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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8847–8854
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Optical tweezers based active microrheology of sodium polystyrene sulfonate (NaPSS)

Chia-Chun Chiang, Ming-Tzo Wei, Yin-Quan Chen, Pei-Wen Yen, Yi-Chiao Huang, Jun-Yeh Chen, Olivier Lavastre, Husson Guillaume, Darsy Guillaume, and Arthur Chiou  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8847-8854 (2011)
http://dx.doi.org/10.1364/OE.19.008847


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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.

© 2011 OSA

1. Introduction

Sodium polystyrene sulfonate (NaPSS) is widely used in both industrial and medical applications [1

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

]. It is used as an ion-exchanger or a cement superplastifier in industry [2

2. 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]

], and also as a medication for patients with hyperkalemia [3

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]

]. Topical antimicrobial effect had also been reported [4

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]

]. Characteristics of the polymer solution have been described by several physical parameters, such as ionic strength [5

5. 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]

], molecular weight [6

6. 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]

], polymer concentration [7

7. 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]

], and mechanical properties [8

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

]. The mechanical properties to describe the dynamic structure of polymer solutions under different shear rate are often described by the complex viscoelastic modulus G*(ω)=G(ω)+iG(ω). The real part G’(ω) is the elastic modulus, which characterizes the ability of the material to store energy (as mechanical potential energy), and the imaginary part G”(ω) is the viscous modulus which characterizes the ability to dissipate energy (often in the form of heat) [9

9. 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]

,10

10. 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]

]. The viscous modulus G”(ω) of NaPSS polymer solutions has been measured by small-angle neutron scattering [11

11. 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]

], dynamic light scattering [12

12. 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]

], and conventional micro-rheometer [1

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

]. However, the elastic modulus G’(ω) of NaPSS has not been well characterized, and the dynamic structure of NaPSS polymer solution is not yet well understood.

In general, the viscoelastic properties of NaPSS solutions depend on NaPSS molecular weight and concentration as well as the ionic strength of the solution. Conventional rheometry generally requires large sample volume (~several milli-liters); thus any method that requires only a smaller amount of solvent and chemicals is of interest. We decided to check if the rheological properties of NaPSS could be obtained with sample volume on the order of microliter and to apply a microrhelogical analysis to the understanding of the dynamic structure of NaPSS polymer solutions.

In this study, we investigated the microrheological properties of NaPSS (Mw = 70kDa) by oscillatory optical tweezers approach with frequencies ranging from 6rad/s to 6000rad/s. We studied the mechanical properties of NaPSS solutions with different polymer concentrations ranging from below to above the overlap concentration as well as the Critical Micelle Concentration (CMC). That includes both the dilute and the semi-dilute regimes [1

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

,13

13. 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]

,14

14. 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]

]. We compared our experimental results with different theoretical models including the Maxwell and the Rouse models, and discussed the structural changes in the polymer solutions at different concentrations.

2. Experimental materials and methods

2.1 Sodium polystyrene sulfonate polymer

Sodium polystyrene sulfonate (NaPSS) is an anionic polyelectrolyte, with a linear chemical formula given by (C8H7SO3 -Na+)n., and the chemical structure shown in Fig. 1
Fig. 1 Chemical structure of Sodium polystyrene sulfonate (NaPSS).
. The polymer samples used in our experiments have a molecular weight of 70kDa with a polydispersity index Mw/Mn < 1.2 (product number 243051 from Sigma Aldrich). As NaPSS solutions rheology is very sensitive to the presence of ions in solutions, as for any type of polyelectrolyte solutions, de-ionized water was used as solvent in all our samples. The polymer solution structure depends on its concentration. The Critical Micelle Concentration is the polymer concentration where the molecules start to form micelles and alter the solution behavior [15

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

]. The Critical Micelle Concentration (CMC) of NaPSS (Mw~70kDa), determined by surface tension measurement, was reported to be equal to 0.06mM [16

16. 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]

]. The polymer overlapping concentration (C*) is the concentration where isolated polymer chains start to overlap and form transient network. At this concentration, the viscosity at zero shear rate increases significantly with a moderate increment in polymer concentration. The polymer overlapping concentration of NaPSS (Mw~70kDa) has been estimated to be 0.7mM [1

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

].

