J. Phys. Chem. 1083, 87,655-661
655
Kinetics of Multicomponent Transport by Structured Flow In Polymer Solutions. 2. Comparison of Varlous Transport Techniques' B. N. Preston, W. D. Comper,' T.
C. Lauren1,2 0. J. Checkley, and R. 0. Kitchen
Blochemishy Department, Monesh University, Clayton, 3 168, Vlctorla, Australla (Received:June 1, 1$82)
The high apparent transport rate of poly(vinylpyrro1idone)(PVP) in concentrated dextran solution which has previously been shown to be associated with the formation of dissipative structures has been confirmed and recognized by the use of a number of different, conventional transport techniques including those associated with analytical ultracentrifuge analysis, open-ended capillary measurement, a newly developed diffusion cell, and tube fractionation experiments. These various techniques do differ in quantitative aspects of transport and the manner in which anomalous transport is measured.
Introduction Our studies on the mechanism of macromolecular transport in gels and polymeric networks in solution have been primarily concerned with relating our observations to biological transport and organizational phenomena. We have particular interest in relating these studies to transport phenomena which occur in the extracellular matrix of connective tissues and within passive membrane
structure^.^*^ In view of the intrinsic complexity and variability of biological systems we have opted, at this stage, to employ simple model systems in order to gain optimal mechanistic interpretations. Studies on macromolecular transport in binary (polymer-solvent) systems have been well documented.4-8 In progressing to studies on ternary systems of polymer-polymer-solvent, we observed several surprising features associated with macromolecular transport which have been hitherto unexplained and have only been briefly reported."" It was early shown, in a limited number of experiments in the analytical ultracentrifuge, that the transport of linear, flexible macromoleculeswithin polymeric networks proceeded at much faster rates than those observed in the absence of the n e t ~ o r k .Further ~ experiments by Preston and Kitchen12 employing radioactive-labeled polymers with an open-ended capillary technique established that the rapid transport appeared to be a general phenomenon associated with the movement of a range of linear flexible macromolecules but not by globular particles. On the contrary, globular proteins, for (1) Part of this work has been presented at the Proceedings of the 2nd Australian Thermodynmics Conference, Melbourne University, 1981. (2)On sabbatical leave from Department of Medical and Physiological Chemistry, Biomedicum, Uppsala University, Uppsala, Sweden. (3)W. D. Comper and T. C. Laurent, Physiol. Rev., 58, 255 (1978). (4)B. N. Preston, T. C. Laurent, and W. D. Comper in 'Glycosaminoglycan Assemblies in the Extracellular Matrix",D. A. Rees and S. Arnott. Eds.. Humana Press. in Dress. (5)R. G.Kitchen, B. N. Preston, and J. D. Wells, J. Polym. Sci., Polym. Symp., 55, 39 (1976). (6)T.C . Laurent, L.-0.Sundelof, K.-0. Wik, and B. Warmegard, Eur. J. Biochem., 68, 95 (1976). (7)B. N.Preston, W. D. Comper, A. E. Hughes, I. Snook, and W. Van Megen, J. Chem. SOC.,Faraday Tram. 1, 78,1209 (1982). (8)K.-0. Wik and W. D. Comper, Biopolymers, 21, 583 (1982). (9)B. N.Preston and J. McK. Snowden in "Biology of Fibroblast",E. Kulonen and J. Pikkarainen, Eds., Academic Press, New York, 1973,pp 215-30. (10)T. C. Laurent, B. N. Preston, and L.-0. Sundelof, Nature (London), 279,60 (1979). (11)L.-0. Sundeltif, Ber. Bumenges. Phys. Chem., 83, 329 (1979). (12)R.G.Kitchen, Ph.D. Thesis, Monash University, Clayton Victoria, Australia, 1976. 0022-3654/83/2087-0655$01.50/0
