J. Phys. Chem. B 2008, 112, 29-35
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Diffusion of Dextran Probes in a Self-Assembled Fibrous Gel Composed of Two-Dimensional Arborols Jirun Sun,† Bethany F. Lyles,† Keunok Han Yu,‡ Jaime Weddell,† John Pople,§ Max Hetzer,| Daniel De Kee,| and Paul S. Russo*,† Department of Chemistry and Macromolecular Studies Group, Louisiana State UniVersity, Baton Rouge, Louisiana 70803, Department of Chemistry, Kunsan National UniVersity, Kunsan City 573-360, South Korea, Stanford Synchrotron Radiation Laboratory, Menlo Park, California 94025, and Department of Chemical and Biological Engineering, Tulane UniVersity, New Orleans, Louisiana 70118 ReceiVed: September 2, 2007; In Final Form: October 5, 2007
Two-dimensional arborols are bolaform amphiphiles in which a central, hydrophobic spacer separates twin hydrophilic ends. Under appropriate conditions, these relatively small molecules assemble into very long fibers; subsequently, the system gels if the arborol concentration is sufficiently high. The diffusion of linear or slightly branched dextran probes in 3 and 6% arborol gels, as determined by fluorescence photobleaching recovery, resembles that of dextrans in water, suggesting a highly open network structure. Melting the gels produces almost no change in diffusion of the dextran probes. Small-angle X-ray scattering (SAXS) of wet arborol gels at different concentrations and temperatures reveals the diameter of the repeating unit of the fibers to be 8.26 ( 0.68 nm. This dimension, which is independent of concentration and temperature, exceeds the length of a single arborol molecule by about a factor of 3. Rheological investigation identifies the linear response regime of the gels and permits an examination of the weak correlation between dextran probe diffusion and gel viscoelasticity.
Introduction Spontaneous assembly of small molecules to transform a lowviscosity liquid to a solid gel is receiving increased attention.1-5 For example, Weiss and co-workers have synthesized and characterized several small-molecule organogelators.6,7 If the solvent is water, the gelators induce hydrogels, which are key ingredients in a number of biological systems8,9 and commercial products such as foods, deodorants, and cosmetics. Chromatographic separations such as capillary gel electrophoresis could benefit from a porous stationary phase that can be flushed away when spent, a process facilitated by the reVersible assembly of small molecules. Production of porous materials around a microscopic scaffold is simplified when the scaffold can be disassembled into small, easily removed parts.10,11 All these applications require a better understanding of self-assembled networks. Arborol networks are thermal reversible hydrogels first described by Newkome et al.,12,13 in the 1980s. The gelators are two-directional, bolaform, dendritic amphiphiles,13-15 in which a central lipophilic spacer separates matched hydrophilic units to make a molecular dumbbell. The length of the spacer and the size of the end group vary. A representative [9]-12-[9] arborol is discussed in this paper; the notation signifies that an aliphatic spacer of 12 methylene units separates a pair of groups, each with 9 hydrophilic hydroxyl functional groups. Arborols with appropriate hydrophilic/lipophilic balance dissolve in warm water. On cooling, they assemble into long fibers that interact * To whom correspondence should be addressed. Telephone: (225) 5785729. Fax: (225) 578-3458. E-mail:
[email protected]. † Louisiana State University. ‡ Kunsan National University. § Stanford Synchrotron Radiation Laboratory. | Tulane University.
by dispersion forces to create a gel. These appear to be true gels, in the sense that dilute samples of typical laboratory-scale size (1 cm × 1 cm × 1 cm) exhibit no discernible flow on any convenient time scale (a year or more) when inverted. The gelation is reversible; application of heat quickly restores fluidity. As opposed to thermoreversible gels of macromolecular parentage, the molten, fluid state is not at all viscous. To better understand the arborol networks, we apply an old strategy for characterizing soft materials: observation of the rate of diffusion of macromolecular probes.16-25 Fluorescence photobleaching recovery (FPR), with sensitive modulation detection26-28 to hold perturbations to a minimum, is used to measure the diffusion of fluorescently tagged dextrans of varied size through arborol gels. The technical advances (including FPR) that made probe diffusion appealing co-evolved with theories of molecular motion in polymeric29,30 and other systems containing obstacles to diffusion.31-34 Mechanistic studies may even outnumber those attempting to glean the nature of some soft structure.35-37 The approach here is true to the original intent: launch probes of a certain size into the matrix (gel), measure how fast they move, and infer qualitatively the nature of the gel. As the diffusive length scale in the typical FPR experiment is long, microscopic details of the motion are lost, which would also be true of standard fluorescence correlation spectroscopy measurements.38-40 Compared to single diffuser tracking,41,42 the present experiments do not reveal anomalous behavior or entrapment of individual particles by obstacles to diffusion. On the contrary, many diffusers are observed simultaneously and average values obtained. This approach will be shown to be appropriate for the arborol gels. To place the present study in the expanding phylogeny of probe diffusion,43,44 the dextran probes are lightly branched random coil polymers. Freeze-fracture electron microscope images and small-angle
10.1021/jp077050b CCC: $40.75 © 2008 American Chemical Society Published on Web 12/11/2007
30 J. Phys. Chem. B, Vol. 112, No. 1, 2008
Sun et al.
