsaw Poland
| | - Gerhard Zifferer
- Department of Physical Chemistry; University of Vienna; Währinger Str. 42 A-1090 Vienna Austria
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25
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Galiceanu M. Hydrodynamic effects on scale-free polymer networks in external fields. J Chem Phys 2014; 140:034901. [DOI: 10.1063/1.4861218] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Kumar A, Biswas P. Orientational relaxation in semiflexible dendrimers. Phys Chem Chem Phys 2013; 15:20294-302. [PMID: 24169643 DOI: 10.1039/c3cp53864h] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The orientational relaxation dynamics of semiflexible dendrimers are theoretically calculated within the framework of optimized Rouse-Zimm formalism. Semiflexibility is modeled through appropriate restrictions in the direction and orientation of the respective bond vectors, while the hydrodynamic interactions are included via the preaveraged Oseen tensor. The time autocorrelation function M(i)(1)(t) and the second order orientational autocorrelation function P(i)(2)(t) are analyzed as a function of the branch-point functionality and the degree of semiflexibility. Our approach of calculating M(i)(1)(t) is completely different from that of the earlier studies (A. Perico and M. Guenza J. Chem. Phys., 1985, 83, 3103; J. Chem. Phys., 1986, 84, 510), where the expression of M(i)(1)(t) obtained from earlier studies does not demarcate the flexible dendrimers from the semiflexible ones. The component of global motion of the time autocorrelation function exhibits a strong dependence on both degree of semiflexibility and branch-point functionality, while the component of pulsation motion depends only on the degree of semiflexibility. But it is difficult to distinguish the difference in the extent of pulsation motion among the compressed (0 < φ < π/2) and expanded (π/2 < φ < π) conformations of semiflexible dendrimers. The qualitative behavior of P(i)(2)(t) obtained from our calculations closely matches with the expression for P(exact)(2)(t) in the earlier studies. Theoretically calculated spectral density, J(ω), is found to depend on the degree of semiflexibility and the branch-point functionality for the compressed and expanded conformations of semiflexible dendrimers as a function of frequency, especially in the high frequency regime, where J(ω) decays with frequency for both compressed and expanded conformations of semiflexible dendrimers. This decay of the spectral density occurs after displaying a cross-over behavior with the variation in the degree of semiflexibility in the intermediate frequency regime. The characteristic area increases with the increase in the semiflexibility parameter, where the expanded conformations of semiflexible dendrimers record the maximum characteristic area. For the compressed conformations the relative increment of this area is considerably lower than that of the expanded conformations of semiflexible dendrimers.
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Affiliation(s)
- Amit Kumar
- Department of Chemistry, University of Delhi, Delhi-110007, India.
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27
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Welch PM. The escape of a charged dendrimer from an oppositely charged planar surface. J Chem Phys 2013; 139:164906. [PMID: 24182078 DOI: 10.1063/1.4826575] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
Many of the envisioned applications of dendrimers revolve around placing these molecules at and removing them from charged interfaces. Herein, we provide a prescription for the conditions needed to release a charged dendrimer from an oppositely charged flat substrate. Identifying an effective segment step length that reflects the intramolecular repulsions due to excluded volume and electrostatics, as well as the dendrimer's branching, provides the essential concept leading to an analytical prediction for the boundary between captured and free molecules. We find that this effective step length obeys trends similar to those predicted for linear chains, but is modified by the dendrimer's connectivity. Moreover, the boundary predicted for the capture of linear chains holds for dendrimers once this effective step length is employed. Monte Carlo computer simulations of coarse-grained model dendrimers escaping from charged surfaces validate these findings. The simulations consider generations 2 through 6 with a range of lengths between the branch points, as well as a range of solution ionic strengths and surface charge densities.
