Abstract

We used oscillatory optical tweezers to investigate the microrheological properties of Sodium polystyrene sulfonate (NaPSS; Mw = 70kDa) polymer solutions with different concentrations from 0.001mM to 10mM in terms of elastic modulus G’(ω) and loss modulus G”(ω) as a function of angular frequency (ω) in the range of 6rad/s to 6000rad/s. The viscoelastic properties (including zero-shear-rate viscosity, crossing frequency and transition frequency) as a function of polymer concentration, deduced from our primary data, reveal the subtle structural changes in the polymer solutions as the polymer concentration increases from dilute to semi-dilute regimes, passing through the critical micelle formation concentration and the polymer overlapping concentration. The experimental results are consistent with the Maxwell model in some regime, and with the Rouse model in other, indicating the transient network character and the micelles formation in different regimes.

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    [CrossRef]
  3. T. Takasu, “[Treatment of hyperkalemia associated with renal insufficiency--clinical effects and side reactions of positive-ion-exchange resins, sodium polystyrene sulfonate (Kayexalate)],” Nippon Rinsho 28(7), 1941–1946 (1970).
    [PubMed]
  4. B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2009 (1)

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

2008 (1)

2007 (2)

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

H.-H. Chu, Y.-S. Yeo, and K. S. Chuang, “Entry in emulsion polymerization using a mixture of sodium polystyrene sulfonate and sodium dodecyl sulfate as the surfactant,” Polymer (Guildf.) 48(8), 2298–2305 (2007).
[CrossRef]

2006 (2)

L. A. Hough and H. D. Ou-Yang, “Viscoelasticity of aqueous telechelic poly(ethylene oxide) solutions: relaxation and structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 031802 (2006).
[CrossRef] [PubMed]

K. Lienkamp, I. Schnell, F. Groehn, and G. Wegner, “Polymerization of styrene sulfonate ethyl ester by ATRP: synthesis and characterization of macromonomers for suzuki polycondensation,” Macromol. Chem. Phys. 207(22), 2066–2073 (2006).
[CrossRef]

2005 (1)

2002 (2)

M. Sedlák, “Mechanical properties and stability of multimacroion domains in polyelectrolyte solutions,” J. Chem. Phys. 116(12), 5236–5245 (2002).
[CrossRef]

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

2000 (2)

J. H. E. Hone, A. M. Howe, and T. Cosgrove, “A small-angle neutron scattering study of the structure of gelatin/polyelectrolyte complexes,” Macromolecules 33(4), 1206–1212 (2000).
[CrossRef]

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

1999 (1)

J. R. Gillmor, R. W. Connelly, R. H. Colby, and J. S. Tan, “Effect of sodium poly (styrene sulfonate) on thermoreversible gelation of gelatin,” J. Polym. Sci., B, Polym. Phys. 37(16), 2287–2295 (1999).
[CrossRef]

1998 (3)

S. Batzill, R. Luxemburger, R. Deike, and R. Weber, “Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength,” Eur. Phys. J. B 1(4), 491–501 (1998).
[CrossRef]

T. Cosgrove, J. H. E. Hone, A. M. Howe, and R. K. Heenan, “A small-angle neutron scattering study of the structure of gelatin at the surface of polystyrene latex particles,” Langmuir 14(19), 5376–5382 (1998).
[CrossRef]

D. C. Boris and R. H. Colby, “Rheology of sulfonated polystyrene solutions,” Macromolecules 31(17), 5746–5755 (1998).
[CrossRef]

1996 (1)

M. Sedlák, “The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions as seen by light scattering: the slow mode dilemma,” J. Chem. Phys. 105(22), 10123–10133 (1996).
[CrossRef]

1995 (1)

I. Astafieva, K. Khougaz, and A. Eisenberg, “Micellization in block polyelectrolyte solutions. 2. fluorescence study of the critical micelle concentration as a function of soluble block length and salt concentration,” Macromolecules 28(21), 7127–7134 (1995).
[CrossRef]

1993 (1)

