Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations

Journal of Chemical Physics

Volumn 113, Issue 7, 2000, Pages 2894-2900

  Jendrejack, Richard M ^a   Graham, Michael D ^a   De Pablo, Juan J ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEBYSHEV APPROXIMATION; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; HYDRODYNAMICS; INTEGRATION; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; MOLECULAR STRUCTURE; POLYNOMIALS; RANDOM PROCESSES; TENSORS;

EULER METHOD; FIXMAN METHOD;

POLYMERS;

EID: 0034247779     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1305884     Document Type: Article

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82. M. Fixman, J. Chem. Phys. 45, 793 (1966).
83. H.-C. Öttinger, J. Chem. Phys. 86, 3731 (1987).
84. H.-C. Öttinger, J. Chem. Phys. 90, 463 (1989).
85. J. J. Magda, R. G. Larson, and M. E. Mackay, J. Chem. Phys. 89, 2504 (1988).
86. R. G. Larson and J. J. Magda, Macromolecules 22, 3004 (1989).
87. W. Zykla and H.-C. Öttinger, J. Chem. Phys. 90, 474 (1989).
88. H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 26, 207 (1987).
89. L. E. Wedgewood and H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 27, 245 (1988).
90. L. E. Wedgewood, D. N. Ostrov, and R. B. Bird, J. Non-Newtonian Fluid Mech. 40, 119 (1991).
91. Y. Oono, Adv. Chem. Phys. 61, 301 (1985).
92. Y. Oono and M. Kohmoto, J. Chem. Phys. 78, 520 (1983).
93. Y. Oono, J. Chem. Phys. 79, 4629 (1983).
94. B. Schaub, B. A. Friedman, and Y. Oono, Phys. Lett. A 110, 136 (1985).
95. A. Jagannathan, B. Schaub, and Y. Oono, Phys. Lett. A 113, 341 (1985).
96. A. Jagannathan, Y. Oono, and B. Schaub, J. Chem. Phys. 86, 2276 (1987).
97. B. Schaub, D. B. Creamer, and H. Johannesson, J. Phys. A 21, 1431 (1988).
98. S. Wang, Phys. Rev. A 40, 2137 (1989).
99. S. Wang, J. Chem. Phys. 92, 7618 (1990).
100. H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 33, 53 (1989).
101. H.-C. Öttinger, Phys. Rev. A 40, 2664 (1989).
102. H.-C. Öttinger, Phys. Rev. A 41, 4413 (1990).
103. W. Zykla and H.-C. Öttinger, Macromolecules 24, 484 (1991).
104. P. R. Baldwin and E. Helfand, Phys. Rev. A 41, 6772 (1990).
105. R. S. Adler, J. Chem. Phys. 69, 2849 (1978).
106. S. Q. Wang and K. F. Freed, J. Chem. Phys. 88, 3944 (1988).
107. Y. Rabin, Europhys. Lett. 7, 25 (1988).
108. Y. Rabin, S. Q. Wang, and K. F. Freed, Macromolecules 22, 2420 (1989).
109. Y. Rabin, S. Q. Wang, and D. B. Creamer, J. Chem. Phys. 90, 570 (1989).
110. H. P. Wittmann and G. H. Fredrickson, J. Phys. I 4, 1791 (1994).
111. B. H. A. A. van den Brule, J. Non-Newtonian Fluid Mech. 47, 357 (1993).
112. J. J. L. Cascales, F. G. Diaz, and J. G. de la Torre, Polymer 36, 345 (1995).
113. M. Herrchen and H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 17, 68 (1997).
114. M. Fixman, J. Chem. Phys. 69, 1527 (1978).
115. M. Fixman, Macromolecules 14, 1710 (1981).
116. D. L. Ermak and J. A. McCammon, J. Chem. Phys. 69, 1352 (1978).
117. S. A. Allison and J. A. McCammon, Biopolymers 23, 167 (1984).
118. C. Pierleoni and J. P. Ryckaert, Macromolecules 28, 5097 (1995).
119. Z. Xu, S. Kim, and J. J. de Pablo, J. Chem. Phys. 101, 5293 (1994).
120. W. S. Stewart and J. P. Sorensen, Trans. Soc. Rheol. 16, 1 (1972).
121. X. Fan, J. Chem. Phys. 85, 6237 (1985).
122. X. Fan, J. Non-Newtonian Fluid Mech. 17, 125 (1985).
123. T. C. B. Kwan and E. S. G. Shaqfeh, J. Non-Newtonian Fluid Mech. 82, 139 (1999).
124. P. G. de Gennes, Proc. Natl. Acad. Sci. USA 96, 7262 (1999).
125. B. H. Zimm, Macromolecules 31, 6089 (1998).
126. B. B. Haab and R. A. Mathies, Anal. Chem. 71, 5137 (1999).
127. R. G. Larson, T. T. Perkins, D. E. Smith, and S. Chu, Phys. Rev. E 55, 1794 (1997).
128. R. G. Larson, H. Hua, D. E. Smith, and S. Chu, J. Rheol. 43, 267 (1999).
129. J. G. H. Cifre and J. G. de la Torre, J. Rheol. 43, 339 (1999).
130. M. Fixman, Macromolecules 19, 1204 (1986).
131. J.-C. Öttinger, B. H. A. A. van der Brule, and M. A. Hulsen, J. Non-Newtonian Fluid Mech. 70, 255 (1997).
132. T. W. Bell, Ph.D. thesis, University of Wisconsin-Madison, 1998.
133. R. M. Jendrejack, T. W. Bell, J. J. de Pablo, and M. D. Graham, Proceedings of the XIIIth International Congress on Rheology, Cambridge, UK 2000 (unpublished).
134. The quantities used for nondimensionalization throughout this article are √kT/H for distance, ζ/4H for time, kT for energy, √kTH for force, and nkT for the stress tensor. The parameter k is Boltzmann's constant, T is temperature, H is Hooke's spring constant, n is the number density of polymer, and ζ is the bead friction coefficient.
135. R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1987), Vol. 2.
136. H.-C. Öttinger, Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996).
137. J. Rotne and S. Prager, J. Chem. Phys. 50, 4831 (1969).
138. A. Rey, J. Freire, and J. G. de la Torre, Macromolecules 24, 4666 (1991).
139. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, Berlin, 1988).
140. C. R. Wylie and L. C. Barrett, Advanced Engineering Mathematics, 6th ed. (McGraw-Hill, New York, 1995).
141. R. B. Lehoucq, D. C. Sorensen, and C. Yang, Arpack Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, 1997, ftp://ftp.caam.rice.edu/pub/software/ARPACK.
142. Y. Saad and M. H. Schultz, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856 (1986).
143. 1 = 2/sin(π/2N) is the longest Rouse relaxation time, and γ̇ is the shear rate (nondimensionalized with ζ/4H).
144. G. R. Strobl, The Physics of Polymers (Springer, Berlin, 1997).
145. B. Li, N. Madras, and A. Sokal, J. Stat. Phys. 80, 661 (1995).
146. Y. Oono and M. Kohmoto, J. Chem. Phys. 78, 520 (1983).