Diffusion in polymer-polymer mixtures (original) (raw)
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Diffusion Coefficient Matrix in Nonionic Polymer−Solvent Mixtures
Journal of Physical Chemistry B - J PHYS CHEM B, 2001
Recent predictive equations for evaluating the value of diffusion coefficients, developed for two hard spheresolvent systems, have been extended to n-hard-sphere-solvent systems. This model has been used to predict the diffusion behavior of nonionic polymer-solvent mixtures as a first-order function of volume fraction from the knowledge of the distribution function. Hence, the entire diffusion matrix for polydisperse systems, which include both main-and cross-term diffusion coefficients, has been built up for the first time. The main-terms diffusion coefficients D ii are mostly affected by the variation in viscosity. The magnitude of the cross-term diffusion coefficients D ij is strictly related to the abundance and diffusivity of solute i and to the molecular volume corresponding to solute j. The predicted diffusion coefficients have been used to calculate the apparent, average diffusion coefficients, which are compared with the experimental values measured by the Gouy interferometry method in the case of the poly(ethylene glycol) homologous series. The agreement between the calculated and experimental Gouy parameters is good. The cross-term diffusion coefficients are found to be significant in the calculation of the apparent diffusion coefficient for a polydisperse solute. Some comments on the study of ternary systems containing a polydisperse solute are done.
Macromolecules, 2009
We present a comprehensive investigation of polymer diffusion in the semidilute regime by fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS). Using single-labeled polystyrene chains, FCS leads to the self-diffusion coefficient while DLS gives the cooperative diffusion coefficient for exactly the same molecular weights and concentrations. Using FCS we observe a new fast mode in the semidilute entangled concentration regime beyond the slower mode which is due to self-diffusion. Comparison of FCS data with data obtained by DLS on the same polymers shows that the second mode observed in FCS is identical to the cooperative diffusion coefficient measured with DLS. An in-depth analysis and a comparison with current theoretical models demonstrates that the new cooperative mode observed in FCS is due to the effective long-range interaction of the chains through the transient entanglement network.
Diffusion phenomena in ternary systems polymer-nonsolvent-solvent
Journal of Solution Chemistry, 1993
Diffusion in a boundary between a polymer + solvent solution and nonsolvent was treated by accounting for the presence of the four diffusion coefficients that describe the isothermal transport process in a three component system. Diffusion equations were integrated assuming a concentration dependence of diffusion coefficients that account for the thermodynamic conditions on the cross diffusion terms of Eq. (1). The presence of non-zero cross terms promotes an incongruent diffusion of polymer whose concentration increases at the boundary between the polymer + solvent solution and the non-solvent. Although our model describes diffusion in the range of homogeneous solution, this incongruent polymer diffusion is a process similar to that promoted by the solvent evaporation from the polymer + soIvent film that some authors suggested as an intermediate step before the film immersion into the coagulation bath to obtain good asymmetric membranes. KEY WORDS: Diffusion; polymer solutions.
Thermal and mass diffusion in a semidilute good solvent-polymer solution
The Journal of Chemical Physics, 1999
The Soret coefficient S T and collective ͑mass͒ diffusion coefficient D c of polystyrene dissolved in the good-solvent toluene has been measured over a range of concentrations and molecular masses with an optical beam-deflection method. Our measurements indicate that S T scales inversely with the polymer translational diffusion coefficient in dilute solutions, exhibits a power-law scaling with polymer concentration, and an independence of polymer molecular mass in semidilute solutions. These findings are consistent with the known scaling of 1/D c in dilute and semidilute polymer solutions, the relative insensitivity of the thermal-diffusion coefficient D th of polystyrene in toluene to polymer concentration, and the relation S T ϭD th /D c from irreversible thermodynamics. We are able to represent our S T and D c data by theoretically motivated reduced-concentration master curves, but the concentration-molecular mass scaling variables are found to be different for each transport property, a result contrary to theoretical expectations. However, the asymptotic concentration scaling exponents deduced from these data fits are compatible with de Gennes' scaling arguments for D c and with modern estimates of the chain-size exponent for swollen polymers in good solvents.
Velocity-correlation analysis in polymer-solvent mixtures
Journal of Polymer Science Part B: Polymer Physics, 2002
The subject of this article is the combined interpretation of intradiffusion and mutual-diffusion data for polymer-solvent mixtures in terms of integrals over velocity self-correlation functions and velocity cross-correlation functions. The combination of mutual-diffusion, intradiffusion, and activity data allows the evaluation of velocity-correlation coefficients (VCCs) and distinct-diffusion coefficients in systems containing one monodisperse solute. This study is the first attempt to extend these approaches to polymers that are polydisperse solutes. Because of the polydispersity, this correlation analysis may become critical for polymers. Its application to polydisperse samples requires the reduction of intradiffusion and mutual-diffusion coefficients to the same average. After such a reduction, the VCCs and distinct-diffusion coefficients are evaluated for a homologous series of poly(ethylene glycol)s (PEGs). Attractive PEG-PEG interactions depend on the chain length and concentration of PEG. In this analysis, network formation in PEG-water systems appears to be a smooth process.
