Direct observation of single molecule mobility in semidilute polymer solutions

Abstract

We determine the mobility of dye-labeled polystyrene molecules in solution by fluorescence correlation spectroscopy (FCS) over a wide range of concentrations and molecular weights (ranging from 3.9 x 10{3} to 1550 x 10{3} g/mol ). In order to obtain absolute values of the diffusion coefficient, which can be compared to diffusion coefficients determined by other methods, the size of the focal volume has been determined by independent experiments and theoretical calculations. All data demonstrate that FCS is uniquely suited to explore polymer dynamics in solution. The mobility of the chains as expressed through the self-diffusion coefficient is significantly slowed down above the overlap concentration c{*}. The dependence of c{*} on molecular weight is well described by the power law c{*} proportional, variant M{w};{1-3nu} ( nu: Flory exponent). A comparison with the data taken from the literature demonstrates that the overlap concentration presents a robust concept that holds for a wide range of molecular weights.

Self-Diffusion and Cooperative Diffusion in Semidilute Polymer Solutions As Measured by Fluorescence Correlation Spectroscopy

“…This crosscorrelation is necessary to prevent distortion of the fluorescence correlation function by detector afterpulsing. 25 For details of the FCSmeasurements see refs 11,12,23 . Cooperative diffusion coefficients D c were measured by DLS using an ALV 4000 light scattering goniometer (Peter, Germany).…”

“…[3][4][5][6][7] The obvious importance of diffusion in polymer physics has led to a rather large number of studies of D c by dynamic light scattering (DLS), [3][4][5][6][7][8][9] while D s can be obtained by pulsedfield gradient nuclear magnetic resonance 4,6,7 and label techniques like forced Rayleigh scattering 10 or fluorescence correlation spectroscopy (FCS). [11][12][13] However, in many cases D s and D c could not be obtained for the same homopolymer using the same technique. Such measurements would be very interesting since a central problem in the dynamics of semidilute entangled polymer solutions is the quantitative understanding of the interplay of self-diffusion and cooperative diffusion.…”

“…Given these problems, the use of FCS for measurements of D s on synthetic polymers has been scarce so far. [11][12][13]18 Moreover, the full potential of this method has not yet fully been exploited yet since FCS should also allow one to obtain D c .…”

“…2 If only a few of the molecules are fluorescently labeled, the self-diffusion coefficient D s can be measured in the FCS experiment. 12 If all of the molecules are fluorescently labeled, the cooperative diffusion coefficient D c can be obtained. 19 In the case that neither of these limits applies, both the self mode and the cooperative mode will be present in the spectrum of the autocorrelation function.…”

“…FCS is not only sensitive to intensity fluctuations due to the motion of labled molecules but also due to photokinetic processes of the fluorescent dyes which occur for short times τ 5 × 10 −3 ms. This additional relaxation has been taken into account as discussed in refs 11,12,21 . DLS allows one to measure the time dependent autocorrelation function of the scattered electric field which can be expressed in terms of the elements of the fluid polarizability tensor.…”