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  • Print publication year: 2011
  • Online publication date: August 2012

9 - Probe diffusion

Summary

Introduction

This chapter examines the diffusion of mesoscopic rigid probe particles through polymer solutions. These measurements form a valuable complement to studies of polymer self- and tracer diffusion, and to studies of self- and tracer diffusion in colloid suspensions. Any properties that are common to probe diffusion and polymer self-diffusion cannot arise from the flexibility of the polymer probes or from their ability to be interpenetrated by neighboring matrix chains. Any properties that are common to probe diffusion and to colloid diffusion cannot arise from the flexibility of the matrix polymers or from the ability of matrix chains to interpenetrate each other. Conversely, phenomena that require that the probe and matrix macromolecules be able to change shape or to interpenetrate each other will reveal themselves in the differences between probe diffusion, single-chain diffusion, and colloid single-particle diffusion.

In a probe diffusion experiment, one examines the motions of dilute mesoscopic particles dispersed in a polymer solution. In some systems, a single relaxation is found. In others, probe motions involve multiple relaxation processes. Probe diffusion is sensitive to the probe radius R, matrix polymer molecular weight M and concentration c, solution viscosity η, solvent viscosity ηs, and other variables.

The literature examined here includes three major experimental approaches, namely (i) optical probe diffusion studies, largely made with quasi elastic light scattering spectroscopy (QELSS), to observe diffusion of dilute probe particles, (ii) particle tracking studies in which the detailed motions of individual particles are recorded, and (iii) true microrheology measurements of the driven motion of mesoscopic probes.

References
[1] D. N., Turner and F. R., Hallett. Astudy of the diffusion of compact particles in polymer solutions using quasi-elastic light scattering. Biochimica et Biophysica Acta, 451 (1976), 305–312.
[2] M. J., Saxton and K., Jacobson. Single particle tracking: applications to membrane dynamics. Annu. Rev. Biophys. Biomol. Struct., 26 (1997), 373–399.
[3] D. A., Weitz and D. J., Pine. Diffusing-wave spectroscopy. In Dynamic Light Scattering. Ed. W., Brown, (Oxford, UK: Oxford University Press, 1993) 652–720.
[4] B. J., Berne and R., Pecora. Dynamic Light Scattering, (New York: Wiley, 1976), especially Chapter 5.
[5] J. L., Doob. The Brownian movement and stochastic equations. Annals Math., 43 (1942), 351–369.
[6] G. D. J., Phillies. Interpretation of light scattering spectra in terms of particle displacements. J. Chem. Phys., 122 (2005), 224905 1–8.
[7] A. M., Jamieson, J. G., Southwick, and J., Blackwell. Dynamical behavior of xan-than polysaccharide in solution. J. Polymer Sci.: Polymer Phys. Ed., 20 (1982), 1513–1524.
[8] T.-H., Lin and G. D. J., Phillies. Translational diffusion of a macroparticulate probe species in salt-free poly(acrylic) acid : water. J. Phys. Chem., 86 (1982), 4073–4077.
[9] T.-H., Lin and G. D. J., Phillies. Probe diffusion in poly(acrylic acid) : water. Effect of probe size. Macromolecules, 17 (1984), 1686–1691.
[10] T.-H., Lin and G. D. J., Phillies. Probe diffusion in polyacrylic acid : water – effect of polymer molecular weight. J. Coll. Interf. Sci., 100 (1984), 82–95.
[11] T.-H., Lin. Diffusion of TiO2 particles through a poly(ethylene oxide) melt. Makromol. Chem., 187 (1986), 1189–1196.
[12] G. D. J., Phillies, J., Gong, L., Li, et al.Macroparticle diffusion in dextran solutions. J. Phys. Chem., 93 (1989), 6219–6223.
[13] R., Furukawa, J. L., Arauz-Lara, and B. R., Ware. Self-diffusion and probe diffusion in dilute and semidilute solutions of dextran. Macromolecules, 24 (1991), 599–605.
[14] O.A., Nehme, P., Johnson, and A. M., Donald. Probe diffusion in poly-l-lysine solution. Macromolecules, 22 (1989), 4326–4333.
[15] W., Brown and R., Rymden. Interaction of carboxymethylcellulose with latex spheres studied by dynamic light scattering. Macromolecules, 20 (1987), 2867–2873.