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Affiliation(s)
- P M Welch
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545-0001, USA
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Li L, Lu Y, An L, Wu C. Experimental and theoretical studies of scaling of sizes and intrinsic viscosity of hyperbranched chains in good solvents. J Chem Phys 2013; 138:114908. [PMID: 23534663 DOI: 10.1063/1.4795577] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Using a set of hyperbranched polystyrenes with different overall molar masses but a uniform subchain length or a similar overall molar mass but different subchain lengths, we studied their sizes and hydrodynamic behaviors in toluene (a good solvent) at T = 25 °C by combining experimental (laser light scattering (LLS) and viscometry) and theoretical methods based on a partially permeable sphere model. Our results show that both the average radii of gyration (<R(g)>) and hydrodynamic radius (<R(h)>) are scaled to the weight-average molar mass (M(w)) as <R(g)> ~ <R(h)> ~ M(w)(γ)M(w,s) (φ), with γ = 0.47 ± 0.01 and φ = 0.10 ± 0.01; and their intrinsic viscosity ([η]) quantitatively follow the Mark-Houwink-Sakurada (MHS) equation as [η] = K(η)M(w)(ν)M(w,s)(μ) with K(η) = 2.26 × 10(-5), ν = 0.39 ± 0.01, and μ = 0.31 ± 0.01, revealing that these model chains with long subchains are indeed fractal objects. Further, our theoretical and experimental results broadly agree with each other besides a slight deviation from the MHS equation for short subchains, similar to dendrimers, presumably due to the multi-body hydrodynamic interaction. Moreover, we also find that the average viscometric radius (<R(η)>) determined from intrinsic viscosity is slightly smaller than <R(h)> measured in dynamic LLS and their ratio (<R(η)>/<R(h)>) roughly remains 0.95 ± 0.05, reflecting that linear polymer chains are more draining with a smaller <R(h)> than their hyperbranched counterparts for a given intrinsic viscosity. Our current study of the "defect-free" hyperbranched polymer chains offers a standard model for further theoretical investigation of hydrodynamic behaviors of hyperbranched polymers and other complicated architectures, in a remaining unexploited research field of polymer science.
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Affiliation(s)
- Lianwei Li
- Hefei National Laboratory for Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China.
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Kumar A, Rai GJ, Biswas P. Conformation and intramolecular relaxation dynamics of semiflexible randomly hyperbranched polymers. J Chem Phys 2013; 138:104902. [DOI: 10.1063/1.4794310] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Fürstenberg F, Dolgushev M, Blumen A. Dynamics of semiflexible regular hyperbranched polymers. J Chem Phys 2013; 138:034904. [DOI: 10.1063/1.4775584] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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31
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Galiceanu M. Relaxation dynamics of scale-free polymer networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041803. [PMID: 23214606 DOI: 10.1103/physreve.86.041803] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2012] [Revised: 09/10/2012] [Indexed: 06/01/2023]
Abstract
We focus on polymer networks with a scale-free topology. In the framework of generalized Gaussian structures, by making use of the eigenvalue spectrum of the connectivity matrix, we determined numerically the averaged monomer displacement under external forces and the mechanical relaxation moduli (storage and loss modulus). First, we monitor these physical quantities and additionally the eigenvalue spectrum for structures of different sizes, but with the same γ, which is a parameter that measures the connectivity of the structure. Second, we vary the parameter γ, and we keep constant the size of the structures. This allows us to study in detail the crossover behavior from a simple linear chain to a starlike structure. As expected we encounter a more chainlike behavior for high values of γ, while for small values of γ a more starlike behavior is observed. In the intermediate time (frequency) domain, we encounter regions of constant slope for some intermediate values of γ.
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Affiliation(s)
- M Galiceanu
- Departamento de Física, Universidade Federal do Amazonas, 69077-000 Manaus, Brazil.
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32
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Kumar A, Biswas P. Conformational transitions in semiflexible dendrimers induced by bond orientations. J Chem Phys 2012; 137:124903. [DOI: 10.1063/1.4754871] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Fürstenberg F, Dolgushev M, Blumen A. Analytical model for the dynamics of semiflexible dendritic polymers. J Chem Phys 2012; 136:154904. [PMID: 22519347 DOI: 10.1063/1.3703757] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Florian Fürstenberg
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany.
