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Deyue Yan - One of the best experts on this subject based on the ideXlab platform.
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mean square Radius of Gyration and degree of branching of highly branched copolymers resulting from the copolymerization of ab2 with ab monomers
Macromolecular Theory and Simulations, 2004Co-Authors: Zhiping Zhou, Deyue YanAbstract:The evolution of the various structural units incorporated into hyperbranched polymers formed from the copolymerization of AB 2 and AB monomers has been derived by the kinetic scheme. The degree of branching was calculated with a new definition given in this work. The degree of branching monotonously increased with increasing A group conversion (x) and the maximum value could reach 2r/(I + r) 2 , where r is the initial fraction of AB 2 monomers in the total. Like the average degree of polymerization, the mean-square Radius of Gyration of the hyperbranched polymers increased moderately with A group conversion in the range x <0.9 and displayed an abrupt rise when the copolymerization neared completion. The characteristic ratio of the mean-square Radius of Gyration remained constant for the linear polymers. However, the hyperbranched polymers did not possess this character. In comparison with the linear polymerization, the weight average and z-avetage degree of polymerization increased due to the addition of the branched monomer units AB 2 and the mean-square Radius of Gyration decreased quickly for the products of copolymerization.
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Mean-square Radius of Gyration of polymer chains
Macromolecular Theory and Simulations, 1997Co-Authors: Zhiping Zhou, Deyue YanAbstract:The calculations of the mean-square Radius of Gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square Radius of Gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square Radius of Gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square Radius of Gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square Radius of Gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square Radius of Gyration on the molecular weight can be expressed by the general formula (S 2 ) = aM b , which was supported by a number of experimental measurements. A comparison of our expression for the mean-square Radius of Gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.
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Mean-square Radius of Gyration of polysiloxanes
Macromolecular Theory and Simulations, 1997Co-Authors: Zhiping Zhou, Deyue YanAbstract:The mean-square Radius of Gyration for polysiloxanes has been derived according to the exact definition. Taking account of the examples of symmetrically substituted poly(dimethylsiloxane) and unsymmetrically substituted poly(methylphenylsiloxane), we find that the dependence of 〈S2〉 on the molecular weight follows the general formula 〈S2〉 = aMb with b = 1 ± 0.016, which is analogous to the theoretical outcomes for vinyl or vinylidene polymers even though the skeletal bone of polysiloxanes consists of alternating heteroatoms. A numerical comparison of the rigorous expression of the mean-square Radius of Gyration given in this paper with that reported by Flory shows that the difference is obvious for low-molecular-weight polymer and it gradually declines with increasing degree of polymerization.
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Improved expression of the mean‐square Radius of Gyration, 2. Poly(1,1‐disubstituted ethylene)s
Macromolecular Theory and Simulations, 1995Co-Authors: Zhiping Zhou, Deyue YanAbstract:The mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every Cα was considered to be concentrated in their center of mass, and the virtual side bond vector runs from Cα to this center. The mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square Radius of Gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S2〉 = aMb, where a and b are constants characteristic of the polymer.
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improved expression of the mean square Radius of Gyration 2 poly 1 1 disubstituted ethylene s
Macromolecular Theory and Simulations, 1995Co-Authors: Zhiping Zhou, Deyue YanAbstract:The mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every Cα was considered to be concentrated in their center of mass, and the virtual side bond vector runs from Cα to this center. The mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square Radius of Gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S2〉 = aMb, where a and b are constants characteristic of the polymer.
Zhiping Zhou - One of the best experts on this subject based on the ideXlab platform.
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The Radius of Gyration of the Products of Hyperbranched Polymerization
Macromolecular Theory and Simulations, 2014Co-Authors: Zhiping ZhouAbstract:The average mean-square radii of Gyration for the products of the linear polymerization, the star-shaped polymerization, and the hyperbranched polymerization of AB2-type monomer in the absence or presence of a multifunctional core initiator are investigated using the Dobson-Gordon's method. The dependence relationships between the average radii of Gyration and the average degree of polymerization calculated using the Dobson-Gordon's method for the linear polymerization products are in good agreement with those obtained from the matrix algebra method of the rotational isomeric state model. The radii of Gyration of the star-shaped and hyperbranched polymers are much smaller than those of the linear polymers if their average degrees of polymerization are equal. The conversion of groups, the core/monomer feed ratio, and the core functionality affect the average Radius of Gyration of the products. However, compared with the other factors, the degree of polymerization is the most influential factor on the average radii of Gyration for the hyperbranched polymer system.
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mean square Radius of Gyration and degree of branching of highly branched copolymers resulting from the copolymerization of ab2 with ab monomers
Macromolecular Theory and Simulations, 2004Co-Authors: Zhiping Zhou, Deyue YanAbstract:The evolution of the various structural units incorporated into hyperbranched polymers formed from the copolymerization of AB 2 and AB monomers has been derived by the kinetic scheme. The degree of branching was calculated with a new definition given in this work. The degree of branching monotonously increased with increasing A group conversion (x) and the maximum value could reach 2r/(I + r) 2 , where r is the initial fraction of AB 2 monomers in the total. Like the average degree of polymerization, the mean-square Radius of Gyration of the hyperbranched polymers increased moderately with A group conversion in the range x <0.9 and displayed an abrupt rise when the copolymerization neared completion. The characteristic ratio of the mean-square Radius of Gyration remained constant for the linear polymers. However, the hyperbranched polymers did not possess this character. In comparison with the linear polymerization, the weight average and z-avetage degree of polymerization increased due to the addition of the branched monomer units AB 2 and the mean-square Radius of Gyration decreased quickly for the products of copolymerization.
