Measurement of translational diffusion

Fig. 7.2.13 [Kim2] Radio-frequency and gradient schemes for measurements of translational diffusion in simple liquids, (a) Hahn echo, (b) Stimulated echo, (c) Scheme for PFG NMR.

Caroline and co-workers have recently reported measurements of translational diffusion coefficients in solutions of PS in two mixed-solvent systems at or near theta conditions. In the solvent CCb-methanol (85), they observed the diffusion theta state, defined when the coefficient y of Equation 41 equals 0.5, to occur at 25°C and a volume fraction of CCI4, (fyCCU = 0.8025. In this system there is strong preferential adsorption of the polymer for CCI4, and it is not possible to define a true theta state such that y = a = V2 and A2 = 0 simultaneously. Under diffusion theta conditions, the concentration dependence of Dt apparently is closely described by the Pyun-Fixman hard-sphere model. In the mixed solvent benzene—2 propanol, polystyrene exhibits a true theta condition at T = 25.5°C and (benzene) = 0.04. Frost and Caroline confirmed that y = 0.5 within experimental error in this system (86) and report that values of the parameter fcf are scattered between the extreme values corresponding to the predictions of Yamakawa (and Imai) and the soft-sphere model of Pyun-Fixman (or the Freed theory). 

It should also be noted that a similar treatment is possible for the translational hydrodynamic radius, Rhj, obtained from measurements of translational diffusion coefficients or sedimentation coefficients of branched polymers. One may define a parameter gn = Rh,fb/Rhji - the ratio of the hydrodynamic radius of the branched polymer relative to that of a linear polymer of the same molecular weight. Again, it is expected that gH < 1. For star polymers with uniform subchain lengths having... 

Measurement of translational diffusion in nematics CLASSICAL EXPERIMENTAL METHODS... 

Determination of translational diffusion rates of proteins requires measurements at longer timescales, one-tenth of a second to several minutes. Eosin derivatives are also commonly used to measure translational diffusion coefficients using the Fluorescence Recovery After Photobleaching technique [138-141],... 

The high frequency relaxation is attributed in part to the modulation of intermolecular dipolar interactions by the translational diffusion. The cutoff frequency (60 MHz at 55°C) corresponds to the local diffusive jump frequency that is estimated from measurements of the diffusion coefficient (D 10"6 cm2/sec at 55°) (19, 21). This cutoff frequency also varies in temperature with the same activation energy (Eact 0.25 eV) as the diffusion frequency. 

MD simulation is advantageous for obtaining dynamic properties directly, since the MD technique provides not only particle positions but also particle velocities that enable us to utilize the response theory (e.g., the Kubo formula [175,176]) to calculate the transport coefficients from time-dependent correlation functions. For example, we will examine the self-diffusion process of a tagged PFPE molecular center of mass (Fig. 1.49) from the simulation to gain insight into the excitation of translational motion, specifically, spreading and replenishment. The squared displacement of the center mass of a molecule or a bead is used as a measure of translational movement. The self-diffusion coefficient D can be represented as a velocity autocorrelation function... 

The traditional fluorescence and electron-spin resonance methods for recording molecular collisions do not allow the study of translational diffusion and rare encounters of molecules in a viscous media because of the short characteristic times of these methods. To measure the rate constants of rare encounters between macromolecules and to investigate the translation diffusion of labelled proteins and probes in a medium of high viscosity (like biomembranes), a new triplet-photochrome labeling technique has been developed (Mekler and Likhtenshtein, 1986 Mekler and Umarova, 1988 Likhtenshtein, 1993 Papper and Likhtenshtein, 2001). 

Pulse field gradient (PFG) NMR spectroscopy is now generally regarded as the method of choice for measuring the translational diffusion coefficients of molecules of virtually any type under many conditions (48). H, H, F, and P variants of this method have been used successfully to study lateral diffusion of cholesterol, phospholipids, and water in model membranes (49,50). This technique introduces two identical gradient pulses of the external magnetic field into the standard spin-echo NMR... 

First we will review the relevant NMR techniques and their most recent developments (1) pulsed-field gradient (PFG) NMR (315-18) for the measurement of translational molecular self-diffusion and (2) (6,7,10,19,20)... 

Quasi-elastic laser light scattering (also called intensity fluctuation spectroscopy, light-beating spectroscopy or photon correlation spectroscopy) is an accurate method to measure the translational diffusion coefficients of macromolecules. The diffusion coefficient is a parameter, that depends on the size and shape of the macromolecules and on the thermodynamic and hydrodynamic interaction between the macromolecules. 

Figure 8. The variation of translational diffusion coefficients, Dr, measured by PCS with different sol concentrations for dilute samples of the dialyzed (+) and undialyzed (%) silica sol SI.

Thus, if ti is in a time range accessible to autocorrelation (roughly 1—10—7 sec), fluorescence fluctuations may be used to measure macromolecular translational diffusion coefficients. The presence of a fluorescent label enables this method to measure the translational diffusion coefficient of a molecule in a complex mixture. Such a measurement would be very difficult in an ordinary light-scattering experiment because all components of the mixture contribute.17 The advantage of fluorescent probes is that they allow particular species to be labeled and thereby separately studied. For or of the order of 10 4 cm and for a particle with a diffusion coefficient of the order 10 5 cm2/sec, tt = 10 3 sec, well within our ability to measure. This leads to the interesting possibility of measuring diffusion coefficients of labeled molecules in membranes, and in cells in vivo. 

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