Neutron transmission and quasi-elastic neutron scattering in polymer hydrogels.
Our aim is to study the influence of porous media on the dynamics of free and bound water in hydrogels using two neutron techniques: quasi-elastic neutron scattering (QENS) and neutron transmission (1) in order to probe liquid motions in different ranges of observation times: [10.sup.-10] - [10.sup.-12] sec (microscopic measurements) and [10.sup.2]-[10.sup.-4] sec (macroscopic measurements).
Two types of polymer hydrogels were chosen for these investigations: gelatin and poly(acrylamide) (PAA) because of their different chemical natures and polymer network structures. Gelatin gels were prepared from the photographic grade gelatin (Polymerphoto, Kazan, Russia). The viscosity of a 10% aqueous solution of gelatin at 40 [degrees] C was 20 CP, pH [approximately]6.2, with an isoelectric point at 4.7. Gels were formed by quenching initially homogeneous aqueous solutions with the volume fractions, [Phi], in the range of [Phi] = 0.018 - 0,2 from 45 [degrees] C to 16 [degrees] C and aged for 12 h. PAA hydrogels with polymer volume fractions [Phi] = 0.4 were synthesized using chemicals Reanal (Budapest, Hungary) according to a standard procedure (2). To obtain gels with varying water contents, vacuum-dried gel samples were swelled in water.
Using quasi-elastic neutron scattering, information on microscopic dynamics of water molecules may be extracted from the energy broadening [Delta]E of quasi-elastic neutron peaks measured at different values of the wave vector transfer q = (4[Pi]/[Lambda]) sin ([Theta]/2), where [Lambda] is the neutron wavelength. The energy broadening [Delta]E measured at the middle of quasielastic neutron peak height. The contribution to [Delta]E from motions of gelatin macromolecules can be neglected since diffusion coefficients of polymers and ordinary liquids differ by more than two orders of magnitude.
Our QENS measurements were performed using a multidetector time-of-flight spectrometer NURMEN with an absolute energy resolution of 0.66 meV (WWR atomic reactor of Nuclear Research Institute, Kiev, Ukraine). A schematic representation of the equipment is given in Fig. 1. In the experiments, a monochromized neutron beam with energy [E.sub.0] = 12.97 meV was used. The neutron spectra were recorded over a range of scattering angles [Theta] = 9.5 - 101.3 [degrees]. A full description of the QENS method is given elsewhere (3). All QENS measurements were performed at 16 [degrees] C.
The plots of [Delta]E vs. [q.sup.2] for PAA gels of different polymer concentrations are given in Fig. 2. The shape of [Delta]E ([q.sup.2]) plots is greatly dependent on the volume fraction, [Phi], of PAA and, thus, on gel pore sizes. When [Phi] [less than] [less than] 1, the linear section of the plot around the origin is observed only at small [q.sup.2]; however, with larger [Phi]'s the function [Delta]E ([q.sup.2]) becomes linear over practically the entire range of [q.sup.2] values.
The quantitative interpretation of the observed effects may be explained by taking into consideration the hierarchy of molecular motions in fluids (rapid single-particle and slower collective motions of molecular clusters) proposed by Bulavin (4). Thus, the total broadening of the quasi-elastic peak can be presented as
[Delta]E = [Delta][E.sub.coll] + [Delta][E.sub.s-p], (1)
where [Delta][E.sub.coll] and [Delta][E.sub.s-p] are contributions to the total broadening from collective and single-particle modes of molecular motions, respectively. Within the Oskotsky-Ivanov model (4), the total broadening is given as
[Mathematical Expression Omitted], (2)
where the first term, linear with [q.sup.2], corresponds to the translational diffusion of the molecular cluster with the self-diffusion coefficient [D.sub.coll] and the second term corresponds to the single-particle jumps with the self-diffusion coefficient [D.sub.s-p]; exp(-2W) [similar to] 1 is the Debye-Waller factor; [[Tau].sub.0] is the residence time of water molecule between two jumps.