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Mean-square Radius of Gyration of polymer chains
Macromolecular Theory and Simulations, 1997Co-Authors: Zhiping Zhou, Deyue YanAbstract:The calculations of the mean-square Radius of Gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square Radius of Gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square Radius of Gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square Radius of Gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square Radius of Gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square Radius of Gyration on the molecular weight can be expressed by the general formula (S 2 ) = aM b , which was supported by a number of experimental measurements. A comparison of our expression for the mean-square Radius of Gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.
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Mean-square Radius of Gyration of polysiloxanes
Macromolecular Theory and Simulations, 1997Co-Authors: Zhiping Zhou, Deyue YanAbstract:The mean-square Radius of Gyration for polysiloxanes has been derived according to the exact definition. Taking account of the examples of symmetrically substituted poly(dimethylsiloxane) and unsymmetrically substituted poly(methylphenylsiloxane), we find that the dependence of 〈S2〉 on the molecular weight follows the general formula 〈S2〉 = aMb with b = 1 ± 0.016, which is analogous to the theoretical outcomes for vinyl or vinylidene polymers even though the skeletal bone of polysiloxanes consists of alternating heteroatoms. A numerical comparison of the rigorous expression of the mean-square Radius of Gyration given in this paper with that reported by Flory shows that the difference is obvious for low-molecular-weight polymer and it gradually declines with increasing degree of polymerization.
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Improved expression of the mean‐square Radius of Gyration, 2. Poly(1,1‐disubstituted ethylene)s
Macromolecular Theory and Simulations, 1995Co-Authors: Zhiping Zhou, Deyue YanAbstract:The mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every Cα was considered to be concentrated in their center of mass, and the virtual side bond vector runs from Cα to this center. The mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square Radius of Gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square Radius of Gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S2〉 = aMb, where a and b are constants characteristic of the polymer.
Andrew L Zydney - One of the best experts on this subject based on the ideXlab platform.
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Radius of Gyration of plasmid dna isoforms from static light scattering
Biotechnology and Bioengineering, 2010Co-Authors: David R Latulippe, Andrew L ZydneyAbstract:Despite the extensive interest in applications of plasmid DNA, there have been few direct measurements of the root mean square Radius of Gyration, R(G), of different plasmid isoforms over a broad range of plasmid size. Static light scattering data were obtained using supercoiled, open-circular, and linear isoforms of 5.76, 9.80, and 16.8 kbp plasmids. The results from this study extend the range of R(G) values available in the literature to plasmid sizes typically used for gene therapy and DNA vaccines. The experimental data were compared with available theoretical expressions based on the worm-like chain model, with the best-fit value of the apparent persistence length for both the linear and open-circular isoforms being statistically identical at 46 nm. A new expression was developed for the Radius of Gyration of the supercoiled plasmid based on a model for linear DNA using an effective contour length that is equal to a fraction of the total contour length. These results should facilitate the development of micro/nano-fluidic devices for DNA manipulation and size-based separation processes for plasmid DNA purification.
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Radius of Gyration of plasmid DNA isoforms from static light scattering.
Biotechnology and Bioengineering, 2010Co-Authors: David R Latulippe, Andrew L ZydneyAbstract:Despite the extensive interest in applications of plasmid DNA, there have been few direct measurements of the root mean square Radius of Gyration, RG, of different plasmid isoforms over a broad range of plasmid size. Static light scattering data were obtained using supercoiled, open-circular, and linear isoforms of 5.76, 9.80, and 16.8 kbp plasmids. The results from this study extend the range of RG values available in the literature to plasmid sizes typically used for gene therapy and DNA vaccines. The experimental data were compared with available theoretical expressions based on the worm-like chain model, with the best-fit value of the apparent persistence length for both the linear and open-circular isoforms being statistically identical at 46 nm. A new expression was developed for the Radius of Gyration of the supercoiled plasmid based on a model for linear DNA using an effective contour length that is equal to a fraction of the total contour length. These results should facilitate the development of micro/nano-fluidic devices for DNA manipulation and size-based separation processes for plasmid DNA purification. Biotechnol. Bioeng. 2010;107: 134–142. © 2010 Wiley Periodicals, Inc.
David R Latulippe - One of the best experts on this subject based on the ideXlab platform.