I. Astafieva, X. F. Zhong, and A. Eisenberg, “Critical micellization phenomena in block polyelectrolyte solutions,” Macromolecules 26(26), 7339–7352 (1993).
[CrossRef]

1992 (2)

M. Sedlák and E. J. Amis, “Dynamics of moderately concentrated salt‐free polyelectrolyte solutions: Molecular weight dependence,” J. Chem. Phys. 96(1), 817–825 (1992).
[CrossRef]

M. Sedlák and E. J. Amis, “Concentration and molecular weight regime diagram of salt‐free polyelectrolyte solutions as studied by light scattering,” J. Chem. Phys. 96(1), 826–834 (1992).
[CrossRef]

1970 (1)

T. Takasu, “[Treatment of hyperkalemia associated with renal insufficiency--clinical effects and side reactions of positive-ion-exchange resins, sodium polystyrene sulfonate (Kayexalate)],” Nippon Rinsho 28(7), 1941–1946 (1970).
[PubMed]

1946 (1)

M. S. Green and A. V. Tobolsky, “A new approach to the theory of relaxing polymeric media,” J. Chem. Phys. 14(2), 80–92 (1946).
[CrossRef]

Amis, E. J.

M. Sedlák and E. J. Amis, “Dynamics of moderately concentrated salt‐free polyelectrolyte solutions: Molecular weight dependence,” J. Chem. Phys. 96(1), 817–825 (1992).
[CrossRef]

M. Sedlák and E. J. Amis, “Concentration and molecular weight regime diagram of salt‐free polyelectrolyte solutions as studied by light scattering,” J. Chem. Phys. 96(1), 826–834 (1992).
[CrossRef]

Anderson, R. A.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Astafieva, I.

I. Astafieva, K. Khougaz, and A. Eisenberg, “Micellization in block polyelectrolyte solutions. 2. fluorescence study of the critical micelle concentration as a function of soluble block length and salt concentration,” Macromolecules 28(21), 7127–7134 (1995).
[CrossRef]

I. Astafieva, X. F. Zhong, and A. Eisenberg, “Critical micellization phenomena in block polyelectrolyte solutions,” Macromolecules 26(26), 7339–7352 (1993).
[CrossRef]

Barham, B. J.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Batzill, S.

S. Batzill, R. Luxemburger, R. Deike, and R. Weber, “Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength,” Eur. Phys. J. B 1(4), 491–501 (1998).
[CrossRef]

Boris, D. C.

D. C. Boris and R. H. Colby, “Rheology of sulfonated polystyrene solutions,” Macromolecules 31(17), 5746–5755 (1998).
[CrossRef]

Bourne, N.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Boyce, M. C.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Brau, R. R.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Castro, C. E.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Chany, C. J.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Chiou, A.

Chu, H.-H.

H.-H. Chu, Y.-S. Yeo, and K. S. Chuang, “Entry in emulsion polymerization using a mixture of sodium polystyrene sulfonate and sodium dodecyl sulfate as the surfactant,” Polymer (Guildf.) 48(8), 2298–2305 (2007).
[CrossRef]

Chuang, K. S.

H.-H. Chu, Y.-S. Yeo, and K. S. Chuang, “Entry in emulsion polymerization using a mixture of sodium polystyrene sulfonate and sodium dodecyl sulfate as the surfactant,” Polymer (Guildf.) 48(8), 2298–2305 (2007).
[CrossRef]

Colby, R. H.

J. R. Gillmor, R. W. Connelly, R. H. Colby, and J. S. Tan, “Effect of sodium poly (styrene sulfonate) on thermoreversible gelation of gelatin,” J. Polym. Sci., B, Polym. Phys. 37(16), 2287–2295 (1999).
[CrossRef]

D. C. Boris and R. H. Colby, “Rheology of sulfonated polystyrene solutions,” Macromolecules 31(17), 5746–5755 (1998).
[CrossRef]

Connelly, R. W.