[16] W., Brown and R., Rymden. Comparison of the translational diffusion of large spheres and high molecular weight coils in polymer solutions. Macromolecules, 21 (1988), 840–846.
[17] S. C., Smedt, A., Lauwers, J., Demeester, et al.Structural information on hyaluronic acid solutions as studied by probe diffusion experiments. Macromolecules, 27 (1994), 141–146.
[18] S. C., Smedt, P., Dekeyser, V., Ribitsch, A., Lauwers, and J., Demeester. Viscoelastic and transient network properties of hyaluronic acid as a function of the concentration. Biorheology, 30 (1994), 31–42.
[19] C. N., Onyenemezu, D., Gold, M., Roman, and W. G., Miller. Diffusion of polystyrene latex spheres in linear polystyrene nonaqueous solutions. Macromolecules, 26 (1993), 3833–3837.
[20] P., Zhou and W., Brown. Translational diffusion of large silica spheres in semidilute polymer solutions. Macromolecules, 22 (1989), 890–896.
[21] X., Cao, R., Bansil, D., Gantz, et al.Diffusion behavior of lipid vesicles in entangled polymer solutions. Biophys. J., 73 (1997), 1932–1939.
[22] Z., Bu and P. S., Russo. Diffusion of dextran in aqueous hydroxypropylcellulose. Macromolecules, 27 (1994), 1187–1194.
[23] D., Langevin and F., Rondelez. Sedimentation of large colloidal particles through semidilute polymer solutions. Polymer, 19 (1978), 875–882.
[24] Y., Cheng, R. K., Prud'homme, and J. L., Thomas. Diffusion of mesoscopic probes in aqueous polymer solutions measured by fluorescence recovery after photobleaching. Macromolecules, 35 (2002), 8111–8121.
[25] N. A., Busch, T., Kim, and V. A., Bloomfield. Tracer diffusion of proteins in DNA solutions. 2. Green fluorescent protein in crowded DNA solutions. Macromolecules, 33 (2000), 5932–5937.
[26] M. R., Wattenbarger, V. A., Bloomfield, B., Zu, and P. S., Russo. Tracer diffusion of proteins in DNA solutions. Macromolecules, 25 (1992), 5263–5265.
[27] G. D. J., Phillies, Diffusion of bovine serum albumin in a neutral polymer solution. Biopolymers, 24 (1985), 379–386.
[28] K., Ullmann, G. S., Ullmann, and G. D. J., Phillies. Optical probe study of a nonentangling macromolecule solution – bovine serum albumin : water. J. Coll. Interf. Sci., 105 (1985), 315–324.
[29] K. M., Keller, E. R., Canales, and S. I., Yum. Tracer and mutual diffusion coefficients of proteins. J. Phys. Chem., 75 (1971), 379–387.
[30] R. G., Kitchen, B. N., Preston, and J. D., Wells. Diffusion and sedimentation of serum albumin in concentrated solutions. J. Polym. Sci., 55 (1976), 39–49.
[31] G. S., Ullmann and G. D. J., Phillies. Implications of the failure of the Stokes–Einstein relation for measurements with QELSS of polymer adsorption by small particles. Macromolecules, 16 (1983), 1947–1949.
[32] G. S., Ullmann, K., Ullmann, R. M., Lindner, and G. D. J., Phillies. Probe diffusion of polystyrene latex spheres in poly(ethylene oxide) : water. J. Phys. Chem., 89 (1985), 692–700.
[33] J., Won, C., Onyenemezu, W. G., Miller, and T. P., Lodge. Diffusion of spheres in entangled polymer solutions: a return to Stokes–Einstein behavior. Macromolecules, 27 (1994), 7389–7396.
[34] C., Konak, B., Sedlacek, and Z., Tuzar. Diffusion of block copolymer micelles in solutions of a linear polymer. Makromol. Chem., Rapid Commun., 3 (1982), 91–94.
[35] K. E., Bremmell, N., Wissenden, and D. E., Dunstan. Diffusing probe measurements in Newtonian and elastic solutions. Adv. Coll. Interf. Sci., 89–90 (2001), 141–154.
[36] K. E., Bremmell and D. E., Dunstan. Probe diffusion measurements of polystyrene latex particles in polyelectrolyte solutions of varying ionic strength. Macromolecules, 35 (2002), 1994–1999.
