Polymer probe diffusion

Tittel J, Kettner R, Basche T, Brauchle C, Quante FI and Mullen K 1995 Spectral diffusion in an amorphous polymer probed by single molecule spectroscopy J. Lumin. 64 1-11... 

D = D° exp(-ac ), where D is the diffusion, D represents the zero-concentration limit, c is the concentration, a and v are parameters, fits the data from a wide variety of probes and matrix polymers ( ). Several theoretical justifications for this behavior have been presented (97-1011. but it is not possible to tell yet which, if any, is uniquely correct. The treatments range from simple physical considerations (98) to treatments of hydrodynsumical interaction of probe and matrix (97,991. Other more complex and general treatments (1001 do not explicitly arrive at the stretched exponential form, but do closely fit the available data. Much more work needs to be done on probe diffusion in such transient networks. Beyond enhancing the arsenal of gel characterization, the problem is quite fundamental to a number of other important processes. 

Spatial Inhomogeneity of Cavities in Polymer Network Systems as Characterised by Field-Gradient NMR Using Probe Diffusant Molecules and Polymers with Different Sizes... 

The use of inverse gas chromatography (IGC) to study the properties of polymers has greatly increased in recent years (1,2). The shape and position of the elution peak contain information about all processes that occur in the column diffusion of the probe in the gas and the polymer phases, partitioning between phases, and adsorption on the surface of the polymer and the support. Traditional IGC experiments aim at obtaining symmetrical peaks, which can be analyzed using the van Deemter (3j or moments method (4). However, the behavior of the polymer-probe system is also reflected in the asymmetry of the peak and its tail. A method that could be used to analyze a peak of any shape, allowing elucidation of all the processes on the column, would be of great use. 

When probed on time scales smaller than tq, the polymer essentially does not move and exhibits elastic response. On time scales longer than tr, the polymer moves diffusively and exhibits the response of a simple liquid. For intermediate time scales tq < < i r, fhe chain exhibits interesting viscoelasticity discussed in Section 8.4.1. 

Phillies, G.D.J. and Clomenil, D. Probe diffusion in polymer solutions under Q and good conditions. Macromolecules, 26, 167, 1993. 

Styrene DODAB 1 2 Sonication CHP/Ee(II), 50 °C Hollow polymer spheres TEM, SEM, paramagnetic probe diffusion Kurja et al. (1993) [8]... 

Probe diffusion rates observed from parachutes or hollow polymer spheres may be indistinguishable since the probe could be bound in either a polymer bead or polymer shell with similar release characteristics. For example, only hydrophobic probes could be trapped in the polymerized vesicles synthesized by Nakache et al. Here, trapping refers to a decrease in the rate of probe release after vesicle polymerization. The trans-membrane diffusion rates of hydrophilic probes should decrease following polymerization if a polymer shell is successfully formed in the surfactant bilayer. Nakache et al. only observed a decrease in the trans-membrane diffusion rate of hydrophobic probes. This is important since the hydrophobic probe may be released from both hollow polymer spheres and polymer latices with similar release kinetics. Again, caution should be taken, as already shown by German et al. [20] in the case of the fluorescence... 

Of all the characterization methods employed to study the morphologies of polymerized vesicles, cryo TEM is perhaps the most powerful. SEM, freeze fracture TEM, QLS, and probe diffusion studies alone cannot adequately distinguish between the polymer morphologies that have been proven to occur such as between hollow polymer shells and phase separated polymer-vesicle systems. 

This approach—which uses Brinkman s equation, with an appropriate correlation to permit estimation of the hydraulic permeability from the structural characteristics of the medium—provides a straightforward method for estimating the influence of hydrodynamic screening in polymer solutions predicted diffusion coefficients for probes of 3.4 and 10 nm in dextran solutions (Pf = 1 nm) are shown in Figure 4.9. This approach should be valid for cases in which probe diffusion is much more rapid than the movement of fibers in the network, although it appears to work well for BSA diffusion in dextran solutions, even though the dextran molecules diffuse as quickly as the BSA probes [54]. 

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. 

Section 2 presents nomenclature and a theoretical background. Sections 3 cind 4 review, respectively, (i) self-diffusion of polymers in solution and (ii) probe diffusion through polymer solutions. Section 5 notes other experimental papers that do not lend themselves to our analytic approach. Section 6 treats experimented studies on polymers in porous media and true gels. Section 7 treats universal phenomenological features in our lncdysis. Section 8 summarizes conclusions. 

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. 

Schweizer and collaborators have elaborated an extensive mode-coupling model of polymer dynamics [52-54]. The model does not make obvious assumptions about the nature of polymer motion or the presence or absence of particular long-lived dynamic structures, e.g., tubes it yields a set of generalized Langevin equations and associated memory functions. Somewhat realistic assumptions are made for the equilibrium structure of the solutions. Extensive calculations were made of the molecular weight dependences for probe diffusion in melts, often leading by calculation rather than assumption to power-law behaviors for various transport coefficients. However, as presented in the papers noted here, the model is applicable to melts rather than solutions Momentum variables have been completely suppressed, so there are no hydrodynamic interactions. Readers should recall that hydrodynamic interactions usually refer to interactions that are solvent-mediated. 

Lodge and collaborators have reported an extensive series of studies of probe diffusion in polymer solutions, using QELSS to measure Dp of dilute probe polystyrenes in polyvinylmethylether orthofluorotoluene. Variables studied include the probe and matrix molecular weights, the matrix concentration, and the topology (linear and star) of... 

Molecular weight dependence of the self and probe diffusion coefficients ) and Dp for molecular weight P probes in solutions of matrix polymers at a fixed concentration c. The fits are to stretched exponentials Z oexp(—aM ) in matrix molecular weight M. The Table gives the best-fit parameters, the percent root-mean-squaxe fractional fit error %RMS, the system, and the reference. Square brackets [ ] denote paxameters that were fixed rather than floated. Abbreviations as per previous Tables, and DBP-dibutylphthalate. 

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... 

---