J. R. Gillmor, R. W. Connelly, R. H. Colby, and J. S. Tan, “Effect of sodium poly (styrene sulfonate) on thermoreversible gelation of gelatin,” J. Polym. Sci., B, Polym. Phys. 37(16), 2287–2295 (1999).
[CrossRef]

Cooper, M. D.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Cosgrove, T.

J. H. E. Hone, A. M. Howe, and T. Cosgrove, “A small-angle neutron scattering study of the structure of gelatin/polyelectrolyte complexes,” Macromolecules 33(4), 1206–1212 (2000).
[CrossRef]

T. Cosgrove, J. H. E. Hone, A. M. Howe, and R. K. Heenan, “A small-angle neutron scattering study of the structure of gelatin at the surface of polystyrene latex particles,” Langmuir 14(19), 5376–5382 (1998).
[CrossRef]

Crocker, J. C.

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

Dasgupta, B. R.

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

De Luca, A. C.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

Deike, R.

S. Batzill, R. Luxemburger, R. Deike, and R. Weber, “Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength,” Eur. Phys. J. B 1(4), 491–501 (1998).
[CrossRef]

Eisenberg, A.

I. Astafieva, K. Khougaz, and A. Eisenberg, “Micellization in block polyelectrolyte solutions. 2. fluorescence study of the critical micelle concentration as a function of soluble block length and salt concentration,” Macromolecules 28(21), 7127–7134 (1995).
[CrossRef]

I. Astafieva, X. F. Zhong, and A. Eisenberg, “Critical micellization phenomena in block polyelectrolyte solutions,” Macromolecules 26(26), 7339–7352 (1993).
[CrossRef]

Ferrer, J. M.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Frisken, B. J.

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

Fusco, S.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

Ghadiali, S. N.

Gillmor, J. R.

J. R. Gillmor, R. W. Connelly, R. H. Colby, and J. S. Tan, “Effect of sodium poly (styrene sulfonate) on thermoreversible gelation of gelatin,” J. Polym. Sci., B, Polym. Phys. 37(16), 2287–2295 (1999).
[CrossRef]

Green, M. S.

M. S. Green and A. V. Tobolsky, “A new approach to the theory of relaxing polymeric media,” J. Chem. Phys. 14(2), 80–92 (1946).
[CrossRef]

Groehn, F.

K. Lienkamp, I. Schnell, F. Groehn, and G. Wegner, “Polymerization of styrene sulfonate ethyl ester by ATRP: synthesis and characterization of macromonomers for suzuki polycondensation,” Macromol. Chem. Phys. 207(22), 2066–2073 (2006).
[CrossRef]

Hallow, M.

Heenan, R. K.

T. Cosgrove, J. H. E. Hone, A. M. Howe, and R. K. Heenan, “A small-angle neutron scattering study of the structure of gelatin at the surface of polystyrene latex particles,” Langmuir 14(19), 5376–5382 (1998).
[CrossRef]

Herold, B. C.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Hone, J. H. E.

J. H. E. Hone, A. M. Howe, and T. Cosgrove, “A small-angle neutron scattering study of the structure of gelatin/polyelectrolyte complexes,” Macromolecules 33(4), 1206–1212 (2000).
[CrossRef]

T. Cosgrove, J. H. E. Hone, A. M. Howe, and R. K. Heenan, “A small-angle neutron scattering study of the structure of gelatin at the surface of polystyrene latex particles,” Langmuir 14(19), 5376–5382 (1998).
[CrossRef]

Hough, L. A.

L. A. Hough and H. D. Ou-Yang, “Viscoelasticity of aqueous telechelic poly(ethylene oxide) solutions: relaxation and structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 031802 (2006).
[CrossRef] [PubMed]

Howe, A. M.

J. H. E. Hone, A. M. Howe, and T. Cosgrove, “A small-angle neutron scattering study of the structure of gelatin/polyelectrolyte complexes,” Macromolecules 33(4), 1206–1212 (2000).
[CrossRef]

T. Cosgrove, J. H. E. Hone, A. M. Howe, and R. K. Heenan, “A small-angle neutron scattering study of the structure of gelatin at the surface of polystyrene latex particles,” Langmuir 14(19), 5376–5382 (1998).
[CrossRef]

Kamm, R.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Khougaz, K.