Average mesh size of NaPSS was estimated to be 5.89nm for 0.06mM NaPSS polymer solution (Mw ~82kDa) [17

17. 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]

]. To characterize the network properties of the polymer solution via a continuum model [9

9. 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]

], we used 1.5μm polystyrene beads as a probe to measure the mechanical properties of the polymer solution by active oscillation of the bead (embedded in the polymer solution) with oscillatory optical tweezers. As the size of probe particle is several times larger than the mesh size of the polymer, the network intrinsic inhomogeniety should not affect the average micromechanical properties sensed by the probe. As a consequence, characterization of the mechanical properties of the polymer solution via the continuum model is justified. In addition, this particular bead size (of 1.5μm) and (polystyrene) material were chosen for several reasons including sufficiently small spatial resolution (~1μm), relatively large trapping force (~tens of pico-Newton), and our familiarity with its characteristics as an optical probe. The possible effects of probe size and material on our results are discussed in more detail in Section 3 (Experimental results and discussion).

2.2 Optical tweezers setup

The main components of our experimental setup are schematically illustrated in 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.
. A linearly polarized laser beam (wavelength = 1064nm) from an Nd: YVO4 laser was expanded three times by a beam expander (BE1) to fill the back aperture of an oil immersion objective (NA = 1.3, 100X), to serve as the trapping beam. The trapping laser power was controlled by a half-wave plate (λ/2) in conjunction with a polarized beam splitter (PBS). A mirror was mounted on a PZT-stage (PZT Mirror) which can be driven by a sinusoidal signal from a lock-in amplifier to generate an oscillating trapping beam. The telescopic relay lens (telescope) imaged the plane of the oscillating mirror onto the entrance aperture of the microscope objective so that there was no beam walk-off during the beam oscillation.

A second laser beam (from a cw laser; λ = 980nm) was used to track the position of the sample particle (a polystyrene bead) trapped and oscillated by the optical tweezers. The tracking beam was expanded by a beam expander (BE2), and combined with the trapping beam via a dichroic mirror (DM1) into the oil immersion objective. A QPD (Quadrant Photo Diode) was used to track the lateral position of the trapped particle. The displacement of the trapped particle on the xy-plane, perpendicular to the optical beam axis, can be deduced directly from the QPD’s output voltages via a standard calibration procedure [18

18. M.-T. Wei and A. Chiou, “Three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers with a pair of orthogonal tracking beams and the determination of the associated optical force constants,” Opt. Express 13(15), 5798–5806 (2005). [CrossRef] [PubMed]

]. The time response of our 2-d particle-tracking system is on the order of millisecond. We used the lock-in amplifier to measure the phase delay of the displacement of the probe particle relative to that of the focal spot of optical trapping beam; the latter was scanned by the reference signal provided by the lock-in amplifier to the PZT-mirror. The force constant in the linear regime of our optical tweezers for a polystyrene bead (with a diameter of 1.5μm) trapped in de-ionized water (with refractive n = 1.330) was determined to be approximately 15pN/μm at 6mW trapping power [19

19. 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]

]. Variation in optical force constant (kOT) due to the change in refractive index from 1.331 (for NaPSS polymer solution with 0.001mM concentration) to 1.414 (for NaPSS polymer solution with 10mM concentration) was calibrated according to the recipe given by Brau et al. [9

9. 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]

].