TABLE 1: Fluorescent Dextrans Used for This Study
stock no.
lot no.
vendor molecular weight
FD-4 FD-10S FD-20 FD-40 FD-70 FD-150 FD-500S FD-2000S
128H-0513 38H-5083 77H-0361 17H-1230 128H-9801 126F-0144 38H-5082 39H-5004
4 400 9 500 21 200 38 260 70 500 148 900 464 000 2 000 000
a
a
Rh a (nm)
Rh (nm) from Bu and Russo46
1.3 2.1 3.9 5.1 6.3 8.7 12.6 20.7
1.3 2.3 3.3 4.5 6.0 8.8 13.3 17.9
The hydrodynamic radius (Rh) was measured by FPR in water.
X-ray scattering (SAXS) data on dried gels45 suggest that the arborol matrix consists of very long, fibrillar bundles. If that is also the case for the wet gels, one may expect the diffusion of various probes to be little affected by the matrix. Rheometric measurements, SAXS profiles of the wet gels, and scanning calorimetry aid in the interpretation of the results designed to test this basic hypothesis. Materials and Methods Labeled Dextran. Fluorescently labeled dextran samples were obtained from Sigma. Relevant data appear in Table 1. Two hydrodynamic radii (Rh) are given for every dextran probe, one from this study and the other from Bu and Russo.46 The agreement is generally very good. The dextran probes FD10S, FD20, and FD500S have the same lot number as Bu’s samples. All the others have the same vendor molecular weights but different lot numbers. Preparation of Gels. Arborol [9]-12-[9] was synthesized divergently according to Newkome’s procedure.13 The chemical structure of this compound has been discussed in previous publications.13,14,45,47 Gels were prepared by adding an appropriate amount of solvent to [9]-12-[9] arborol weighed in vials. The solvent was water, sometimes spiked with FITC-dextran at a concentration less than 1 mg/mL. The sample was placed on a hot plate and heated until a clear, homogeneous liquid resulted. The visual gel melting temperature was unaffected by the presence of the FITC-dextran. The sample was either placed in an ice bath or allowed to cool to room temperature to induce gelation. Fluorescence Photobleaching Recovery. The apparatus has been described previously46,48 and is a variant of the type described by Ware and co-workers.21,49 A low-contrast striped pattern of spatial period Λ is written into the sample using a bright 488 nm laser beam to illuminate a coarse diffraction grating, which is held in a confocal plane with respect to the sample, situated on the stage of an epifluorescence microscope. After a 2000-fold reduction of laser beam intensity, the diffusive recovery of fluorescence in brightly illuminated portions of the fringe pattern is recorded as a reduction in contrast between dark and bright zones. An electromechanical modulation system enables the detection of very shallow bleaches and eliminates higher harmonics in the signal, so that diffusion takes place on a well-defined distance scale with each diffuser being associated with just one exponential recovery term. Flame-sealed, rectangular capillaries (Vitrocom) of 200 µm path length are used. Samples are loaded hot and allowed to gel inside the cell. Most experiments are carried out using a 10× objective lens and a Ronchi ruling of 50 lines/inch, corresponding to Λ ) 0.0155 cm; the corresponding spatial frequency is K ) 2π/Λ ) 405.3 cm-1. Shallow bleaches (from 1 to 5% of dyes are bleached) produce adequate signal quality in single-shot experiments (no
signal averaging). The contrast detected by the modulation detector follows an exponential decay:
C(t) ) Coe-Γt + B
(1)