I. Astafieva, K. Khougaz, and A. Eisenberg, “Micellization in block polyelectrolyte solutions. 2. fluorescence study of the critical micelle concentration as a function of soluble block length and salt concentration,” Macromolecules 28(21), 7127–7134 (1995).
[CrossRef]

Kirkpatrick, R.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Lang, M. J.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Lee, H.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Lienkamp, K.

K. Lienkamp, I. Schnell, F. Groehn, and G. Wegner, “Polymerization of styrene sulfonate ethyl ester by ATRP: synthesis and characterization of macromonomers for suzuki polycondensation,” Macromol. Chem. Phys. 207(22), 2066–2073 (2006).
[CrossRef]

Luxemburger, R.

S. Batzill, R. Luxemburger, R. Deike, and R. Weber, “Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength,” Eur. Phys. J. B 1(4), 491–501 (1998).
[CrossRef]

Marcellino, D.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Matsudaira, P.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Netti, P. A.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

Ou-Yang, H. D.

M.-T. Wei, A. Zaorski, H. C. Yalcin, J. Wang, M. Hallow, S. N. Ghadiali, A. Chiou, and H. D. Ou-Yang, “A comparative study of living cell micromechanical properties by oscillatory optical tweezers,” Opt. Express 16(12), 8594–8603 (2008).
[CrossRef] [PubMed]

L. A. Hough and H. D. Ou-Yang, “Viscoelasticity of aqueous telechelic poly(ethylene oxide) solutions: relaxation and structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 031802 (2006).
[CrossRef] [PubMed]

Pesce, G.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

Rusciano, G.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

Sasso, A.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

Schnell, I.

K. Lienkamp, I. Schnell, F. Groehn, and G. Wegner, “Polymerization of styrene sulfonate ethyl ester by ATRP: synthesis and characterization of macromonomers for suzuki polycondensation,” Macromol. Chem. Phys. 207(22), 2066–2073 (2006).
[CrossRef]

Sedlák, M.

M. Sedlák, “Mechanical properties and stability of multimacroion domains in polyelectrolyte solutions,” J. Chem. Phys. 116(12), 5236–5245 (2002).
[CrossRef]

M. Sedlák, “The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions as seen by light scattering: the slow mode dilemma,” J. Chem. Phys. 105(22), 10123–10133 (1996).
[CrossRef]

M. Sedlák and E. J. Amis, “Dynamics of moderately concentrated salt‐free polyelectrolyte solutions: Molecular weight dependence,” J. Chem. Phys. 96(1), 817–825 (1992).
[CrossRef]

M. Sedlák and E. J. Amis, “Concentration and molecular weight regime diagram of salt‐free polyelectrolyte solutions as studied by light scattering,” J. Chem. Phys. 96(1), 826–834 (1992).
[CrossRef]

Stanberry, L. R.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Strauss, D. M.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Takasu, T.

T. Takasu, “[Treatment of hyperkalemia associated with renal insufficiency--clinical effects and side reactions of positive-ion-exchange resins, sodium polystyrene sulfonate (Kayexalate)],” Nippon Rinsho 28(7), 1941–1946 (1970).
[PubMed]

Tam, B. K.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Tan, J. S.

J. R. Gillmor, R. W. Connelly, R. H. Colby, and J. S. Tan, “Effect of sodium poly (styrene sulfonate) on thermoreversible gelation of gelatin,” J. Polym. Sci., B, Polym. Phys. 37(16), 2287–2295 (1999).
[CrossRef]

Tarsa, P. B.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

Tee, S.-Y.

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

Tobolsky, A. V.

M. S. Green and A. V. Tobolsky, “A new approach to the theory of relaxing polymeric media,” J. Chem. Phys. 14(2), 80–92 (1946).
[CrossRef]

Waller, D. P.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Wang, J.

Weber, R.

S. Batzill, R. Luxemburger, R. Deike, and R. Weber, “Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength,” Eur. Phys. J. B 1(4), 491–501 (1998).
[CrossRef]

Wegner, G.