[37] D. E., Dunstan and J., Stokes. Diffusing probe measurements in polystyrene latex particles in polyelectrolyte solutions: deviations from Stokes–Einstein behavior. Macromolecules, 33 (2000), 193–198.
[38] I., Delfino, C., Piccolo, and K., Lepore. Experimental study of short- and long-time diffusion regimes of spherical particles in carboxymethylcellulose solutions. Eur. Polym. J., 41 (2005), 1772–1780.
[39] S., Gorti and B. R., Ware. Probe diffusion in an aqueous polyelectrolyte solution. J. Chem. Phys., 83 (1985), 6449–6456.
[40] S. C., Lin, W. I., Lee, and J. M., Schurr. Brownian motion of highly charged poly(l-lysine). Effects of salt and polyion concentration. Biopolymers, 17 (1978), 1041–1064.
[41] G. D. J., Phillies, C., Malone, K., Ullmann, et al.Probe diffusion in solutions of long-chain polyelectrolytes. Macromolecules, 20 (1987), 2280–2289.
[42] G. D. J., Phillies, T., Pirnat, M., Kiss, et al.Probe diffusion in solutions of low-molecular-weight polyelectrolytes. Macromolecules, 22 (1989), 4068–4075.
[43] G. D. J., Phillies, M., Lacroix, and J., Yambert. Probe diffusion in sodium polystyrene sulfonate–water: experimental determination of sphere–chain binary hydrodynamic interactions. J. Phys. Chem., 101 (1997), 5124–5130.
[44] G. D. J., Phillies and P. C., Kirkitelos. Higher-order hydrodynamic interactions in the calculation of polymer transport properties. J. Polymer Sci. B: Polymer Physics, 31 (1993), 1785–1797.
[45] D., Gold, C., Onyenemezu, and W. G., Miller. Effect of solvent quality on the diffusion of polystyrene latex spheres in solutions of poly(methylmethacrylate). Macromolecules, 29 (1996), 5700–5709.
[46] G. D. J., Phillies and D., Clomenil. Probe diffusion in polymer solutions under θ and good conditions. Macromolecules, 26 (1993), 167–170.
[47] A. R., Altenberger, M., Tirrell, and J. S., Dahler. Hydrodynamic screening and particle dynamics in porous media, semidilute polymer solutions and polymer gels. J. Chem. Phys., 84 (1986), 5122–5130.
[48] G. D. J., Phillies. Dynamics of polymers in concentrated solution: the universal scaling equation derived. Macromolecules, 20 (1987), 558–564.
[49] G. D. J., Phillies and P., Peczak. The ubiquity of stretched-exponential forms in polymer dynamics. Macromolecules, 21 (1988), 214–220.
[50] G. D. J., Phillies, A., Saleh, L., Li, et al.Temperature dependence of probe diffusion in solutions of low-molecular-weight polyelectrolytes. Macromolecules, 24 (1991), 5299–5304.
[51] G. D. J., Phillies, D., Rostcheck, and S., Ahmed. Probe diffusion in intermediate-molecular-weight polyelectrolytes: temperature dependence. Macromolecules, 25 (1992), 3689–3694.
[52] G. D. J., Phillies and C. A., Quinlan. Glass temperature effects in probe diffusion in dextran solutions. Macromolecules, 25 (1992), 3110–3116.
[53] G. D. J., Phillies and C. A., Quinlan. Analytic structure of the solutionlike–meltlike transition in polymer solution dynamics. Macromolecules, 28 (1995), 160–164.
[54] G. D. J., Phillies. Range of validity of the hydrodynamic scaling model. J. Phys. Chem., 96 (1992), 10061–10066.
[55] G. D. J., Phillies. Quantitative prediction of α in the scaling law for self-diffusion. Macromolecules, 21 (1988), 3101–3106.
[56] W., Brown and R., Rymden. Diffusion of polystyrene latex spheres in polymer solutions studied by dynamic light scattering. Macromolecules, 19 (1986), 2942–2952.
[57] T., Yang and A. M., Jamieson. Diffusion of latex spheres through solutions of hydroxypropylcellulose in water. J. Coll. Interf. Sci., 126 (1988), 220–230.
[58] P. S., Russo, M., Mustafa, T., Cao, and L. K., Stephens. Interactions between polystyrene latex spheres and a semiflexible polymer, hydroxypropylcellulose. J. Coll. Interf. Sci., 122 (1988), 120–137.