where Co represents the initial contrast in the sample’s bleached and unbleached regions and B is a baseline that reflects noise arising from electrical sources and imperfections in the cell or sample. The decay rate, Γ, is equal to DK2. Small-Angle X-ray Scattering. SAXS was carried out at the Stanford Synchrotron Radiation Laboratory (SSRL) on beamline 1-4, using a wavelength of 1.488 Å. The [9]-12-[9] arborol was dissolved in water at about 80 °C. The solution was loaded into X-ray capillary cells (Charles Supper) of diameter 1.0, 1.5, or 2.0 mm and centrifuged to the bottom before sealing the cells by flame. A Mettler FP80 microscopy oven provided convenient and rapid temperature control. The background scattering was measured from room-temperature water, and corrections for absorption were applied. The data were not placed on an absolute intensity scale. Rheology. Rheology studies were performed on a TA 2000 equipped with a 20 mm, 1° cone-and-plate rotor. The arborol gel (3% [9]-12-[9]) was prepared before the experiment and loaded on the plate using a spatula. The same gel was used for all the rheology experiments. After each test, the cone and plate were cleaned and a new portion of the gel was loaded. The cone and plate were covered by a metal mantle to minimize solvent evaporation. The temperature was fixed at 25 ( 0.1 °C by a water bath circulator. An oven was used for experiments at temperatures higher than room temperature. The viscoelasticity of the gel was examined by using the oscillation procedure at continuously changed strains and a frequency of 0.01 rad‚s-1. Within the linear elastic region of the gel, at a constant strain (0.5%), an oscillation frequency scan was run from 0.1 to 100 rad‚s-1. Finally, the gel was tested in a temperature range between 25 and 80 °C at an oscillation frequency of 1 rad‚s-1 and a 0.5% strain. Differential Scanning Calorimeter. DSC was performed on a Seiko DSC 120, which was calibrated with In and Pb standards. The [9]-12-[9] was dissolved in hot water. A small portion of the solution (about 30 mg) was transferred to an aluminum pan, which was sealed with an aluminum cap. An empty pan with cap was used as the reference. Results and Discussion The main probe diffusion measurements are intended to illuminate the nature of structures using a dynamic probe, but it is convenient to begin instead with the static structure and viscoelastic response, as revealed by SAXS and rheological measurements, respectively. SAXS. Small-angle X-ray scattering by wet arborol gels is used to obtain structural information without the potential for deformation of the samples, as in SAXS measurements on dried fibers or previous microscopy studies13,15 which relied on various forms of sample preparation. The SAXS results of three arborol gels at concentrations of 1.5, 3, and 4% (by weight) are shown in a two-dimensional (2D) Guinier representation, ln[qI(q)] vs q2 version (Figure 1). The intensities, I, are corrected for background and transmission, and the scattering vector magnitude, q, is 4πλ-1 sin(θ/2), where θ is the scattering angle and λ is the wavelength of the synchrotron light source after the monochromator. As the concentration increases, a linear fit to the data improves, which suggests a more perfect fibrillar
Fibrous Gel Composed of 2D Arborols
J. Phys. Chem. B, Vol. 112, No. 1, 2008 31
Figure 3. Structure of [9]-12-[9]. The largest distance is 2.73 nm, from H(33) to H(83).
Figure 1. SAXS data in ln(qI(q)) vs q2 representation to calculate Rcg of 1.5, 3, and 4% [9]-12-[9] arborol gels. Inset: if the cross-section of the fiber is represented by a thin disc, Rcg ) Ro/x2.
Figure 4. Storage modulus (G′) and loss modulus (G′′) of a 3% [9]-12[9] gel as functions of shear strain.
TABLE 2: Rcg of [9]-12-[9] Arborol Gels from SAXS at Different Concentrations and Temperatures
Figure 2. SAXS of 8% [9]-12-[9] at temperatures indicated to calculate Rcg. Plots are offset vertically for convenience.