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34
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Dolgushev M, Berezovska G, Blumen A. Branched Semiflexible Polymers: Theoretical and Simulation Aspects. MACROMOL THEOR SIMUL 2011. [DOI: 10.1002/mats.201100049] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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36
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Kumar A, Biswas P. Intramolecular relaxation dynamics in semiflexible dendrimers. J Chem Phys 2011; 134:214901. [DOI: 10.1063/1.3598336] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amit Kumar
- Department of Chemistry, University of Delhi, Delhi-110007, India
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Affiliation(s)
- Jaroslaw T. Bosko
- Department of Chemical Engineering, Monash University, Melbourne, Victoria 3800, Australia
| | - J. Ravi Prakash
- Department of Chemical Engineering, Monash University, Melbourne, Victoria 3800, Australia
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38
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Affiliation(s)
- Amit Kumar
- Department of Chemistry, University of Delhi, Delhi-110007, India
| | - Parbati Biswas
- Department of Chemistry, University of Delhi, Delhi-110007, India
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39
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Dolgushev M, Blumen A. Dynamics of chains and dendrimers with heterogeneous semiflexibility. J Chem Phys 2010; 132:124905. [DOI: 10.1063/1.3366662] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Affiliation(s)
- R. J. Sadus
- Centre for Molecular Simulation, Swinburne University of Technology, PO Box 218, Hawthorn, Vic., 3122, Australia
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Dolgushev M, Blumen A. Dynamics of semiflexible treelike polymeric networks. J Chem Phys 2009; 131:044905. [DOI: 10.1063/1.3184797] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Affiliation(s)
- Maxim Dolgushev
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Alexander Blumen
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
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Esquivel R, Flores-Gallegos N, Carrera E, Dehesa J, Angulo J, Antolín J, Soriano-Correa C. Theoretic-information entropies analysis of nanostructures:ab initiostudy of PAMAM precursors and dendrimers G0 to G3. MOLECULAR SIMULATION 2009. [DOI: 10.1080/08927020902833087] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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44
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Bosko JT, Ravi Prakash J. Effect of molecular topology on the transport properties of dendrimers in dilute solution at Θ temperature: A Brownian dynamics study. J Chem Phys 2008; 128:034902. [DOI: 10.1063/1.2823034] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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Newkome GR, Shreiner CD. Poly(amidoamine), polypropylenimine, and related dendrimers and dendrons possessing different 1→2 branching motifs: An overview of the divergent procedures. POLYMER 2008. [DOI: 10.1016/j.polymer.2007.10.021] [Citation(s) in RCA: 313] [Impact Index Per Article: 19.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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47
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Konkolewicz D, Gilbert RG, Gray-Weale A. Randomly hyperbranched polymers. PHYSICAL REVIEW LETTERS 2007; 98:238301. [PMID: 17677941 DOI: 10.1103/physrevlett.98.238301] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2007] [Indexed: 05/16/2023]
Abstract
We describe a model for the structures of randomly hyperbranched polymers in solution, and find a logarithmic growth of radius with polymer mass. We include segmental overcrowding, which puts an upper limit on the density. The model is tested against simulations, against data on amylopectin, a major component of starch, on glycogen, and on polyglycerols. For samples of synthetic polyglycerol and glycogen, our model holds well for all the available data. The model reveals higher-level scaling structure in glycogen, related to the beta particles seen in electron microscopy.
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Rathgeber S, Monkenbusch M, Hedrick JL, Trollsås M, Gast AP. Starlike dendrimers in solutions: Structural properties and internal dynamics. J Chem Phys 2006; 125:204908. [PMID: 17144741 DOI: 10.1063/1.2364895] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We measured the shape and the internal dynamics of starlike dendrimers under good solvent conditions with small-angle neutron scattering and neutron spin-echo (NSE) spectroscopy, respectively. Architectural parameters such as the spacer length and generation were varied in a systematic manner. Structural changes occurring in the dendrimers as a function of these parameters are discussed, i.e., in terms of the fractal dimension and deviations of the radius of gyration from the Gaussian value. A first cumulant evaluation of the NSE spectra for each scattering vector q separately yields the length scale dependent relaxation rates. We observe a local minimum in the normalized relaxation rates Omega(q)q(3) on length scales corresponding to the overall dendrimer dimension. The dynamics is discussed within a Rouse-Zimm approach generalized to the case of starlike dendrimers of arbitrary geometry. The model allows an identification of the modes contributing to the relaxation of the dendrimer in the q and time range of the NSE experiment. The local minimum is due to collective breathing motions of (parts of) the dendrons relative to each other. Shape fluctuations are not observed.
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Affiliation(s)
- Silke Rathgeber
- Max-Planck Institut für Polymerforschung, Polymer Physik, D-55128 Mainz, Germany.
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Affiliation(s)
- Tong Zhou
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117576, Republic of Singapore
| | - Shing Bor Chen
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117576, Republic of Singapore
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Koslowski T, Jurjiu A, Blumen A. Models of Irregular Hyperbranched Polymers: Topological Disorder and Mechanical Response. MACROMOL THEOR SIMUL 2006. [DOI: 10.1002/mats.200600004] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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