[59] M., Mustafa and P. S., Russo. Nature and effects of nonexponential correlation functions in probe diffusion experiments by quasielastic light scattering. J. Coll. Interf. Sci., 129 (1989), 240–253.
[60] G. D. J., Phillies, C., Richardson, C. A., Quinlan, and S. Z., Ren. Transport in intermediate and high molecular weight hydroxypropylcellulose/water solutions. Macromolecules, 26 (1993), 6849–6858.
[61] K. L., Ngai and G. D. J., Phillies. Coupling model analysis of polymer dynamics in solution: probe diffusion and viscosity. J. Chem. Phys., 105 (1996), 8385–8397.
[62] K. L., Ngai. In Disorder Effects In Relaxation Processes. Eds. R., Richert and A., Blumen, (Berlin, Germany: Springer-Verlag, 1994).
[63] G. D. J., Phillies and M., Lacroix. Probe diffusion in hydroxypropylcellulose–water: Radius and line-shape effects in the solutionlike regime. J. Phys. Chem. B, 101 (1997), 39–47.
[64] K. A., Streletzky and G. D. J., Phillies. Translational diffusion of small and large mesoscopic probes in hydroxypropylcellulose–water in the solutionlike regime. J. Chem. Phys., 108 (1998), 2975–2988.
[65] K. A., Streletzky and G. D. J., Phillies. Relaxational mode structure for optical probe diffusion in high molecular weight hydroxypropylcellulose. J. Polym. Sci. B, 36 (1998), 3087–3100.
[66] K. A., Streletzky and G. D. J., Phillies. Confirmation of the reality of the viscoelastic solutionlike–meltlike transition via optical probe diffusion. Macromolecules, 32 (1999), 145–152.
[67] K. A., Streletzky and G. D. J., Phillies. Coupling analysis of probe diffusion in high molecular weight hydroxypropylcellulose. J. Phys. Chem. B, 103 (1999), 1811–1820.
[68] K. A., Streletzky and G. D. J., Phillies. Optical probe study of solution-like and melt-like solutions of high molecular weight hydroxypropylcellulose. In Scattering from Polymers. Ed. B.S., Hsiao, (Washington, D.C.: Am. Chem. Soc. Symp. Ser., 2000) 739, 297–316.
[69] G. D. J., Phillies, R., O'Connell, P., Whitford, and K. A., Streletzky. Mode structure of diffusive transport in hydroxypropylcellulose : water. J. Chem. Phys., 119 (2003), 9903–9913.
[70] R., O'Connell, H., Hanson, and G. D. J., Phillies. Neutral polymer slow mode and its rheological correlate. J. Polym. Sci. B. Polym. Phys., 43 (2005), 323–333.
[71] S. A., Kivelson, X., Zhao, D., Kivelson, T. M., Fischer, and C. M., Knobler. Frustration-limited clusters in liquids. J. Chem. Phys., 101 (1994), 2391–2397.
[72] G. H., Koenderink, S., Sacanna, D. G. A. L., Aarts, and A. P., Philipse. Rotational and translational diffusion of fluorocarbon tracer spheres in semidilute xanthan solutions. Phys. Rev. E, 69 (2004), 021804 1–12.
[73] R., Cush, D., Dorman, and P. S., Russo. Rotational and translational diffusion of tobacco mosaic virus in extended and globular polymer solutions. Macromolecules, 37 (2004), 9577–9584.
[74] R., Cush, P. S., Russo, Z., Kucukyavuz, et al.Rotational and translational diffusion of a rodlike virus in random coil polymer solutions. Macromolecules, 30 (1997), 4920–4926.
[75] T., Jamil and P. S., Russo. Interactions between colloidal poly(tetrafluoroethylene) latex and sodium poly(styrenesulfonate). Langmuir, 14 (1998), 264–270.
[76] J. G., Phalakornkul,A. P., Gast, and R., Pecora. Rotational dynamics of rodlike polymers in a rod/sphere mixture. J. Chem. Phys., 112 (2000), 6487–6494.
[77] G. D. J., Phillies, W., Brown, and P., Zhou. Chain and sphere diffusion in polyisobutylene–CHCl3: A reanalysis. Macromolecules, 25 (1982), 4948–4954.
[78] W., Brown and P., Zhou. Dynamic behavior in ternary polymer solutions. Polyisobutylene in chloroform studied using dynamic light scattering and pulsed field gradient NMR. Macromolecules, 22 (1989), 4031–4039.