example, showed a decrease in their transport rates in polymer networks as compared to their value in the absence of the network. In view of the highly unusual nature of these results, and the lack of a definitive, routine method for transport measurements to establish unambiguously that rapid transport was indeed a real manifestation of the system, these studies remained unpublished. However, in a recent article13 we demonstrated that rapid polymer transport was actually occurring in these systems through the formation of ordered macroscopic structures which move rapidly. This rapid transport was shown not to be the result of bulk convection, as normal diffusion kinetics were observed for solvent markers, such as [14C]sorbitol.The striking feature of this new type of transport process is that it is accompanied by ordered structured flows in the form of fingerlike projections emanating in both directions perpendicular to the initial boundary, as observed by tagging the polymers with colored dye. The occurrence of these structured flows is not influenced by the presence of low-molecular-weight solutes or D,O used below the boundary to afford macroscopic density stabilization. In this paper, we shall present much of the extensive data on polymer transport in networks that we have performed and which can now be analyzed in the light of our new findings cited above. An important feature of this presentation is the comparison of polymer transport obtained from a newly developed transport cell14-16to that obtained by a modified7open-ended capillary technique'l and the analytical ultracentrifuge so that the result of the latter two methods can now be placed in proper context. It is emphasized that most of the results so far are qualitative and that much detailed work remains to be done. The phenomena investigated are nevertheless significant since there are such striking differences between the various cases considered. While application of the characteristic features of this new transport process to biological systems is not immediate and direct, it is clear that developing and understanding the basic parameters associated with the etiological events leading to the formation of structured flows and factors required for their stability (13)B. N.Preston, T. C. Laurent, W. D. Comper, and G. Checkley, Nature (London),287,499 (1980). (14)T. C. Laurent, B. N. Preston, W. D. Comper, G. J. Checkley, K. Edsman, and L.-0. SundelBf, J . Phys. Chem., preceding article in this issue (paper 1). (15)L.-0. Sundelof, Anal. Biochem., in press. (16)T.C. Laurent, B. N. Preston, L.-0. Sundelof, and M.-P. Van Damme, Anal. Biochem., in press. (17)J. S.Anderson and K. Saddington,J. Chem. SOC.,S 381 (1949).
0 1983 American Chemical Society
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will eventually delineate those biological systems in which this phenomenon may occur.
Experimental Section Materials. Dextran T10 (various lot numbers used including Lot No. To536, To5400,0094,4202,3205) 10400) was obtained from Pharmacia Fine _Chemicals (Uppsala, Sweden). Poly(vinylpyrro1idone) (M,, 3.0 X lo5) (PVP-360; Lot No. 81C-2090) was from Sigma Chemical Co. (St. Louis, Mo). Tritiated water (Lot No. 1275-133; 0.25 mCi 8-l was from New England Nuclear (Boston, MA). [14C]Sorbitol (Code CFB28, Batch 45; 33 mCi mmol-') was from the Radiochemical Centre (Amersham, UK). The polymers were labeled with tritium as described by Preston et aL7 Polymer solutions were prepared by weight in distilled water either from the polymers as supplied or from dried samples. Solutions were made up by weight and conversion into mass/volume concentrations was carried out on the basis of the dry weight of solids (measured by heating over Pz05at 60 O C and 133.3-Pa pressure until constant weight was obtained) and the partial specific volume of the polymer. Methods. Measurement of Transport Coefficients. General Comment. All transport techniques which have been used in this study normally yield a diffusion coefficient which is time independent. However, we have clearly established by the use of certain transport techniques, to be described below, that the structured flow system may yield anomalous time-dependent diffusion coefficients. At present, we cannot offer any unified transport treatment. The complexity of the structured flow kinetics is clearly demonstrated in paper 4,18 where it is shown that a multistep process operates in their development and movement. For certain transport techniques we have persisted with conventional diffusion analysis to yield an arbitrary transport coefficient. No emphasis is placed on the absolute value of this parameter; rather, it is highly useful for comparative purposes. On the other hand, it is convenient to discuss linear rates of flow with certain techniques. Analytical Ultracentrifuge, These transport experiments were performed in a Spinco Model E ultracentrifuge equipped with RTIC unit electronic speed control and interference, schlieren, and absorbance optics (with associated photoelectric scanning system). All runs were performed at 20 "C at a rotor speed of 4980 rpm except where indicated in the text. Double-sector (2.5') capillary-type synthetic boundary cells (12 mm) with slightly enlarged capillaries were used to form boundaries between polymer solutions. Schlieren Runs. Three types of transport coefficients have been measured in the "diffusional" analysis of the schlieren curves. These are (1)the reduced height-area ratio