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Radius of Gyration of plasmid dna isoforms from static light scattering
Biotechnology and Bioengineering, 2010Co-Authors: David R Latulippe, Andrew L ZydneyAbstract:Despite the extensive interest in applications of plasmid DNA, there have been few direct measurements of the root mean square Radius of Gyration, R(G), of different plasmid isoforms over a broad range of plasmid size. Static light scattering data were obtained using supercoiled, open-circular, and linear isoforms of 5.76, 9.80, and 16.8 kbp plasmids. The results from this study extend the range of R(G) values available in the literature to plasmid sizes typically used for gene therapy and DNA vaccines. The experimental data were compared with available theoretical expressions based on the worm-like chain model, with the best-fit value of the apparent persistence length for both the linear and open-circular isoforms being statistically identical at 46 nm. A new expression was developed for the Radius of Gyration of the supercoiled plasmid based on a model for linear DNA using an effective contour length that is equal to a fraction of the total contour length. These results should facilitate the development of micro/nano-fluidic devices for DNA manipulation and size-based separation processes for plasmid DNA purification.
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Radius of Gyration of plasmid DNA isoforms from static light scattering.
Biotechnology and Bioengineering, 2010Co-Authors: David R Latulippe, Andrew L ZydneyAbstract:Despite the extensive interest in applications of plasmid DNA, there have been few direct measurements of the root mean square Radius of Gyration, RG, of different plasmid isoforms over a broad range of plasmid size. Static light scattering data were obtained using supercoiled, open-circular, and linear isoforms of 5.76, 9.80, and 16.8 kbp plasmids. The results from this study extend the range of RG values available in the literature to plasmid sizes typically used for gene therapy and DNA vaccines. The experimental data were compared with available theoretical expressions based on the worm-like chain model, with the best-fit value of the apparent persistence length for both the linear and open-circular isoforms being statistically identical at 46 nm. A new expression was developed for the Radius of Gyration of the supercoiled plasmid based on a model for linear DNA using an effective contour length that is equal to a fraction of the total contour length. These results should facilitate the development of micro/nano-fluidic devices for DNA manipulation and size-based separation processes for plasmid DNA purification. Biotechnol. Bioeng. 2010;107: 134–142. © 2010 Wiley Periodicals, Inc.
Erica Uehara - One of the best experts on this subject based on the ideXlab platform.
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Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers
arXiv: Statistical Mechanics, 2020Co-Authors: Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, Erica UeharaAbstract:We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropriate multivariate Gaussian which takes into account the constraints imposed by the graph type. We recover the result that the expected Radius of Gyration can be given exactly in terms of the Kirchhoff index of the graph. We then consider the expected Radius of Gyration of a topological polymer whose edges are subdivided into $n$ pieces. We prove that the contraction factor of a subdivided polymer approaches a limit as the number of subdivisions increases, and compute the limit exactly in terms of the degree-Kirchhoff index of the original graph. This limit corresponds to the thermodynamic limit in statistical mechanics and is fundamental in the physics of topological polymers. Furthermore, these asymptotic contraction factors are shown to fit well with molecular dynamics simulations.
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Mean-square Radius of Gyration and the hydrodynamic Radius for topological polymers expressed with graphs evaluated by the method of quaternions revisited
Reactive and Functional Polymers, 2018Co-Authors: Erica Uehara, Tetsuo DeguchiAbstract:Abstract We revisit the numerical quaternionic study on the mean-square Radius of Gyration and the hydrodynamic Radius for topological or graph-shaped polymers. We show that it is consistent with other approaches although we apply a nontrivial modification of the quaternionic method [51] for generating random polygons. In the modified method we generate random walks that connect two given points by rescaling the bond length and assign them some weight. We evaluate by it the mean-square Radius of Gyration and the hydrodynamic Radius for several topological polymers. We correct the plots of Ref. [46] for the hydrodynamic Radius versus the segment number and for the ratio of the Gyration to the hydrodynamic Radius versus the segment number. The estimated ratios are close to the values derived from an analytic assumption of the pair distribution function. The Gyration Radius of the multi-theta chain evaluated by the modified method agrees with exact Gaussian results [48]. We derive the moments of the bond vectors' coordinates distribution in random polygons generated by the quaternionic method.
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Mean-square Radius of Gyration and hydrodynamic Radius for topological polymers evaluated through the quaternionic algorithm
Reactive and Functional Polymers, 2014Co-Authors: Erica Uehara, Ryota Tanaka, Mizue Inoue, Fukiko Hirose, Tetsuo DeguchiAbstract:Abstract We evaluate numerically the mean-square (MS) Radius of Gyration and the diffusion coefficient for topological polymers such as ring, tadpole, double-ring, and caged polymers and catenanes. We consider caged polymers with any given number of subchains, and catenanes consisting of two linked ring polymers with a fixed linking number. Through Kirkwood’s approximation we evaluate the hydrodynamic Radius, which is proportional to the inverse of the diffusion coefficient, for various topological polymers. Here we take the statistical averages over configurations of topological polymers constructed through the quaternionic algorithm, which generates uniform random walks connecting given two points. It gives ideal chains with no excluded volume. We evaluate numerically the ratio of the square root of the MS Radius of Gyration to the hydrodynamic Radius for several topological polymers, and show for them that the ratio decreases as the topology becomes more complex.