Complex Tracer Diffusion Dynamics in Polymer Solutions
Physical Review Letters, 2013
We employ fluorescence correlation spectroscopy (FCS) and coarse-grained molecular dynamics simulations to study the mobility of tracers in polymer solutions. Excluded volume interactions result in crowding-induced slowdown, depending only on the polymer concentration. With specific tracerpolymer attractions, the tracer is slowed down at much lower concentrations, and a second diffusion component appears that is sensitive to the polymer chain length. The two components can be resolved by FCS, only if the distance traveled by the tracer in the polymer-bound state is greater than the FCS focal spot size. The tracer dynamics can be used as a sensitive probe of the nature and strength of interactions, which-despite their local character-emphasize the role of chain connectivity.
Thermodynamic slowing down of mutual diffusion in isotopic polymer mixtures
Macromolecules, 1987
The mutual diffusion coefficient, D(9), determined at finite blend compositions, 9, in blends of normal (hydrogenated) and deuteriated polystyrene was found to be highly dependent on composition. D (9) experiences a minimum, or "thermodynamic slowing down", in the vicinity of the critical composition, 9'c. This effect increases with decreasing temperature. This result is consistent with recent small-angle neutron-scattering measurements which indicate that this system exhibits an upper critical solution temperature. The temperature dependence of the Flory interaction parameter, x, was extracted from the data by using a mean field prediction for the compositional dependence of D. We found that x = 0.22(&0.06)/T-3.2(*1.2) x 10-4. 5, 519. There is a second prediction for D(Q) (Brochard, F.; Jouffory, J.; Levinston, P. Macromolecules 1984, 17, 2925) which differs from eq 3 such that Q (Q) = 2O(1-3)[(1-O)/ DD*ND + O./DH*NJ1. Since we have chosen N H = N D , both predictions for D(O) yield essentially the same result.
Free diffusion data in some polymer-solvent systems at 20° C
1991
DWusion cotlIlclents. denstties, and viscosltks have been measured ior dilute aoluttons of poIy(vinylldcn fluoride) In N.N-dlmethylformamlde and N-methylpixrolydone. and for two commercial samples of poly(suUone) in dlmethylacetatide. The results have been brIefly discussed with the nld of Flory-HuggIns and Stokes-Elnstdn equutlons.
Journal of Colloid and Interface Science, 1997
This paper presents diffusion studies of two ''model'' associative at relatively high shear rates. polymers (hydrophobically end-capped poly(ethylene oxide)) (AP) Numerous investigations with various techniques have differing in end-group length, a factor of great significance in the been carried out on AP systems to obtain information about transport rate of APs in aqueous solution. An increase in endthe association mechanism, aggregate size, and solution group length was found to reduce the self-diffusion coefficient. As structure (1-13). It is now generally accepted that the rheoexpected, it also greatly influences the onset of aggregation, as monilogical characteristics of APs originate from assembly of tored by static fluorescence, and the phase behavior. The longer the their hydrophobic end groups into micelle-like aggregates hydrocarbon end group, the lower the critical aggregation concenat low concentrations and a gradual formation of network tration and the lower the cloud point of the polymer solution; i.e., the structures at higher concentrations. For aqueous solutions of lower critical solution temperature decreases. In line with oscillatory relaxation results obtained by T. Annable et al. (J. Rheol. (N.Y.) 37, sufficiently low-molecular-weight APs (M W õ 6000) at high 695 (1993)), the data of the present paper show that AP transport in concentrations this network structure can also become highly equimolar mixtures of the two APs is characterized by two-compoordered into a cubic array (10-11). nent behavior over a wide range of semidilute polymer concentra-During the AP aggregation process the transport mechations. The diffusion of the polymer is therefore judged to be molecunism gradually changes from overall cluster diffusion to diflarly determined in this concentration region; i.e., the polymers fusion of individual AP molecules. This action has been diffuse independently within a network structure. The dynamic found to result in a distribution of self-diffusion coefficients hydrophobic domains, keeping the network together, are considered (D i) that changes with polymer content (7-9, 12-13). At to be mixed, containing end groups of both lengths. We also find that low polymer concentrations there is a significant distribution the cloud point temperature of these mixed solutions are situated of D i due to a broad cluster size distribution. between those of the single component solutions following a two-The aim of the present study is primarily to explore the state relation. ᭧ 1997 Academic Press influence of the hydrocarbon end group on the overall poly-Key Words: associative polymer (AP); associative thickener mer dynamics, i.e., the self-diffusion coefficient and its dis-(AT); end-group length; hydrocarbon chain length; cloud point tribution. Previous studies show that the transport rate in temperature (CPT); NMR; self-diffusion; static fluorescence; cac; activation energy; molecular transport. aqueous solution of relatively polydisperse commercial type APs, containing isocyanate groups, is significantly affected by the length of the hydrocarbon end group (8-9). This study complements previous work by using several methods 137
Interdiffusion in dilute polymer mixtures. A subtle concentration effect
The Journal of Chemical Physics, 1994
Dynamic light scattering has been used to investigate the diffusional dynamics in very dilute polystyrene/poly(propylene oxide), PS/PPO, polymer blends. Compared to previous investigations in the field, this system is more suitable for this type of investrgation due to the significant refractive index difference between the two components and the fact that the matrix (PPO) dynamics do not interfere with the measurements. The tracer diffusion coefficient of PS thus obtained in the limit of. .. infinite drlutron scales as NPS-".8~a.04 with the PS degree of polymerization, i.e., behavior intermediate between the limits of nondraining Zimm and free-draining Rouse behavior. The effect of the addition of a third component even at tracer concentrations on the diffusion dynamics~ was investigated both experimentally and theoretically in the framework of the dynamic random phase approximation. Similarities and differences between theory and experiment were found that are rather due to a modification of hydrodynamic interactions.-')Also at