-
(au
-
T A = (An)2/[4at(an/ax),,,21
(1)
(2) the reduced second moment 1 TM = -
an x2- dx 2tAn ax and (3) the width at half-height7 Tw = w/(16t In 2 )
1-
(3)
and W is the width of the curve at 'I2 (anlax),,. The estimate of Tw was most frequently undertaken, since in our hands it was less time-consuming. The plates were read on a comparator (Nikon 6C) equipped with a reversible counter (Nikon ERC-251). The integrations required for the evaluation of TA and TM were performed by Simpson's trapezoidal method. Refractive index increments were measured on a Brice-Phoenix differential refractometer (Phoenix Precision Instrument Co., Philadelphia, PA) at 546 nm (Hg lamp). The instrument was calibrated with potassium chloride solutions. The refractive index increments of a series of solutions containing different concentrations of PVP-360 (over the range 1-5 kg m-3) and a constant concentration of Dextran T10 (55 kg m-3) were determined relative to the Dextran T10 solution. The specific refractive index increment of PVP-360 was found to be constant and had a value of 0.169 f 0.004 cm3g-'; this compares to a previously published value with water as solvent of 0.185 cm3 g-' (ref 19). Absorption Optics. We have utilized absorption optics to monitor the distribution of PVP-360 (which absorbs at 237 nm) in Dextran T10 solutions. The absorbance of PVP at 237 nm is linear up to 5 kg m-3 in dextran at a concentration of 130 kg m-3. Transport coefficients measured by this technique based on diffusion analysis (Tu)were calculated from the spreading of the boundary by employing the measured distance between 'I4 and 3 / 4 concentrations.20 Other measurements associated with the analysis of these runs will be discussed below. Diffusion Cells. Newly developed diffusion cells for measuring diffusion coefficients have been described in detail elsewhere.15J6The diffusion cell referred to here as the Sundelof cell consists of two identical cylindrical chambers (diameter 5.0 mm; height, 10 mm) which can be filled separately. By a shearing mechanism they can be moved over each other so that a horizontal boundary is formed between the solutions in the two chambers. All experiments were performed at 20 f 1 "C. The total quantity (mass) of diffusing solute transported across the boundary, Q, of cross-sectional area A during the time t after the formation of an initially sharp interface is given by21 Q 2 / A 2= AC2(Z%/a)
(4)
where AC is the initial concentration difference across the boundary and p is the transport coefficient obtained by this diffusional analysis. If the initial concentration of solute in the upper compartment is zero, then eq 4 can be written as = Q2r/(A2C;t)
(5)
where Co is initial concentration of solute. Thus, ?ij can be evaluated from a plot of (Q/Co)2vs. t. Open-Ended Capillary Technique. Capillaries for diffusion measurements were made from precision-bore tubing (internal diameter, 0.92 mm) of length about 10 mm. The ends were ground flat and the lengths of the individual capillaries measured with vernier calipers to fO.O1 mm. One end was closed by a glass cover slip sealed with epoxy resin. A ring of polythene tubing was placed around the top of the capillary and filled with solution of known radioactivity. The capillary was centrifuged in a
where n is the refractive index of the solution, t is the time, (19) G. B. Levy, J. Polym. Sci., 17, 247 (1955). (18) W. D. Comper, B. N. Preston, T. C. Laurent, G. J. Checkley, and
W. H. Murphy, J.Phys. Chem., second of two following articles in this issue (paper 4).
(20) V. N. Schumacher and H. K. Schachman, Biochim. Biophys. Acta, 23, 628 (1957). (21) L-0. Sundelof, Ark. Kemi, 25, 1 (1966).