3. Experimental results and discussion

We used 1.5μm polystyrene beads as probe, and we suspended them in NaPSS solutions with different concentrations. In the experiment, a single bead was trapped and oscillated with optical tweezers; a sinusoidal voltage with a peak-to-peak value of 0.1 voltage and an angular frequency ranging from 6 to 6000rad/s was applied to a PZT-stage with a mirror to scan the trapping laser beam (λ = 1064nm) such that the focal spot oscillated with an amplitude of approximately 36nm, while another laser beam (λ = 980nm) was used to track the amplitude and the phase delay of the particle relative to that of the focal spot of the trapping beam. The elastic modulus and the viscous modulus (G’, G”) as a function of the angular frequency (ω) were determined by the following equations [19

19. 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]

,20

20. 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]

]
G(ω)=kOT6πa(Acosδ(ω)D(ω)1);     G(ω)=kOT6πa(Asinδ(ω)D(ω))
(1)
where A is the oscillation amplitude of the focal spot (of the trapping beam), D the oscillation amplitude of the bead, δ the relative phase delay, kOT the optical spring constant, and a the bead radius. Although we did not measure the viscoelastic properties of NaPSS solution with beads of different sizes and different material, we did in the case of T-PEO polymer solution (which is beyond the scope of this paper), and we did not observed any significant difference in the results obtained with different bead size (for example, 1.6μm vs. 0.7μm diameter silica beads) and different materials (for example, 1.5μm diameter silica vs. polystyrene beads), as the size of probe particle is several times larger than the mesh size of the polymer. Besides, Dasgupta et al. [21

21. 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]

] has shown that the effect of absorptions onto the surface of a probe bead can be negligible in microrheological studies. Hence, we anticipate that the effect on our experimental results for NaPSS due to the size, surface coating, and materials of the probing beads will be relatively small. Even in the worst scenario when there is some small effect, it will affect only the absolute values of the measurements, but not the relative values, the general trend, and the main conclusions of this work.

The elastic modulus and the viscous modulus (G’, G”) of NaPSS solution as a function of the angular frequency (ω), at different polymer concentrations, are shown in 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].
. All the data in Fig. 3 represent the mean value obtained by averaging over 6 repeated measurements under identical condition. The typical standard deviation is approximately ± 50% for G’, and ± 15% for G”. For the sake of clarity, error bars representing the standard deviation are not shown in Fig. 3. In contrast to the loss modulus G”(ω), which is proportional to ω for all polymer concentrations (in the range of 0.001mM to 10mM) and throughout the whole frequency range from 6 to 6000rad/s, the frequency response of the elastic modulus G’(ω) is quite different. In the low frequency range (~6 to 100rad/s), G’ is essentially independent of frequency for all polymer concentrations. In the higher frequency range (~100 to 6000rad/s), the value of G’ increases with frequency which can be approximated by a power law dependence. The characteristic exponent of this power law depends on polymer concentrations, varying from G’~ω0.5 at low polymer concentration (~C < 1mM), to G’~ω1.0 at higher polymer concentration (~C > 1mM).

Since the loss modulus G”(ω) is linearly proportional to frequency (ω), the viscosity η, defined by η = G”/ω, is approximately constant, independent of frequency. Hence the zero-shear-rate viscosity defined by (η0=limω0G/ω), can be approximated by the constant slope of G”(ω) in a linear plot of our experimental data associated with Fig. 3(b). The zero-shear-rate viscosity (η 0) as a function of polymer concentration is shown in 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.
. Obviously, the polymer solution viscosity cannot be lower than the viscosity of the pure solvent (i.e., water in this case). The viscosity of water at 27 °C is taken to be 0.0008513N*s/m2 which is indicated by the purple dash line in Fig. 4.

For NaPSS polymer concentrations (C) in the range of 0.001mM to 10mM investigated in this work, the polymer structure can be approximately divided into 3 regimes, each characterized by a different exponent in the power law which expresses the zero-shear-rate viscosity as a function of polymer concentration (confer Fig. 4). For polymer concentration C< 0.05mM, η 0 ~C0.04; for 0.05mM < C <1.0mM, η 0 ~C0.3 ; for C > 1.0mM, η 0 ~C3 . The transition concentration (of ~0.05mM) from the 1st to the 2nd regimes is fairly consistent with the Critical Micelle Concentration (of 0.06mM reported in the literature [16

16. 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]

]); and that from the 2nd to the 3rd regimes at the concentration (of ~1.0mM) is also consistent with the polymer-overlapping concentration (of ~0.7mM [1

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

]). The polymer-overlapping concentration (C*) is revealed as the polymer concentration at which η 0 increases drastically with a moderate increment in polymer concentration. These results indicate that microstructural changes in polymer solutions such as micelles formation and transient network formation can be revealed via this active microrheology approach.