K. Lienkamp, I. Schnell, F. Groehn, and G. Wegner, “Polymerization of styrene sulfonate ethyl ester by ATRP: synthesis and characterization of macromonomers for suzuki polycondensation,” Macromol. Chem. Phys. 207(22), 2066–2073 (2006).
[CrossRef]

Wei, M.-T.

Weitz, D. A.

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

Yalcin, H. C.

Yeo, Y.-S.

H.-H. Chu, Y.-S. Yeo, and K. S. Chuang, “Entry in emulsion polymerization using a mixture of sodium polystyrene sulfonate and sodium dodecyl sulfate as the surfactant,” Polymer (Guildf.) 48(8), 2298–2305 (2007).
[CrossRef]

Zaneveld, L. J.

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

Zaorski, A.

Zhong, X. F.

I. Astafieva, X. F. Zhong, and A. Eisenberg, “Critical micellization phenomena in block polyelectrolyte solutions,” Macromolecules 26(26), 7339–7352 (1993).
[CrossRef]

Eur. Phys. J. B (1)

S. Batzill, R. Luxemburger, R. Deike, and R. Weber, “Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength,” Eur. Phys. J. B 1(4), 491–501 (1998).
[CrossRef]

J. Chem. Phys. (5)

M. S. Green and A. V. Tobolsky, “A new approach to the theory of relaxing polymeric media,” J. Chem. Phys. 14(2), 80–92 (1946).
[CrossRef]

M. Sedlák, “The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions as seen by light scattering: the slow mode dilemma,” J. Chem. Phys. 105(22), 10123–10133 (1996).
[CrossRef]

M. Sedlák and E. J. Amis, “Dynamics of moderately concentrated salt‐free polyelectrolyte solutions: Molecular weight dependence,” J. Chem. Phys. 96(1), 817–825 (1992).
[CrossRef]

M. Sedlák and E. J. Amis, “Concentration and molecular weight regime diagram of salt‐free polyelectrolyte solutions as studied by light scattering,” J. Chem. Phys. 96(1), 826–834 (1992).
[CrossRef]

M. Sedlák, “Mechanical properties and stability of multimacroion domains in polyelectrolyte solutions,” J. Chem. Phys. 116(12), 5236–5245 (2002).
[CrossRef]

J. Infect. Dis. (1)

B. C. Herold, N. Bourne, D. Marcellino, R. Kirkpatrick, D. M. Strauss, L. J. Zaneveld, D. P. Waller, R. A. Anderson, C. J. Chany, B. J. Barham, L. R. Stanberry, and M. D. Cooper, “Poly(sodium 4-styrene sulfonate): an effective candidate topical antimicrobial for the prevention of sexually transmitted diseases,” J. Infect. Dis. 181(2), 770–773 (2000).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt. (2)

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[CrossRef]

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[CrossRef]

J. Polym. Sci., B, Polym. Phys. (1)

J. R. Gillmor, R. W. Connelly, R. H. Colby, and J. S. Tan, “Effect of sodium poly (styrene sulfonate) on thermoreversible gelation of gelatin,” J. Polym. Sci., B, Polym. Phys. 37(16), 2287–2295 (1999).
[CrossRef]

Langmuir (1)

T. Cosgrove, J. H. E. Hone, A. M. Howe, and R. K. Heenan, “A small-angle neutron scattering study of the structure of gelatin at the surface of polystyrene latex particles,” Langmuir 14(19), 5376–5382 (1998).
[CrossRef]

Macromol. Chem. Phys. (1)

K. Lienkamp, I. Schnell, F. Groehn, and G. Wegner, “Polymerization of styrene sulfonate ethyl ester by ATRP: synthesis and characterization of macromonomers for suzuki polycondensation,” Macromol. Chem. Phys. 207(22), 2066–2073 (2006).
[CrossRef]

Macromolecules (4)

D. C. Boris and R. H. Colby, “Rheology of sulfonated polystyrene solutions,” Macromolecules 31(17), 5746–5755 (1998).
[CrossRef]