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Multicomponent Transport in Polymer Solutions
bench centrifuge at 2000 rpm to force the fluid into the capillary. The excess solution was removed and the capillary (without the tubing) was placed in a vertical glass holder within the transport vessel containing solvent. Prior to immersion of the capillary into the solution, the system was allowed to equilibrate for 30 min. The solvent was then allowed to gradually submerge the capillary through a hydrostatic head. After sufficient time had elapsed, the capillary was removed and rinsed in distilled water, and the contents were transferred directly, by centrifugation, into a vial for counting. When transport was studied in the direction opposite to that of the gradient in macroscopic density of the system, the capillary was inverted beneath the glass capillary holder and held in place by a piece of polythene tubing fixed to the glass by epoxy resin. All transport runs were performed in a thermostated water bath a t 20 f 0.1 OC. A simpler, less expensive transport vessel was occasionally used. This was a single large test tube sealed with a rubber stopper, which was pierced to accommodate the stem of the glass capillary holder. The capillary was held above the solvent to allow the temperature to equilibrate and then mechanically lower into the solution. In view of the possibility of introducing convectional disturbances at the boundary of the capillary face during the mechanical movement, this technique was only used where large macroscopic density gradients operated across the boundary. Evaluation of the transport coefficient, based on diffusional analysis, from measurements with the capillaries ( F )was made by integration of Fick’s second law as applied to diffusion from a plane sheet of thickness 1 (or length of capillary in our case) initially at uniform concentration into a solvent of zero concentration22such that
where Q’is the amount of solute remaining in the capillary after time t, and Qo is original amount. When Q’/Qo < 0.6, it has been shownz3that the first term of the series gives F with an accuracy better than 0.5%. Thus 412 In 8 Q F =7r2t
7r2
80
(7)
For early times, where Q’/Qo > 0.6, evaluation of F can be made through the following equation
These equations for F apply to the capillary if a large, well-stirred external solution is used. However, stirring can cause mixing inside the top of the capillary.24 In experiments performed in this study, the outer solution was left unstirred. Corrections for the unstirred case%were not applied as previous preliminary studies have shown that with polymer transport the correction was within experimental error of the measurement and there was essentially no difference between stirred and unstirred systems. Phase Separation. In order to establish that the PVP360 and Dextran T10 polymers were “compatible” in the (22)A. T. McKay, Proc. Phys. Soc., 42, 547 (1930). (23)H.Magdelenat, P.Turq, and M. Chemla,Biopolymers, 13, 1535 (1974). (24)R. Mills, J.Am. Chem. SOC.,77, 6116 (1955). (25)L. Nanis, M.Litt, and J. Chen, J. Electrochem. SOC.,120, 509 (1973).
Dextran
Concentration
/ kg m - 3
Flgure 1. Phase diagram of the PVP-360-Dextran T10-water system at 25 O C . The solution represented by the open circle consisted of one phase only. Note that solutions containing PVP-360 at 5 kg m3 are all in the one-phase region.
concentration used in this study, we carried out phaseseparation experiments on the system, following the procedures described by Edmond and Ogston.26 Measurement of the specific polymer concentration in the immiscible phases was achieved by the use of tritium-labeled samples of known specific activity. Radioactivity Counting Procedures. Determination of 3H and 14Cradioactivity was measured by liquid scintillation counting (Packard Tri-Carb spectrometer, Model 3003 and LKB-Wallac 1215 Rack-beta scintillation counter). The activity of a 1.0-mL aqueous sample was determined by using 4.0 mL of a scintillation mixture described by Foxan Care was taken that polymer samples were suitably diluted to avoid precipitation in the scintillation fluid. All samples were made to contain equal amounts of polymer and thus were equally quenched. The samples were stored in the dark cold room overnight prior to analysis. A summary of the nomenclature used for the measured T values by various techniques is given in the Glossary. Results and Discussion The standard system that we have chosen to investigate for this comparative analysis of various transport techniques is a solution of Dextran T10 of concentration 135 kg m-3 with an imposed gradient within it of PVP-360 initially extending from 5 kg m-3 to zero concentration. The choice of using a dextran solution of this concentration was based upon our earlier work,1°J2in which it was shown that near-maximal transport rates of PVP-360 occur in such a system. The phase diagram of the system PVP360-Dextran T10-water shown in Figure 1 clearly demonstrates that the transport experiments are performed well within the one-phase region of this system. Sundelof Diffusion Cell. In this cell, the dextran solution of concentration 135 kg m-3 was used in both upper and lower compartments while the PVP-360 was added to the solution in the lower compartment to give a concentration of 5 kg m-3. Previous work13J4has shown that the transport of [3H]PVPin a similar system does not show normal diffusional kinetics (Le., a plot of (Q/ACo)2vs. t was nonlinear, as indicated in Figure 2b). However, a plot of QIAC, vs. t. displays an approximately linear response (regression coefficient >0.99) over a relatively long time (26)E. Edmond and A. G. Ogston, Biochem. J., 109, 569 (1968). (27)S.Fox, Int. J. Appl. Radiat. Isot., 19, 717 (1968).
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Preston et al.
a
2ot .
b
.*
I
2
1
Time /10’5rec
Flgure 3. Variation of T Cfor [3H]PVP-360 (0)and [‘4C]sorbitol (0) transport for the standard solution system, described in the legend of Figure 2, with time.