While the scaling of loss modulus with polymer concentration, deduced from our experimental data, is compatible with the expectation from polymer theory [22

22. 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]

,23

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

], our experimental results for the elastic modulus G’(ω) deviate from the trend predicted by the transient network theory (Maxwell model) [22

22. 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]

]. Maxwell model, which is a theory often used to describe polymer behavior, predicts that G’(ω) ~ω 2 in the lower frequency regime (where ωτΜ << 1) and G’(ω) ~ω 0, i.e., independent of frequency (ω), in the higher frequency regime (where ωτΜ >> 1), where τΜ is the characteristic time of a relatively slow relaxation process of the transient polymer network. However our experimental data show the opposite trend with G’(ω) ~ω 0 in the lower frequency regime (~6 to 100rad/s), and G’(ω) ~ω 0.5 to G’(ω) ~ω 1 in the higher frequency regime (~100 to 6000 rad/s). The Rouse model [20

20. 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]

,23

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

] represents another theoretical model which describes the behavior of polymer solutions as micelles connected by elastic springs. According to the Rouse model, both G’ and G” are proportional to ω0.5 at high frequency (where ωτΜ >> 1). At low polymer concentrations (~0.001mM to 1mM), our experimental data in the higher frequency range (~100rad/s to 6000rad/s) follow approximately the power law [G’ ~ω0.5] predicted by the Rouse model. As the concentration increases, the exponent in the power law also increases, approaching G’ ~ω at the polymer concentration ~10mM. We speculate that such a change is due to the polymer entanglements and formation of transient network. Hence, our results indicate that the rheological behavior of NaPSS solutions may be a combination of the transient network effect and the micelle bridging effect, leading to an exponent of 0 to 1.0 in frequency response, in between the values of 0 and 2.0 predicted by the Maxwell model and the values of 0.5 to 2.0 predicted by the Rouse model. Quantitative interpretation of the details of the power law dependence requires further studies.

Two other parameters often used for the polymer behavior characterization are the crossing frequency (ω c) and the transition frequency (ω τ), which are discussed below in this section. The crossing frequency (ω c), is defined as the frequency where G’ and G” crossed over. It is shown in the inset in the lower left of Fig. 5(a)
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.
. The inverse of the crossing frequency is often referred to as the polymer relaxation time (τR=1/ωc). In the regime where G” is larger than G’, the polymer is expected to behave more like a (dissipative) liquid than an elastic solid; in contrast, in the regime where G” is smaller than G’, the polymer is expected to behave more like an elastic solid than a dissipative liquid.

The transition frequency (ω τ), defined as the frequency where G’(ω) changes from a constant value (independent of frequency) to a power law dependence on frequency (with a positive exponent), is shown in the inset in the lower left in Fig. 5(b), and determined by fitting the experimental data with a power law dependence in each of the two regimes, and subsequently the crossing point of the two fitted lines. We fit our experimental data from 6rad/s to 30rad/s with G(ω)=aω0 to define the constant value regime, and those from 2000rad/s to 6000rad/s with G(ω)=aωb to determine the exponent in the power-law regime. The transition frequency (ω τ) as a function of polymer concentration is shown in Fig. 5(b). Although the general trend of the dependence of the crossing frequency (ω c) and the transition frequency (ω τ) on polymer concentration, as shown in Figs. 5(a) and 5(b), respectively, looks somewhat similar, the physical meaning of latter is not clear and needs further investigation.