structure. The highly linear trends seen for the 3 and 4% gels reveal rigid fibrillar structures, confirming the impressions of microscopy. The fibers can be modeled as cylinders of radius Ro and crosssectional radius of gyration Rcg ) Ro/x2. When qRcg < 1, the two-dimensional Guinier approximation for rods can be used, and the radius of gyration of the cross-section is calculated according to50
(
)
-q2Rcg2 L I(q) ∼ exp q 2
(2)
where L is the length of the rod. In the arborol gels, L often exceeds any dimension that can be measured by SAXS. Values of Rcg were derived from the slopes of the linear fits of the data in Figure 1. The result for 1.5, 3, and 4% arborol gels was Rcg ) 2.92 ( 0.24 nm, corresponding to an apparent diameter, in this cylindrical model, of 2x2Rcg ) 8.26 ( 0.68 nm. This value did not change significantly with temperature (Figure 2 and Table 2; the minor curvature in Figure 2 is attributed to a baseline shift and does not significantly affect the results). The largest end-to-end distance of one [9]-12-[9] molecule is about 2.7 nm (estimated by ChemDraw software after minimizing the molecular energy using a 3-D model). This is the largest distance between two hydroxyl hydrogen atoms (H33 and H83 in Figure 3) located in opposing hydrophilic zones. Thus, if the fibers
concentration (wt %) 1.5 3 4 8 (at 30 °C) 8 (at 80 °C) Rcg (nm) 2.89 2.97 2.89 2.98 2.88 error of Rcg (nm) 0.14 0.28 0.14 0.28 0.37 average Rcg (nm) 2.92 ( 0.24
are modeled as uniform cylinders, the diameter of those cylinders exceeds molecular dimensions by a factor of about 3. In a previous SAXS investigation14 of dried [6]-n-[6] and [9]-n[9] arborol gels, “bumps” were observed in the scattering envelopes at q ∼ 3 nm-1. This behavior was shown to be consistent with side-by-side arrangements of “stacked dumbbell” fibrils, although no claim was made regarding the details of the arrangements, apart from being nominally parallel. The twodimensional Guinier analysis just presented suggests that the fibrils undergo some association even in the wet state, bolstering confidence in the freeze fracture images previously published,15 which resemble an aerial view of a railway switchyard. Rheometry. The viscoelastic behavior of a 3% [9]-12-[9] gel is examined first. In Figure 4, the storage modulus (G′) and the loss modulus (G′′) are plotted as functions of shear strain at an oscillation frequency of ω ) 0.01 rad‚s-1. The gel exhibits a linear viscoelastic response below a shear strain ∼1%, where G′ > G′′. In this linear viscoelastic regime, the gel behaves like an elastic solid. At higher strains, G′ decreases while G′′ increases. At a shear strain of ∼10%, G′ ) G′′, indicating that the gel is beginning to behave more like a viscous liquid. Frequency-dependent oscillatory shear experiments at low deformation appear in Figure 5. These data were acquired at 0.5% strain, within the linear viscoelastic regime. The storage moduli are always larger than the loss moduli, indicating the gel behaves like an elastic solid in this frequency range.
32 J. Phys. Chem. B, Vol. 112, No. 1, 2008
Figure 5. Frequency dependence of G′ and G′′ for the 3% [9]-12-[9] arborol gel.
Sun et al.
Figure 7. Typical FPR decay curve.
Figure 8. Diffusion of fluorescently labeled dextrans in water and 3 and 6% [9]-12-[9] arborol gels. Figure 6. Storage modulus (G′, upper data set) and loss modulus (G′′) of a 3% [9]-12-[9] gel at different temperatures. The temperature was increased from 25 to 80 °C at 2 °C/min. The data were collected at a shear strain of 0.5% and a frequency of 1 rad‚s-1. Because G′ is about six times larger than G′′, the appearance of the complex viscosity calculated from G′ and G′′ at different temperatures is similar to that of G′ (not shown).