‘“I Time
/
a
sec
r
Figure 2. Transport of [3H]PVPover a boundary formed by la ering 135 kg m-3 Dextran T10 over a solution containing 5 kg m- [3H] PVP-360 and 135 kg m-3 Dextran T10. Q is the amount transported over a boundary of surface area A and C , is the initial concentration in the lower compartment. a represents a plot of Q/ACovs. time and b represents a plot of (Q/ACo)2vs. time.
interval (Figure 2a). In Figure 2a at least two distinct transport rates for the [3H]PVPare observed. In the first 3 h, about 35% of the PVP moves across the boundary at a rate of 1.4 X m h-l. At later times the rate falls to a much smaller value. In using trace quantities of [14C]sorbitolas a solvent marker, in a similar system, we previously demonstrated that normal diffusion kinetics were obeyed by this compound.13J4 This suggested that there is no bulk convection occurring in the system. We have also demonstrated13J4 that the kinetics of dextran transport, as measured by both forward and back fluxes of [3H]Dextran T10, displayed behavior similar to that of the PVP-360. Capillary Technique. As pointed out by us earlier,1° evaluation of a transport coefficient, IC by the open-ended capillary technique is difficult with this system since there is a marked dependence of ‘IC upon time. In the earlier report,1° we had attempted to minimize this problem by reporting values measured after an arbitrary time of 41 h. The time dependence of F for the [3H]PVP-360 in the dextran media is shown in Figure 3 together with the observed behavior of the solvent marker [14C]sorbitol. It is evident that the conventional transport analysis of [3H]PVP by use of eq 6 and 7 yields sharply increasing values of IC for times up to 8-12 h followed by a gradual decrease at longer times. In contrast, the behavior of [14C]sorbitol is ideal in that it exhibits no time dependence. The data of [3H]PVP-360transport for the capillary can be analyzed to allow for a direct comparison to that observed in the Sundelof cell. Since Qo = Q Q’, then it follows that Q / ( A C o ) = (1 - Q / Q o ) L (9) When the transport of [3H]PVP-360from the capillary is plotted as the function (Q/AC0)2vs. time as in Figure 4b, a sigmoidal curve is obtained while the behavior of the solvent marker, [ 14C]sorbitol,exhibits normal diffusional
+
1
,’i
0.8
Time/’10’5
sec
Flgwe 4. Plot, similar to Figure 2, of the variation of (QIACo)2vs. time and QIAC, vs. time for standard PVP-dextran transport system (described in F!gwe 2) as measued by the operwnded capillary technique: [3H]PVPtransport (O), [ ‘‘C]sorbitol transport (0).
kinetics. When the [3H]PVPtransport is plotted as Q/ACo vs. time, a linear region extending for 7 days is obtained with the subsequent onset of a second mode of transport (Figure 4a). Note the qualitative similarity of these kinetic data to those obtained in the Sundelof cell as described in Figure 2 and elsewhere.13J4 The transport rate of [3H]PVP in the first region in Figure 4a is evaluated as m h-l 3.75 X lo4 m h-’ as compared to a rate of 1.4 X as obtained in the Sundelof cell in Figure 2a. It is noteworthy that, although these transport rates have incorporated a boundary area term, we are led to suggest that the differences in PVP transport observed by the two techniques are due to the nonlinear relationship between PVP transport and the geometric dimensions of the system. Alternatively, by assuming that the function (Q/ACo)2 is linear with time, we can estimate an apparent diffusion
Multicomponent Transport in Polymer Solutions 3
7
a Boundary
I
l5
I
t
Meniscus c
cell
/ -
base I
5t 0 .-,
i
? .
i
t I
A
: I
1
L
Flgure 6. Time evolution of UV scans monitored at 237 nm in the analytical ultracentrifuge of a solution of Dextran T10 at 135.2 kg m3 layered onto a solution of dextran at 135.2 kg m3 and PVP-360 at 5.3 kg m-3 at times (a) 180, (b) 306, and (c) 780 s.