J. H. E. Hone, A. M. Howe, and T. Cosgrove, “A small-angle neutron scattering study of the structure of gelatin/polyelectrolyte complexes,” Macromolecules 33(4), 1206–1212 (2000).
[CrossRef]

I. Astafieva, K. Khougaz, and A. Eisenberg, “Micellization in block polyelectrolyte solutions. 2. fluorescence study of the critical micelle concentration as a function of soluble block length and salt concentration,” Macromolecules 28(21), 7127–7134 (1995).
[CrossRef]

I. Astafieva, X. F. Zhong, and A. Eisenberg, “Critical micellization phenomena in block polyelectrolyte solutions,” Macromolecules 26(26), 7339–7352 (1993).
[CrossRef]

Nippon Rinsho (1)

T. Takasu, “[Treatment of hyperkalemia associated with renal insufficiency--clinical effects and side reactions of positive-ion-exchange resins, sodium polystyrene sulfonate (Kayexalate)],” Nippon Rinsho 28(7), 1941–1946 (1970).
[PubMed]

Opt. Express (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

L. A. Hough and H. D. Ou-Yang, “Viscoelasticity of aqueous telechelic poly(ethylene oxide) solutions: relaxation and structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 031802 (2006).
[CrossRef] [PubMed]

B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. J. Frisken, and D. A. Weitz, “Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(5), 051505 (2002).
[CrossRef] [PubMed]

Polymer (Guildf.) (1)

H.-H. Chu, Y.-S. Yeo, and K. S. Chuang, “Entry in emulsion polymerization using a mixture of sodium polystyrene sulfonate and sodium dodecyl sulfate as the surfactant,” Polymer (Guildf.) 48(8), 2298–2305 (2007).
[CrossRef]

Other (2)

J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, 1970).

J. M. Dealy and R. G. Larson, Structure and Rheology of Molten Polymers: From Structure to Flow Behaviour and Back Again (Hanser Publishers, 2006).

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Figures (5)

Fig. 1
Fig. 1

Chemical structure of Sodium polystyrene sulfonate (NaPSS).

Fig. 2
Fig. 2

A schematic diagram of the experimental setup. A linearly polarized laser beam (λ = 1064nm) was used to trap and oscillate a polystyrene bead; another laser beam (λ = 980nm) was used to track the position of the bead. A sinusoidal voltage from a lock-in amplifier was applied to a PZT mirror to generate the oscillating trapping beam. λ/2: half-wave plate; PBS: polarizing beam splitter; BE: beam expander; DM: dichroic mirror; QPD: quadrant photodiode; M1, M2,: mirrors.

Fig. 3
Fig. 3

(a) The elastic modulus (G’), and (b) the viscous modulus (G”) as a function of angular frequency (ω) for eleven different polymer concentrations. In (a) the green solid line below the experimental data represents a power law dependence characterized [G’(ω) ~ω 0.5] and the red dashed line above the experimental data represents a power law dependence characterized by [G’(ω) ~ω]; likewise, in (b), the red dashed line above the experimental data represents a power law dependence characterized by [G”(ω) ~ω].

Fig. 4
Fig. 4

Zero-shear-rate viscosity as a function of concentration; the purple dashed straight line, with a constant value of 0.0008513Ns/m2, represents the zero-shear-rate viscosity of pure water at 27°C.

Fig. 5
Fig. 5

(a) Crossing frequency of G’ and G”, and (b) Transition frequency of G’ as a function of polymer concentration. The inset figure of Fig. 5(a) shows that the crossing frequency (ω c) is defined as the frequency where G’ and G” crossed over, and the inset figure of Fig. 5(b) shows that the transition frequency (ω τ) is defined as the frequency where G’(ω) changes from a constant value to a power law dependence on frequency.

Equations (1)

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G ( ω ) = k O T 6 π a ( A cos δ ( ω ) D ( ω ) 1 ) ;       G ( ω ) = k O T 6 π a ( A sin δ ( ω ) D ( ω ) )

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