Self-diffusion probe concentration

NMR Self-Diffusion of Desmopressin. The NMR-diffusion technique (3,10) offers a convenient way to measure the translational self-diffusion coefficient of molecules in solution and in isotropic liquid crystalline phases. The technique is nonperturbing, in that it does not require the addition of foreign probe molecules or the creation of a concentration-gradient in the sample it is direct in that it does not involve any model dependent assumptions. Obstruction by objects much smaller than the molecular root-mean-square displacement during A (approx 1 pm), lead to a reduced apparent diffusion coefficient in equation (1) (10). Thus, the NMR-diffusion technique offers a fruitful way to study molecular interactions in liquids (11) and the phase structure of liquid crystalline phases (11,12). 

To date, D coefficients of carbohydrates established with the PFGSE approactf - " have been undertaken to (1) validate the theoretical self-diffusion coefficients calculated from MD trajectories, (2) demonstrate the complexation of lanthanide cations by sugars,(3) probe the geometry of a molecular capsule formed by electrostatic interactions between oppositely charged P-cyclodextrins, (4) study the influence of concentration and temperature dependence on the hydrodynamic properties of disaccharides, and (5) discriminate between extended and folded conformations of nucleotide-sugars. ... 

Local motions which occur in macromolecular systems can be probed from the diffusion process of small molecules in concentrated polymeric solutions. The translational diffusion is detected from NMR over a time scale which may vary from about 1 to 100 ms. Such a time interval corresponds to a very large number of elementary collisions and a long random path consequently, details about mechanisms of molecular jump are not disclosed from this NMR approach. However, the dynamical behaviour of small solvent molecules, immersed in a polymer melt and observed over a long time interval, permits the determination of characteristic parameters of the diffusion process. Applying the Langevin s equation, the self-diffusion coefficient Ds is defined as... 

The alternative NMR approach that has provided information on microemuisions is relaxation. However, on the whole, relaxation has been less informative than anticipated from earlier studies of micellar solutions and has provided little unique information on microemulsion structure, although in the case of droplet structures it is probably the most reliable way of deducing any changes in droplet size and shape, particularly for concentrated systems. The reason for this is that NMR relaxation probes the rotational diffusion of droplets, which is relatively insensitive to interdroplet interactions. This is in contrast to, for example, translational collective and self-diffusion and viscosity which depend strongly on interactions. Furthermore, NMR relaxation is a useful technique for characterizing the local properties of the surfactant film. 

The literature on self-diffusion of polymers in solution, and on tracer diffusion of probe polymers through solutions of matrix polymers, is systematically reviewed. Virtually the entirety of the published experimental data on the concentration dependence of polymer self— and probe- diffusion is represented well by a single functional form. This form is the stretched exponential exp(—ac"), where c is polymer concentration, a is a scaling prefactor, and is a scaling exponent. 

If Dp depends significantly on Cp, extrapolation to Cp 0 must be performed. The initial slope of the dependence of Dp on probe concentration, and the slope s dependence on matrix concentration, have been measured in some systems and should be accessible to theoretical analysis. In this review If the probe and matrix polymers differ appreciably in molecular weight or chemical nature, the phrase probe diffusion coefficient is applied. If the probe and matrix polymers differ primarily in that the probes are labelled, the phrase self diffusion coefficient is applied. The tracer diffusion coefficient is a single-particle diffusion coefficient, including both the self cind probe diffusion coefficients as special cases. The interdiffusion and cooperative diffusion coefficients characterize the relaxation times in a ternary system in which neither m lcrocomponent is dilute. 

Concentration and molecular weight dependences of and Pp for molecular weight P probes in solutions of molecular weight M matrix polymers (for Ps, one has P = M) at concentration c. The fits are to stretched exponentials ><,P exp(—ac P M ), with the percent root-mean-squEire fractional fit error %R, the material, and the reference. Molecular weights are in kDa concentrations except as noted are in g/L. Square brackets ] denote parameters that were fixed rather than floated. Notes (a) Various, with M/P > 10 (b) Various, see text (c) All four probes, see text (d) Excluding styrene monomer, see text (e) Not all data points, see text (f) P = M, self diffusion. 

The above sections summarize a detjuled examination [1] of nearly the entirety of the published literature on polymer self-diffusion and probe diffusion in polymer solutions. Dependences of D, and Dp on polymer concentration, probe molecular weight, and matrix molecular weight were determined. We now attempt to extract systematic behaviors from the above particular results, asking What features are common to self- and probe-diffusion of all polymers in solution ... 

