“…At higher temperatures, the distributions of the micelles of the three poly(ethylene glycol) n-alkyl monoethers become bimodal in dilute or semidilute solutions. This happens at temperatures where the particle systems undergo a thermal transition, as found by calorimetry with C 14 E 8 42 and later with C 12 E 8 and C 16 E 8 . 43 The transition temperature, which depends on the surfactant as well as on its concentration, increases with decreasing chain length.…”
Laser drifts, dust, and impurities in a sample are physical reasons for offsets in both field and intensity autocorrelation functions. In this paper, a method is described by which the two offsets are determined by a variation method. Data were analyzed with the size distribution algorithm CONTIN, using the selection method of L-curves for getting the offsets and a combination of the methods of F-test, stability plot, and L-curve for getting the final solution from the corrected data. This solution was selected according to the parsimony principle, under which the preferred solution is that with the simplest size distribution. Consistency was checked by means of two additional tools. The first is the difference between the field autocorrelation function of a regularized solution and the least-squares solution, called the difference in g1, which is compared with the residuals of the least-squares solution. The second is the relative increase in variance or the discrepancy from the best fit solution. The procedure for the determination of the offsets is described by means of experimental data of high statistical accuracy from a semidilute aqueous solution of the surfactant octaethylene glycol dodecyl monoether (C12E8). The method was tested with data containing different contributions of dust and with data from different poly(ethylene glycol) n-alkyl monoethers (C12E8, C14E8, and C16E8). After correction of the data for the two offsets, the size distributions obtained from data analysis were free of elements of unstable solutions such as side peaks at the integration limits. It is shown that differences in the size characteristics of narrow monomodal distributions of about 0.3-0.4 nm can be distinguished and that two peaks of a bimodal size distribution with a size ratio of 2:1 can be resolved.
“…At higher temperatures, the distributions of the micelles of the three poly(ethylene glycol) n-alkyl monoethers become bimodal in dilute or semidilute solutions. This happens at temperatures where the particle systems undergo a thermal transition, as found by calorimetry with C 14 E 8 42 and later with C 12 E 8 and C 16 E 8 . 43 The transition temperature, which depends on the surfactant as well as on its concentration, increases with decreasing chain length.…”
Laser drifts, dust, and impurities in a sample are physical reasons for offsets in both field and intensity autocorrelation functions. In this paper, a method is described by which the two offsets are determined by a variation method. Data were analyzed with the size distribution algorithm CONTIN, using the selection method of L-curves for getting the offsets and a combination of the methods of F-test, stability plot, and L-curve for getting the final solution from the corrected data. This solution was selected according to the parsimony principle, under which the preferred solution is that with the simplest size distribution. Consistency was checked by means of two additional tools. The first is the difference between the field autocorrelation function of a regularized solution and the least-squares solution, called the difference in g1, which is compared with the residuals of the least-squares solution. The second is the relative increase in variance or the discrepancy from the best fit solution. The procedure for the determination of the offsets is described by means of experimental data of high statistical accuracy from a semidilute aqueous solution of the surfactant octaethylene glycol dodecyl monoether (C12E8). The method was tested with data containing different contributions of dust and with data from different poly(ethylene glycol) n-alkyl monoethers (C12E8, C14E8, and C16E8). After correction of the data for the two offsets, the size distributions obtained from data analysis were free of elements of unstable solutions such as side peaks at the integration limits. It is shown that differences in the size characteristics of narrow monomodal distributions of about 0.3-0.4 nm can be distinguished and that two peaks of a bimodal size distribution with a size ratio of 2:1 can be resolved.
“…Calorimetric Studies. DSC data of the binary systems C 14 E 8 /water and C 16 E 8 /water have already been presented in previous papers. , As a characteristic example, we reproduce here one of the DSC curves of 60 mM C 16 E 8 , which we use for the fit with the micelle aggregation model (eq 1). The experimental curve, characterized by squares in Figure a,b, indicates a rather narrow endothermic transition with a halfwidth of about 5 K. 1 Heat capacity changes as a function of temperature for 60 mM C 16 E 8 /H 2 O.…”
Section: Resultsmentioning
confidence: 99%
“…DSC studies were performed with the MCS DSC instrument of Microcal by applying a temperature gradient of 30 K per hour. To apply fit procedures for a detailed analysis, the DSC curve of 60 mM C 14 E 8 has been remeasured, leading to parameters that differ slightly from the published mean values . The solutions were degassed under reduced pressure prior to every measurement.…”
Section: Methodsmentioning
confidence: 99%
“…Concerning the sphere-to-rod transition of micelles, it has been argued long before by Porte et al that there must be an energy barrier involved in the elongation process. In recent investigations, , it was possible to provide direct evidence for the existence of such a barrier and to measure its energy as well as to determine the transition temperature ( T U ) by differential scanning calorimetry (DSC). Using various C i E j surfactants, it was shown that the change in specific heat exhibits a rather narrow endothermic transition, a few kelvins wide.…”
Section: Introductionmentioning
confidence: 99%
“… The energetics and dynamics of the growth of nonionic n -alkyl poly(ethylene glycol) ether surfactant micelles in the isotropic L 1 phase have been analyzed on the basis of a recently described, concentration dependent thermal transition . This highly cooperative endothermic transition is assigned as a sphere-to-rod transition.…”
The energetics and dynamics of the growth of nonionic n-alkyl poly(ethylene glycol) ether surfactant micelles in the isotropic L1 phase have been analyzed on the basis of a recently described, concentration dependent thermal transition. 1 This highly cooperative endothermic transition is assigned as a sphereto-rod transition. We analyze the thermodynamic data in terms of aggregation-fusion of complete micelles and also discuss the kinetics in the frame of this "random micelle aggregation" model. The analysis of the calorimetric data leads to a cooperative unit of about 160 detergent molecules undergoing simultaneously the transition from spheroidal to cylindrical structure. We investigate the aggregation kinetics in the microsecond to millisecond range using the temperature-jump (TJ) method with observation of scattered and transmitted light and the stress relaxation dynamics monitoring transient electric birefringence (TEB).As expected from the model, the aggregation dynamics gets faster with increasing temperature, while the stress relaxation dynamics slows down with temperature, leading to apparent negative activation energies. At the transition temperatures, the dynamics of the structural transition for C14E8 is characterized by an association and dissociation rate constant of 4.4 × 10 6 M -1 s -1 and 1.8 × 10 3 s -1 , respectively, compared to the much slower dynamics of C16E8 with the corresponding rate constants 8.5 × 10 4 M -1 s -1 and 29 s -1 , respectively. The rate constants of micelle fusion increase, while those of micelle scission decrease with increasing temperature. The TEB results are discussed using the relations derived in the literature for the competition between rotational motion and chain scission. The fast dynamics of C14E8 compared to the much slower dynamics of C16E8 provides an understanding of the differences in stress compliance and viscosity for these systems. As a major result of the study, we present a consistent mechanism of micellar growth which involves the aggregation-fusion of two micelles in a single, rate-limiting reaction step and not the stepwise incorporation of single surfactant molecules into pre-existing micelles. The speeding up of the TJ kinetics in C16E8 at higher temperatures indicates a further structural transition, possibly network formation.
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