4. Summary and conclusions

In this study, we investigated the microrheological properties of NaPSS (Mw = 70kDa) solution with oscillatory optical tweezers to probe its viscoelasticity, in terms of its elastic modulus G’ and loss modulus G” as a function of angular frequency (ω). For polymer concentrations ranging from 0.001mM to 10mM, from dilute to semi-dilute regimes with or without micelles and polymer network formation. The zero-shear-rate viscosity, the crossing frequency, and the transition frequency were defined and determined from the experimental data as a function of polymer concentration. The power law dependence of the zero-shear-rate viscosity on the polymer concentration clearly reveals 3 different concentration regimes, each with a distinct exponent, which is consistent with the formation of micelles structure and polymer network reported in the literatures. Quantitatively, the Critical Micelle Concentration and the polymer overlapping concentration deduced from these results are also comparable to the corresponding values reported in literature. Our experimental results indicate that the rheological behavior of NaPSS solution may be a combination of the transient network and the micelle bridging effect, predicted by the Maxwell model and the Rouse model, respectively. Although a deeper understanding of the physics and the chemistry of the polymer behavior requires further studies, we have clearly demonstrated that subtle structural changes in polymer solutions can be probed by active microrheology with a single particle trapped and oscillated by oscillatory optical tweezers. Potential biological applications in microrheology of bio-fluid samples, available only in very small quantity, such as cerebral-spinal fluid, blood plasma, vitreous and synovial fluids, as well as studies of a large diversity of polyelectrolyte/medium combinations using small amount of solvent and chemicals look very promising.

Acknowledgments

This work is jointly supported by The National Science Council, Taiwan, ROC (Projects No. NSC98-2627-M010-004 & NSC 99-2923-E-010-001-MY3; I-RiCE Program, Project No. NSC-99-2911-I-010-101) and by the Ministry of Education (The Top University Project). Co-authors from France are supported by the Centre National de la Recherche Scientifique (CNRS), the MENRT and thank the Analytical Platform ONIS (granted by the European Community FEDER, Rennes Metropole, Departement Ille et Vilaine and the Région Bretagne). C.-C. Chiang and M.-T. Wei have made equal contributions to this work.

References and links

1.

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

2.

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]

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]

5.

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]

6.

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]

7.

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]

8.

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

9.

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]

10.

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]

11.

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]

12.

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]

13.

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]

14.

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]

15.

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

16.

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]

17.

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]

18.

M.-T. Wei and A. Chiou, “Three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers with a pair of orthogonal tracking beams and the determination of the associated optical force constants,” Opt. Express 13(15), 5798–5806 (2005). [CrossRef] [PubMed]

19.

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]

20.

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]

21.

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]

22.

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]

23.

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

24.

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

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(160.5470) Materials : Polymers
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: March 1, 2011
Revised Manuscript: April 7, 2011
Manuscript Accepted: April 18, 2011
Published: April 21, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Chia-Chun Chiang, Ming-Tzo Wei, Yin-Quan Chen, Pei-Wen Yen, Yi-Chiao Huang, Jun-Yeh Chen, Olivier Lavastre, Husson Guillaume, Darsy Guillaume, and Arthur Chiou, "Optical tweezers based active microrheology of sodium polystyrene sulfonate (NaPSS)," Opt. Express 19, 8847-8854 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8847


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References

  1. D. C. Boris and R. H. Colby, “Rheology of sulfonated polystyrene solutions,” Macromolecules 31(17), 5746–5755 (1998). [CrossRef]
  2. 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]
  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]
  5. 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]
  6. 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]
  7. 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]
  8. M. Sedlák, “Mechanical properties and stability of multimacroion domains in polyelectrolyte solutions,” J. Chem. Phys. 116(12), 5236–5245 (2002). [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. I. Astafieva, X. F. Zhong, and A. Eisenberg, “Critical micellization phenomena in block polyelectrolyte solutions,” Macromolecules 26(26), 7339–7352 (1993). [CrossRef]
  16. 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]
  17. 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]
  18. M.-T. Wei and A. Chiou, “Three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers with a pair of orthogonal tracking beams and the determination of the associated optical force constants,” Opt. Express 13(15), 5798–5806 (2005). [CrossRef] [PubMed]
  19. 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]
  20. 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]
  21. 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]
  22. 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]
  23. J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, 1970).
  24. 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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