At different temperatures from 25 to 80 °C, the moduli of the 3% [9]-12-[9] gel were measured at a shear strain of 0.5% and an oscillation frequency of 1 rad‚s-1 (Figure 6). Both G′ and G′′ remained relatively constant at temperatures below 50 °C; above that they dropped continuously. Up to 80 °C, G′ exceeded G′′; even at this temperature, a 3% [9]-12-[9] gel is more solid-like. The value of G′ is about six times bigger than that of G′′ throughout the measured temperature range. Probe Diffusion. A typical FPR decay curve appears in Figure 7. For diffusion of the dextrans in water and arborol gels, most data sets could be well fit to a single-exponential decay, but the FD2000 polymer exhibited enough polydispersity that analysis by the inverse Laplace transform algorithm, CONTIN,51,52 was also performed. The difference in average decay rate was not significant in the context of this study. A plot of the probe diffusion coefficient (D) as a function of probe molecular weight (M) for arborol concentrations of 0, 3, and 6% appears in Figure 8. The data follow a power law, D ∼ M-β with β ) 0.42-0.65. In pure water, β ) 0.53 ( 0.02, which lies within the range of results seen previously;46 as discussed elsewhere,53 the exponent depends on the span of molecular weights selected. For the 3 and 6% arborol gels, the
exponent is -0.59 ( 0.01 and -0.62 ( 0.03, respectively. This compares to β ∼ 1 for the diffusion of dextran or pullulan probes through dextran matrices of widely varying concentration. A particularly interesting matrix for comparison is hydroxypropylcellulose (HPC). This polymer adopts an extended conformation (not rodlike, but semiflexible with persistence length of about 10 nm 54). The exponent β increases from about 0.5 to about 1 as the HPC concentration rises. Also, the diffusion of dextran probes depends strongly on the concentration of the HPC.46 Even at modest concentrations, and without forming a true gel, HPC dramatically modifies the diffusion of dextran probes, both in terms of value and molecular weight dependence.46 The arborol gels do not. Dextran diffusion in HPC was framed in terms of a microviscosity, ηm, introduced by rearrangement of the StokesEinstein equation:
ηµ )
kBT f ≡ 6πRhD 6πRh
(3)
In eq 3, kB is Boltzmann’s constant, T is the absolute temperature, and f is the friction factor associated with the tracer self-diffusion coefficient of the fluorescently tagged probe. For dextrans diffusing in HPC, the microviscosity increased strongly, while still remaining well below the macroscopic viscosity, η, at high matrix concentrations. This constitutes a failure of the Stokes-Einstein relation, implying that the solution does not behave as a bulk fluid insofar as its ability to restrict probe
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J. Phys. Chem. B, Vol. 112, No. 1, 2008 33
diffusion. It was possible to analyze the diffusion behavior in terms of the matrix correlation length, ξ, using the scaling analysis of Langevin and Rondelez, who suggest55 δ D ηo ) + e-(Rh/ξ) Do η
(4)
The parameters ξ and δ could be estimated for dextrans diffusing in HPC. Such an analysis was found to be imprecise for dextrans diffusing in arborol gels because the reduction in diffusion is so small; this was true for either 3 or 6% gels. The weak reduction in diffusion is attributed to large values of ξ compared to the probe Rh values. Simply put, big pores exist in arborol gels. An obstruction-scaling model proposed by Amsden44 predicts the following decline in diffusion when probes of radius R diffuse through a matrix of fibers of cylinder radius Rf separated on average by correlation length ξ:
[ (
R + Rf D ) exp -π 0 ξ + 2Rf D
)]
Figure 9. FPR-determined diffusion coefficient of FD40 in water and 3% [9]-12-[9] as a function of temperature.
2
(5)
On insertion of a fiber radius of 4.15 nm, as suggested by the SAXS results, a dynamic correlation length of several tens of nanometers is obtained, sensibly larger for 3% than for 6% solutions and at least a little larger than the diameter of even the largest dextran probe. More detail than this is not warranted by the small relative reductions in diffusion coefficient. To further understand the differences between the arborol gels and the HPC-300,000 matrix, many parameters35,54,56,57 should be considered. One difference traces to the construction of the rigid fibers (arborols) or semiflexible filaments (HPC). Confining the restraining matrix material into a fiber of diameter 8.3 nm leaves the solution with larger pores compared to the filamentous HPC. For example, in a 3.78% solution of HPC with M ) 300 000 the correlation length between filaments was estimated as 3 nm. The analysis above suggests a much larger correlation length for 3 or 6% arborol gels. Another important difference may lie in the rigidity of the fibers (arborol) or filaments (HPC). Despite their small size, arborol molecules self-assemble to form unbranched, long, and thin fibers with a persistence length on the scale of microns. Dynamic light scattering (DLS) measurements58 suggest that some mobility remains in arborol gels, or that structural rearrangements occur, but this motion is only observed using very long acquisition times. Under the usual DLS measurement conditions (several minutes of acquisition time) the arborol gels behave almost as transparent solids do: very weak intensity fluctuations, leading to no measurable correlation function. By contrast, at high concentrations HPC solutions exhibit relaxations typical of a viscous fluid,37,43 which is sensible for a semiflexible (persistence length ∼ 10 nm46,59) polymer dissolved beyond the overlap condition. One may speculate that constantly moving filaments may prove more effective at retarding the probe particle diffusion than immobile ones (which is oddly reminiscent of the increased electrical resistance with temperature in metals). The issue is not settled by the extensive work of Lodge and Rotstein,60,61 who compared diffusion of various probes in transient and permanent networks of random flight polymers, because local chain mobility was assured even in their permanent networks. There appears to be no comparative study of probe diffusion in rigid networks and solutions of the same rigid polymer, and the arborol gels do not readily afford this opportunity; neverthe-