(28) B. N. Preston, W. D. Comper, G. J. Checkley, and R. G. Kitchen, J. Phys. Chem., following paper in this issue (paper 3).
the various measurements of T (eq 2 and 3) from the schlieren curve do register a comparable increase in the transport rate of PVP at relatively high dextran concentrations, in accordance with the behavior observed by other techniques. In none of the experiments reported in Figure 5 was it observed that the schlieren patterns noticeably deviated from being linear functions with time, thus indicating a “diffusion-type” process. Furthermore, there was no measurable displacement of the initial boundary during the course of the experiments. These apparently normal features of diffusion in this system have yet to be fully explained in the light of evidence cited above as to the kinetics of this process. However, one anomalous feature of this technique is that there is an apparent rapid removal of material from the concentration gradient at the boundary as evidenced by a reduction in the area under the schlieren curve. For the standard PVP-Dextran T10 system, we observed a reduction of -20% during the 10 min after the initial boundary formation; no further changes in the area occurred after this initial event. This reduction in area was not accompanied by the appearance of refractive index gradients elsewhere in the cell. This redistribution of material within the cell has been shown to occur by monitoring the presence of PVP-360 directly
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The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
500 lime/
1000
sec
Flgure 7. Variation of A,IA with time where A, is the average absorbance at 237 nm on the left-hand side of the boundary at time t and A is the initial absorbance at 237 nm on the right-hand side of the boundary for solutions described In the legend of Figure 2 (0).The arrow indicates the time at which the rotor was at speed. The corresponding experiment when the Dextran T10 concentrations was lowered to 40 kg m-3 is also shown (0).
by use of absorption optics at 237 nm. Absorption Optics. By observation of the changes in absorption occurring in the system at two different wavelengths, namely, 237 and 280 nm, we were able to differentiate between the transport of the PVP-360 and that of the dextran. At 237 nm the extinction coefficients of the two polymers are for PVP-360 = 86.2 m2kg-' and E1%237for Dextran T10 = 6.0 m2 kg-', while at the higher wavelength for PVP-360 = 70 m2 kg-' and for dextran = 7.3 m2 kg-l. In the standard system (with dextran concentration of 135 kg m-9, the dextran accounts for -50% of the totaJ absorption of 237 nm, with water as solvent reference. However, in the centrifuge cell, a dextran solution of 135 kg m-3 was used as reference so that the migration of PVP-360 is monitored specifically provided no concentration gradients of dextran are generated during the course of the experiment. The absence of any significant gradients can be shown by observing the experiment at 280 nm. The time evolution of the initial absorption scans of PVP transport in dextran, monitored at 237 nm, is shown in Figure 6. The anomalous feature of these scans is that, with time, material which absorbs at 237 nm rapidly accumulates on the left-hand side of the boundary. This material appears to be evenly distributed in this region. We have shown that accumulation of material of the left-hand side of the boundary is exactly balanced by depletion of absorbing material on the right-hand side of the boundary. For the same system, an apparently normal schlieren pattern is registered. Absorption scans at 280 nm, which specifically detect dextran, demonstrated that no measurable gradients of this material were formed at these times. We conclude that changes in the net distribution of material as observed at 237 nm are singularly due to the net transport of PVP. The PVP-360 transport in a Dextran T10 medium of 40 kg m-3 demonstrates that the rate of absorbing material accumulating at the lefthand side of the boundary is very slow indeed (Figure 7). At this dextran concentration we also know that [3H]PVP transport is relatively slowa and that structured flows are not present. Analysis of the increase in absorbance on the left-hand side of the boundary in terms similar to that shown for the Sundelof cell in Figure 2 indicates that the change is in-
b.
Figure 8. (A) Time distribution of [3H]PVP and [14C]sorbitolfor solutions described in Figure 2. The boundary was formed in plastic tubes (10 X 60 mm) between solutions of 19 mm in column height. Underlay fluid of tetrabromoethane was placed in the bottom of the tube. The contents of the tube were fractionated at various times by displacement with tetrabromoethane and the distribution of [3H]PVP (0) and [ 14C]sorbitol(0)was determined. The position of the original boundary (. or --) is indicated. The ordinate represents the fractional percent of radioactivity in the sample, C,, as compared to that originally placed in the bottom of the tube Co. The abscissa represents the fractional percent distance along the tube containing solution which was approximately 38 mm in total length. The time of the fractionation was (a) 11, (b) 73, (c) 134, (d) 251, (e) 490 mln. (B) Time distribution of [%]PVP for system described in part but with [l'C]sorbitd absent. The time of fractionation was (a) 9 and (b) 152 min. (c) Time distribution of [3H]PVP across the boundary formed by layering water over a solution containing 5 kg m-3 [3H]PVP and 135 kg m-3 Dextran T10. The time of fractionation was (a) 9 and (b) 147 min.