At small and large values of q we find two asymptotes of [Delta]E([q.sup.2])
[Mathematical Expression Omitted]; (3)
[Mathematical Expression Omitted]. (4)
Thus, the linear section in the observed experimental [Delta]E([q.sup.2]) and the deviation from linearity may be ascribed to changes in relative contributions from collective and single-particle diffuse modes of water in gels of different concentrations.
To study macroscopic mass transfer of liquid molecules in porous media, the neutron transmission technique was used [ILLUSTRATION FOR FIGURE 3A OMITTED]. In this method, protonated solvent molecules diffuse into the gel originally saturated with a deuterated analog of the same solvent and are then used as probe particles (tracers). The experimental procedures and data processing are given in (5). Since the bulk cross section of slow neutrons interacting with hydrogen is much larger that of deuterium, the transmission (i.e. the ratio of the intensities of transmitted and incident neutron beams) is greatly dependent on the quantity of protonated molecules diffused into the gel. To observe the diffusion process, a flat neutron beam with a wavelength of 1.54 [Angstrom] and a small height of 0.5 mm was formed. In the experiment the kinetic variation of the transmission perpendicular to the direction of the tracer flow through a chosen gel cross section was measured. The corresponding function [Phi](t), where [Phi] is the volume fraction of tracers in the above cross section, was calculated from the transmission data by a procedure given by Mel'nichenko and Klepko (6).
To determine the macroscopic diffusion coefficient of tracers, [D.sub.macr], from the function [Phi](t), we used the equation
[Mathematical Expression Omitted], (5)
which is the solution of Fick's equation for the one-dimensional tracer diffusion in a polymer gel (12). In Eq 5 [Mathematical Expression Omitted] is an average concentration of tracers in the system gel-reservoir; z is a distance from gel-reservoir interface.
To determine the friction coefficient f, which characterizes the friction between polymer network and liquids, we measured the velocity v of liquid flow through the fixed network at constant pressure as it is schematically illustrated in Fig. 3B. The thin-wall quartz cell reservoir is almost neutron transparent and is initially filled with the deuterated analog of the solvent which saturates the gel. The experiment begins (t = 0) when the solvent is poured in the vertical tube over the gel "plug," which is put into contact with the deuterated liquid in the reservoir. The liquid flow that results leads to the progressive increase in the concentration of the hydrogenated solvent in the reservoir. The experimentally measured variation of the neutron transmission with time, P(t), can be used to extract the velocity of liquid flow (7):
v = [m.sub.0] A [multiplied by] ln (P(t)/[P.sub.0])/1 - A [multiplied by] ln (P(t)/[P.sub.0]) [multiplied by] 1/t, (6)
where v is the velocity of liquid flow through the fixed gel network at constant pressure; [m.sub.0] is the initial solvent mass in the reservoir; [P.sub.0] and P(t) are the neutron transmissions of the reservoir at "zero" time and at time t, respectively (the value of neutron transmission is determined as the ratio of the intensity, I, of a neutron beam passed through the reservoir to the intensity of the incident beam, [I.sub.0]: P = I/[I.sub.0]), and A is the slope of the calibration curve. To determine f, we used equation
f = [Rho]ghS/lv [1 + 2 [multiplied by] [summation of] exp (- [n.sup.2][[Pi].sup.2][Theta]) where n = 1 to [infinity]], (7)
which is the solution of Darcy's equation for liquid flow through a porous medium under pressure (8). In Eq 7, S is the area of the horizontal cross section of the gel; [Theta] = t/[Tau] is the dimensionless time normalized to a certain characteristic time [Tau] = [l.sup.2]/D; l is a gel sample size; [Rho] is the density of liquid filling the tube of height h.