[79] P., Zhou and W., Brown. Translational diffusion of large silica spheres in semidilute polyisobutylene solutions. Macromolecules, 22 (1989), 890–896.
[80] J., Apgar, Y., Tseng, E., Federov, et al.Multiple-particle tracking measurements of heterogeneities in solutions of actin filaments and actin bundles. Biophys. J., 79 (2000), 1095–1106.
[81] Y., Tseng and D., Wirtz. Mechanics and multiple-particle tracking microheterogeneity of α-actinin-cross-linked actin filament networks, Biophys. J., 81 (2001), 1643–1656.
[82] J. C., Crocker, M. T., Valentine, E. R., Weeks, et al.Two-point microrheology of inhomogeneous soft materials. Phys. Rev. Lett., 85 (2000), 888–891.
[83] M. L., Gardel, M. T., Valentine, J. C., Crocker, A. R., Bausch, and D. A., Weitz. Microrheology of entangled F-actin solutions. Phys. Rev. Lett., 91 (2003), 158302 1–4.
[84] D. T., Chen, E. R., Weeks, J. C., Crocker, et al.Rheological microscopy: local mechanical properties from microrheology. Phys. Rev. Lett., 90 (2003), 108301 1–4.
[85] A. J., Levine and T. C., Lubensky. Two-point microrheology and the electrostatic analogy. Phys. Rev. E, 65 (2001), 011501 1–13.
[86] M. A., Dichtl and E., Sackmann. Colloidal probe study of short time local and long time reptational motion of semiflexible macromolecules in entangled networks. New J. Physics, 1 (1999), 18.1–18.11.
[87] A., Goodman, Y., Tseng, and D., Wirtz. Effect of length, topology, and concentration on the microviscosity and microheterogeneity of DNA solutions. J. Mol. Bio., 323 (2002), 199–215.
[88] A. W. C., Lau, B. D., Hoffman, A., Davies, J. C., Crocker, and T. C., Lubensky. Microrheology, stress fluctuations, and active behavior of living cells. Phys. Rev. Lett., 91 (2003), 198101 1–4.
[89] A., Papagiannopolis, C. M., Ferneyhough, and T. A., Waigh. The microrheology of polystyrene sulfonate combs in aqueous solution. J. Chem. Phys., 123 (2005), 214904 1–10.
[90] B., Schnurr, F., Gittes, F. C., MacKintosh, and C. F., Schmidt. Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations. Macromolecules, 30 (1997), 7781–7792.
[91] M. T., Valentine, Z. E., Perlman, M. L., Gardel, et al.Colloid surface chemistry critically affects multiple particle tracking measurements of biomaterials. Biophys. J., 86 (2004), 4004–4014.
[92] Z., Cheng and T. G., Mason. Rotational diffusion microrheology. Phys. Rev. Lett., 90 (2003), 018304 1–4.
[93] D.A., Hill and D. S., Soane. Measurement of rotational diffusivity of rodlike molecules in amorphous polymer matrices by the dynamic Kerr effect. J. Polymer Science B, 27 (1989), 2295–2320.
[94] J., Xu, Y., Tseng, C. J., Carriere, and D., Wirtz. Microheterogeneity and microrheology of wheat gliadin suspensions studied by multiple-particle tracking. Biomacro-molecules, 3 (2002), 92–99.
[95] F., Amblard, A. C., Maggs, B., Yurke, A. N., Pargellis, and S., Leibler. Subdiffusion and anomalous local viscoelasticity in actin networks. Phys. Rev. Lett., 77 (1996), 4470–4473.
[96] A. I., Bishop, T. A., Nieminen, N. R., Heckenberg, and H., Rubinsztein-Dunlop. Optical microrheology using rotating laser-trapped particles. Phys. Rev. Lett., 92 (2004), 198104 1–4.
[97] L.A., Hough and H. D., Ou-Yang. Anew probe for mechanical testing of nanostructures in soft materials. J. Nanoparticle Research, 1 (1999), 495–499.
[98] F. G., Schmidt, B., Hinner, and E., Sackmann. Microrheometry underestimates the values of the viscoelastic moduli in measurements on F-actin solutions compared to macrorheometry. Phys. Rev. E, 61 (2000), 5646–5653.