--
-
itially linear with time and falls off at later times (Figure 7). For the experiment depicted in Figure 7, which was carried out at a rotor speed of 4000 rpm, the initial PVPm h-'; this value is 360 transport rate was 3.8 X somewhat higher than the rates measured at unit gravity in the Sundelof cell (Figure 2) which gave a value of 1.4 X m h-'. An unexpected feature of these systems is that while an initial rapid but partial redistribution of material appears to occur in the cell the relaxation of the concentration gradient of absorbing material still remaining at the initial boundary appears to follow a normal diffusion process. It should be stressed that the perceived concentration gra-
Multicomponent Transport In Polymer Solutions
dient at the boundary is a space-averaged measurement and does not reflect any changes in concentration that occur in the plane at right angles to the optical axis. The lateral movement of this boundary is negligible within the time of measurements performed so that the sedimentation of the PVP is negligible. Diffusional spreading of the boundary is also minimal within the time period (which is approximately 5 4 min) for initial linear PVP transport rate measurements. An approximate evaluation of Tu made on the standard PVP-36CkDextran T10 system gives a high value in the range of (100 f 20) X lo-" m2 s-l. Time Evolution of [3H'lPVPDistribution in a Vertical Test Tube. The spatiotemporal-averaged transport measurements of [3H]PVP and [14C]sorbitolhave been performed in a vertical test tube which was fractionated at various times (Figure 8A). The distributions of both PVP and sorbitol appear to be sigmoidal, with gradual spreading with time. We had claimed previously13that a wavelike distribution of [3H]PVP analyzed in the tube-ractionated system was a characteristic feature of PVP transport; it now appears that a good deal of noise associated with the profile of [3H]PVP in this system is associated with an approximate 10% counting error associated specially with 3H determination. Similar profiles for the distribution of [3H]PVP are seen in Figure 8B in which the [14C]sorbitol is now absent and [3H]PVPis monitored specifically. In addition, noisy [3H]PVP profiles are observed when water has been overlaid onto the solution containing [3H]PVP and dextran (Figure 8C). We know that this system does not generate observable structured flows, and we presume the normal diffusion of [3H]PVPshould occur. Therefore, it is more nearly correct to state that no definite conclusions can be drawn from the noisy distribution of [3H]PVP in a structured follow system, as it is likely to be derived from a counting effect. Perhaps the most remarkable feature of the PVP-dextran-sorbitol system, which is exemplified in Figure 8A, is the preferential spreading of PVP over that of sorbitol. At 8 h the PVP gradient has relaxed completely whereas the sorbitol gradient has not changed to any great extent. Conclusion. The study of poly(vinylpyrro1idone) transport in dextran solution, in a region where no irreversible phase separation occurs, has demonstrated that the PVP may move at very high rates. This rapid transport has been confirmed through the use of a variety of
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983 661
transport measurements, which commonly employ spatiotemporal-averaged quantities. Because of the different boundary conditions that operate in these various techniques, the details of the anomalous rapid transport may vary. The kinetics of the process are clearly depicted through the use of the Sundelof and transport by the open-ended capillary method may be interpreted in a similar fashion. Studies associated with various forms of analysis associated with the schlieren and absorption optics in the analytical ultracentrifuge are in essential agreement in that there appear to be two modes of relaxation of the PVP concentration gradient: (a) one involving a rapid redistribution of PVP in the cell and (b) a process which is essentially a local boundary phenomenon in which the observed concentration gradient gradually dissipates as in a diffusion-type process. These processes have been observed also in the quantitative examination of the distribution of PVP in boundaries formed in vertical test tubes. These results clearly substantiate and confirm the highly anomalous nature of rapid transport of this particular flexible polymer in polysaccharide solution networks and yield a unification of the comprehensive measurements that we have made.
Acknowledgment. This project was supported by the Australian Research Grants Committee (Grant Nos. D68/168988, D273/14137 and DS79/15252). We acknowledge the assistance of Geoffrey Wilson with analytical ultracentrifugation. Glossary TA
transport coefficient determined by reduced height-area schlieren optics
TM
transport coefficient determined by reduced second moment schlieren optics transport coefficient determined by width at half-height schlieren optics transport coefficient determined by absorption optics transport coefficient determined with Sundelof diffusion cell transport coefficient determined with open-ended capillary
Tw TU
P P
Registry No. PVP, 9003-39-8; dextran, 9004-54-0.