Following the hierarchy of molecular motion time scales, the experimental data were processed in the following way. Using the asymptotes of [Delta]E([q.sup.2]) for small q, the total self-diffusion coefficient D = [D.sub.coll] + [D.sub.s-p] was found by the Eq 3. The contribution to D corresponding to the collective motions (D.sub.coll]) was found from the asymptotes of [Delta]E([q.sup.2]) for large q (Eq 4). With known D and [D.sub.coll], the self-diffusion coefficient corresponding to the single-particle motion was found by substitution: [D.sub.s-p] = D-[D.sub.coll]. The D, [D.sub.coll] and [D.sub.s-p] for different volume fractions of polymer in gelatin and PAA gels are given in Fig. 4 and Fig. 5, respectively. In Fig. 4, the data of macroscopic diffusion coefficient [D.sub.macr] for gelatin gels obtained by neutron transmission are also given. As is seen, [D.sub.macr] ([Phi]) is in good agreement with [D.sub.s-p]. Since the tracer technique measures the mass transfer of water which is naturally identified with the self-diffusion of free water in the gel, the observed agreement makes it possible to conclude that the self-diffusion of free water in gelatin gel pores proceeds by a single-particle mechanism.
As seen from Figs. 4 and 5, a higher content of polymer per unit volume of the system leads to a corresponding growth in the fraction of bound water. Bound water dusters, together with the macromolecules of a gel matrix, make slow collective diffuse motions about the equilibrium centers, remaining stationary on average. As follows from the data obtained, a growing fraction of bound water in the gel results in considerable retardation of mass transfer, revealed by the tracer technique as well as in the pumping of single-particle diffuse modes into collective ones probed by QENS. From [Phi] [approximately equal to] 0.4 for gelatin and [Phi] [approximately equal to] 0.75 for PAA gels, the self-diffusion of water proceeds exclusively by a collective mechanism, and all water in the gel is bound. The last result is in good agreement with calorimetric data for PAA gels (9), but for gelatin gels all water should become bound at much higher concentrations of gelatin [Phi] [similar to] 0.7 (4). The observed discrepancy may be explained by a microspace effect, which appears as active cooperative behavior of water molecules within microscopic ranges corresponding to the pore sizes of the gelatin gels when the value of the latter are small enough (4).
Data describing concentration dependence of friction coefficient for gelatin gels are given in Fig. 6. As is seen in Fig. 6, gelatin gels exhibit a linear growth of f with the concentration of polymer network
f([Phi]) = 2 [multiplied by] [10.sup.8] (1 + 29 [multiplied by] [Phi]) dyn [multiplied by] s [multiplied by] [cm.sup.-4].
This result leads to the conclusion that the flow of solvents through the moderately concentrated gels is consistent with the predictions of the effective medium approach by Altenberger and Tirrell (10) and Cukier (11). The linear variation of f with [Phi] indicates that the flow under pressure corresponds to the macroscopic regime and the dominant retardation mechanism is the scattering from obstacles. At the same time, the macroscopic diffusion coefficient, [D.sub.macr], for the same gels vary with concentration as
[D.sub.macr] = 1,35 [multiplied by] [10.sup.-5] (1-1,87 [[Phi].sup.0.5]) [cm.sup.2]/s,
also confirm the effective medium theoretical predictions (10, 11). However, the undistorted root-mean-square relation valid for the whole range of polymer concentrations investigated ([ILLUSTRATION FOR FIGURE 3 OMITTED], solid line of curve 4) is indicative of the purely hydrodynamic nature of self-diffusion of water in gelatin gels.
In conclusion, it should be noted that the effective medium approach adequately describes self-diffusion processes of liquids molecules in other types of polymer gels, such as silica (12) and polysaccharide (13).
I wish to thank V. Slisenko from Kiev Nuclear Research Institute for making available to us his QENS apparatus and for useful comments. I have also benefited from interesting discussions with V. Shilov and Yu. Mel'nichenko from the Institute of Macromolecular Chemistry (Kiev, Ukraine), and L. Bulavin from Kiev State University. Financial support by INTAS (93-3379-EXT) is gratefully acknowledged.
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|Title Annotation:||5th International Conference on Polymer Characterization|
|Publication:||Polymer Engineering and Science|
|Date:||Mar 1, 1999|
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