First, the above summarized the published literature on self-diffusion and probe diffusion of random-coil polymers in solution. The concentration dependences of > and Dp are essentially always described well by a stretched exponential (eq. 15) in the matrix concentration c. On a log-log plot of D, against c, stretched exponentials appear as smooth curves, while scaling ( power-law) behavior leads to straight lines. Almost without exception, log-log plots of measured D,(c) give smooth curves, not straight lines. Correspondingly, the hypothesis that the concentration dependence of D, c) shows scaling ( power-law) behavior is uniformly rejected by the published literature. 

In the above, virtually the entirety of the published literature on polymer self-diffusion and on the diffusion of chain probes in polymer solutions has been reviewed. Without exception the concentration dependences of Dg and Dp are described by stretched exponentials in polymer concentration. The measured molecular weight dependences compare favorably with the elaborated stretched exponential, eq. 16, except that, when P M or M P, there is a deviation from eq. 16, that deviation referring only to the molecular weight dependences. The deviation uniformly has the same form The elaborated stretched exponential overestimates the concentration dependence of Dp, so that at elevated c the predicted Dp/Do is less than the measured Dp/Dp. Contrarywise, almost without exception the experimental data on solutions is inconsistent with models that... 

Mandal, A. B. Nair, B. C. U. Cyclic Voltammetric Technique for the Determination of the Critical Micelle Concentration of Surfactants, Self-diffusion Coefficient of the Micelles and Partition Coefficient of an Electrochemical Probe. /. Phi/s. Chem., 1991, 95, 9008-9013. 

When multiple scattering is discarded from the measured signal, DLS can be used to study the dynamics of concentrated suspensions, in which the Brownian motion of individual particles (self-diffusion) differs from the diffusive mass transport (gradient or collective diffusion), which causes local density fluctuations, and where the diffusion on very short time-scales (r < c lD) deviates from those on large time scales (r c D lones and Pusey 1991 Banchio et al. 2000). These different diffusion coefficients depend on the microstructure of the suspension, i.e. on the particle concentration and on the interparticle forces. For an unknown suspension it is not possible to state a priori which of them is probed by a DLS experiment. For this reason, a further concentration limit must be obeyed when DLS is used for basic characterisation tasks such as particle sizing. As a rule of thumb, such concentration effects vanish below concentrations of 0.01-0.1 vol%, but certainty can only be gained by experiment. 

Nuclear magnetic resonance (NMR) spectrometers offer spectral capabilities to elucidate polymeric structures. This approach can be used to perform experiments to determine comonomer sequence distributions of polymer products. Furthermore, the NMR can be equipped with pulsed-liied gradient technology (PFG-NMR), which not only allows one to determine self-diffusion coefficients of molecules to better understand complexation mechanisms between a chemical and certain polymers, but also can reduce experimental time for acquiring NMR data. Some NMR instruments can be equipped with a microprobe to be able to detect microgram quantities of samples for analysis. This probe has proven quite useful in GPC/NMR studies on polymers. Examples include both comonomer concentration and sequence distribution for copolymers across their respective molecular-weight distributions and chemical compositions. The GPC interface can also be used on an HPLC, permitting LC-NMR analysis to be performed too. Solid-state accessories also make it possible to study cross-linked polymers by NMR. 

For highly concentrated polymer solutions, FCS measurements revealed subdiffusive motion as an additional mode on an intermediate timescale between the fast collective diffusion and the slow self-diffusion [24]. In such slow systems, however, FCS reaches its limits when probe motion becomes so slow that the number of molecules moving into or out of the confocal volume within the measurement time is too small to allow for reliable statistics. Increasing the measurement time is often not straightforward since all fluorescence dyes have only a limited photostability. If a dye bleaches within the confocal volume, it will fake a faster diffusional motion than its real value. Therefore, for the study of such concentrated systems, wide-field fluorescence microscopy and subsequent single molecule tracking is a much better method [120] and has been utilized to study the glass transition [87, 121]. 

Translational motions of solvent and other small molecules in polymer solutions are quite different from their behaviors in viscous liquids. The self-diffusion coefficient of the solvent has a transition at a polymer volume fraction 0.4. At smaller (j), Ds follows a simple exponential exp(-a) in polymer concentration, but at larger Ds(c) follows a stretched exponential with large exponent. The exponential factor a is independent of polymer molecular weight, while rj depends strongly on M, so Ds and A must be nearly independent of solution rj. Probes somewhat... 

E. D. von Meerwall, E. J. Amis, and J. D. Ferry. Self-diffusion in solutions of polystyrene in tetrahydrofuran Comparison of concentration dependences of the diffusion coefficient of polymer, solvent, and a ternary probe component. Macromolecules, 18(1985), 260-266. 

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