[99] M., Keller, J., Schilling, and E., Sackmann. Oscillatory magnetic bead rheometer for complex fluid microrheometry. Rev. Sci. Instr., 72 (2001), 3626–3634.
[100] A. C., Maggs. Micro-bead mechanics with actin filaments. Phys. Rev. E, 57 (1998), 2091–2094.
[101] F. G., Schmidt, B., Hinner, E., Sackmann, and J. X., Tang. Viscoelastic properties of semiflexible filamentous bacteriophage fd. Phys. Rev. E, 62 (2000), 5509–5517.
[102] D., Morse. Viscoelasticity of concentrated isotropic solutions of semiflexible polymers. 2. Linear response. Macromolecules, 31 (1998), 7044–7067.
[103] F., Madonia, P. L. San, Biagio, M. U., Palma, et al.Photon scattering as a probe of microviscosity and channel size in gels such as sickle haemoglobin. Nature, 302 (1983), 412–415.
[104] L., Johansson, U., Skantze, and J.-E., Loefroth. Diffusion and interaction in gels and solutions. 2. Experimental results on the obstruction effect. Macromolecules, 24 (1991), 6019–6023.
[105] I. H., Park, C. S., Johnson Jr., and D. A., Gabriel. Probe diffusion in polyacrylamide gels as observed by means of holographic relaxation methods: search for a universal equation. Macromolecules, 23 (1990), 1548–1553.
[106] J. Newman, N. Mroczka, and K. L., Schick. Dynamic light scattering measurements of the diffusion of probes in filamentatious actin solutions. Biopolymers, 28 (1989), 655–666.
[107] C. F., Schmidt, M., Baermann, G., Isenberg, and E., Sackmann. Chain dynamics, mesh size, and diffusive transport in networks of polymerized actin. A quasielastic light scattering and microfluorescence study. Macromolecules, 22 (1989), 3638–3649.
[108] K., Luby-Phelps, P. E., Castle, D. L., Taylor, and F., Lanni. Hindered diffusion of inert tracer particles in the cytoplasm of mouse 3T3 cells. Proc. Natl. Acad. Sci., 84 (1987), 4910–4913.
[109] M., Arrio-Dupont, S., Cribier, J., Foucault, P. F., Devaux, and A., D'Albis. Diffusion of fluorescently labelled macromolecules in cultured muscle cells. Biophys. J., 70 (1996), 2327–2332.
[110] M., Arrio-Dupont, G., Foucault, M., Vacher, P. F., Devaux, and S., Cribier. Translational diffusion of globular proteins in the cytoplasm of cultured muscle cells. Biophys. J., 78 (2000), 901–907.
[111] L., Hou, F., Lanni, and K., Luby-Phelps. Tracer diffusion in F-actin and ficoll mixtures. Toward a model for cytoplasm. Biophys. J., 58 (1990), 31–43.
[112] I. M., Wong, M. L., Gardel, D. R., Reichman, et al.Anomalous diffusion probes microstructure dynamics of entangled F-actin networks. Phys. Rev. Lett., 92 (2004), 178101 1–4.
[113] L. F., Rojas-Ochoa, S., Romer, F., Scheffold, and P., Schurtenberger. Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions. Phys. Rev. E, 65 (2002), 051403 1–8.
[114] For this insight I must thank the late P. J. Elving, Professor of Analytical Chemistry, the University of Michigan. Private communication.
[115] P. D., Kaplan, A. G., Yodh, and D. F., Townsend. Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light. J. Coll. Interf. Sci., 155 (1993), 319–324.
[116] G., Popescu, A., Dogariu, and R., Rajagopalan. Spatially resolved microrheology using localized coherence volumes. Phys. Rev. E, 65 (2002), 041504 1–8.
[117] G., Popescu and A., Dogariu. Dynamic light scattering in localized coherence volumes. Optics Letters, 26 (2001), 551–553.
[118] I. S., Sohn, R. Rajagopalan, and A. C., Dogariu. Spatially resolved microrheology through a liquid/liquid interface. J. Coll. Interf. Sci., 269 (2004), 503–513.
[119] M. H., Kao, A. G., Yodh, and D. J., Pine. Observation of Brownian motion on the time scale of hydrodynamic interactions. Phys. Rev. Lett., 70 (1993), 242–245.
[120] P.-G., Gennes. Scaling Concepts in Polymer Physics. Third Printing, (Ithaca, NY: Cornell UP, 1988).