less, one can test whether the collapsing of the fiber network affects the mobility of the probes. To this end, the diffusion of FD40 in 3% [9]-12-[9] was measured from 50 to 76 °C in steps of 2°. One sample was examined for the whole temperature range. At each temperature, it was measured 3 times after a 15 min equilibration period. Corroboration was sought from DSC experiments. Scanning calorimetry does not speak directly to the physical nature of a system (i.e., whether fluid or solid), but changes of state do often leave telltale thermal signals, which can quantify the completeness of the structural changes that underlie the transitions. The temperature was increased from 5 to 70 °C at a rate of 1 °C/min, held at 70 °C for 90 min, and then raised further at 1 °C /min to 105 °C. An endothermic peak was found 12 min after the oven reached 70 °C, and no other peak was found in the temperature range from 70 to 105 °C. This suggests that the structures holding the gel together disappear if a sample is held at 70 °C for about 12 min; accordingly, an upper limit temperature a bit higher at 76 °C was set for the FPR probe diffusion measurements. The 3% arborol solution was visibly fluid at this point. The diffusion of FD-40 in water and 3% gel at different temperatures are plotted in Figure 9. The two data sets in this figure are indistinguishable, so the disassembling of the fiber network during the gel-sol transition neither hinders nor enhances probe mobility. The diffusion is almost unaffected by the arborol gel/solution across a range of temperature. In Figure 10, the data are corrected for temperature and viscosity. Absence of a trend implies agreement with the Stokes-Einstein relation; this is almost the case when water viscosity is used, but very large deviations are observed when the solution complex viscosity is used. To explore the behavior of a large probe in an arborol system, DLS measurements were made on a 0.3 µm latex particle suspended in [9]-12-[9] arborol gel. The scattering in the latexarborol system was dominated by the latex particles. As the gels strengthened below about 65 °C, the intensity autocorrelation functions were driven down toward the baseline, indicating that the latex particle is strongly restrained; however, some motion was retained at short times, as shown in Figure 11. DLS studies by Engelhard et al.58 on the gels themselves (no probe particle) suggest that [9]-10-[9] arborol gels do undergo slow structural rearrangements (using very long acquisition times, ergodic correlograms62 could be obtained). Such an observation does not require the sample to be a torpid fluid instead of a gel. As pointed out by Schmidtke et al., fully reversible systems
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Sun et al. probes. Collapse or melting of the arborol fibers during the solgel transition produces no discernible effects on the diffusion of dextran probes. Acknowledgment. This work was supported primarily by Grants NSF-DMR-0075810 and NASA NNC06AA02A. J.W. was supported as a summer intern by the NSF-REU program (Grant CHE-9732195). J.P. acknowledges the support of the Stanford Synchrotron Radiation Laboratory in providing facilities used in these experiments: this work was supported by Department of Energy Contract DEAC03-76SF00515. References and Notes
Figure 10. FD40 in aqueous 3% [9]-12-[9] at different temperatures. The FPR diffusion has been scaled for temperature and macroscopic complex solution viscosity (left-pointing arrows; Y-axis left) or water viscosity (right-pointing arrows; Y-axis right).
Figure 11. DLS correlograms for 0.3 µm latex in [9]-12-[9] arborol at various temperatures spanning the melting transition. Although the t ) 0 intercept is depressed by the gel structure at low temperatures, some probe mobility is evident.
may stand as true solids while undergoing internal, structural rearrangements.63 Conclusion The [9]-12-[9] arborol creates a remarkably open, easily reversible network structure. The present study confirms the impression of earlier investigations on dried or freeze-fractured samples that very large fibrils stabilize these gels, which behave as elastic solids at low shear strain and low frequencies. Inside the gels, long and unbranched fibers or bundles of fibers cross each other to form scaffolds. The diameter of the fibers is 8.26 ( 0.68 nm, independent of concentration and temperature. As calculated by ChemDraw, the largest end-to-end distance of one [9]-12-[9] molecule is 2.73 nm; thus, the diameter is about three times the length of one arborol molecule. The reduction of dextran probe diffusion with arborol concentration in gels is minute compared to hydroxypropylcellulose solutions. This appears to be the result of the tight assembly of the arborols into rigid fibers, leaving behind large pores for diffusion of the
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