13426
J. Phys. Chem. 1994, 98, 13426-13431
Effects of Simple Salts on the Transport of Polyvinylpyrrolidone in Dextran Solutions Hiroshi Maeda," Takehiro Mashita, Hiroaki Ojima, Shigeo Sasaki, Yoko Tomita, Tsuyoshi Fukuda, and Michio Yamanaka Department of Chemistry, Faculty of Science, Kyushu University, Fukuoka 812, Japan Received: July 15, 1994; In Final Form: September 26, 1994@
Rapid transport of polyvinylpyrrolidone (PVP) in dextran solutions accompanied by a 'finger'-like dissipative structure, first reported by Preston et al. [Nature, 1980, 287,4991,was found to be further accelerated when a simple salt was present in both upper and lower compartments of a diffusion cell. The enhancement effect was found on various salts to different extents when compared at a given salt concentration C. The effect depended on C for a given kind of salt. The effect was suggested to be of mechanical origin rather than of thermodynamic one. When the transport rates, after conected for different viscosities, were plotted against the densities of the solutions, most data for different salts at 2 M as well as those for different salt concentrations in the case of CsCl and NaBr approximately fell on a single curve. The curves differed for different PVP concentrations. Effect of the salts were examined on the flow patterns, such as the width of fingers, onset time and the critical PVP concentration for the appearance of fingers. Effect of the molecular weight of PVP was also examined.
When an aqueous solution of dextran (a-1,6-glucan), a polysaccharide composed of D-glucose, is placed above another aqueous solution consisting of dextran of the same concentration and polyvinylpyrrolidone (PVP), the diffusion of PVP from the lower solution to the upper one is expected to occur. However, when both dextran and PVP concentrations exceed respective critical values, a rapid transport of PVP has been observed by Preston et a1.l This rapid transport was ascribed to the Occurrence of a finger-like structured flow and was characterized by the linear dependence of the transported amount on time t rather than on square root of t.l,* The molecular mechanism of the phenomenon is not yet fully elucidated in spite of the extensive research by Preston and Camper.'-" Also, extension to systems other than dextran-PVP has been scarcely reported. This phenomenon can be regarded as a kind of mechanochemical system. Hydrodynamic flow is created at the expense of chemical potential not of gravitational potential. We have preliminarily reported12 that the PVP transport in the PVP-dextran system is enhanced in the presence of a simple salt (at the same concentration in both upper and lower solutions), the extent of enhancement depending on the kind of ions. In the preliminary report, we have shown that the enhancement effect of the salts can not be ascribed to their effect on the coil dimension of PVP.12 The intrinsic viscosity of PVP in aqueous solutions considerably decreased in the presence of 2 M CsCl. In the presence of 80 kg m-3 dextran, however, the coil dimension of PVP was decreased so as not to be influenced by the addition of CsCl. The biological significance of the phenomenon has been inferred and extensively examined by Comper.13 The present salt effect may provide another controlling factor of the phenomenon in biological context in terms of changing ionic strength of the media, in addition to that in terms of biosynthesis of polymers. In the present study, we extend our investigation to include the effect of several anions and to examine the effects of salt concentration in the case of three salts, CsCl, NaBr, and NaSCN. We measured the viscosities and the densities of the four component solutions and found a relation between the density @Abstractpublished in Advance ACS Abstracts, November 15, 1994.
and the transport rate corrected for the viscosity at given concentrations of PVP and dextran.
Experimental Section Polyvinylpyrrolidone (PVP) (Nacalai Tesque Inc.) was labeled with remazol brilliant blue under the following conditions. PVP (50 g) and the dye (0.75g) were reacted in 50 mM aqueous NaOH (2L) at 50 "C for 84 h. Dialysis fust against 2 M NaN03 and then against distilled water was repeated several times followed by lyophilization. Although an unfractionated sample was used in most of the present study, we have examined the effect of the molecular weight on the enhancement effect. Fractionation of labeled PVP samples was canied out according to Jirgen~0ns.l~ A solution of 20.7 g of PVP (5 wt %) in 0.71 M (NH4)2S04 prepared at 0 "C was brought to 25 "C and kept for 2 days to complete liquid-liquid phase separation. The bottom phase was collected, dialyzed against distilled water, and freeze-dried. The sample was referred to as Fraction I (Fr. I). To the supematant a certain amount of 2 M (NH&S04 solution was added to make the final concentration of 0.72 M, and the solution was kept for 2 days to induce liquid-liquid phase separation. From the bottom phase Fraction I1 was recovered. Fractions I11 and IV were obtained from the bottom phase with the supematant at a (NEi4)2S04 concentration of 0.75 M. Yield: Fr. I, 8.20 g; Fr. 11, 2.74 g; Fr. 111, 3.46 g; Fr. IV, 2.74 g. Number average molecular weights were determined from the osmotic pressures with a Knauer membrane osmometer at 33.0 f 0.1 "C. Their values (lo5)were 5.8 f 0.2,5.5 f 0.1,4.5f 0.3,0.96 f 0.01,and 3.2 f 0.2for Fr. I-IV and the unfractionated sample, respectively. The second virial coefficients of these five samples were mol cm3 gg2) 4.8 f 0.4,4.8f 0.4,5.6 f 0.2,5.9f 1.2,and 5.1 f 1.2.The number average molecular weights of dextran (Nacalai Tesque Inc.) determined from the osmotic pressure were (3.7f 0.2) x lo4 (MOF3306)and (3.9f 0.1) x lo4 (MlE5640). The second virial coefficients of these samples were (4.5f 0.4) x mol cm3 g-2 and (2.4f 0.2) x mol cm3 gP2. Labeled dextran was prepared by the reaction with remazol brilliant blue in 0.05 M NaOH at room temperature for 24 h. After extensive dialysis against distilled water, the sample was freeze-dried.
0022-365419412098-13426$O4.50/0 0 1994 American Chemical Society
Polyvinylpyrrolidone in Dextran Solutions
J. Phys. Chem., Vol. 98, No. 50, 1994 13421 3.5 I
I
I
0
3.0 0 0
E E
0
8
0
t
A
0
0
2.5
. .
0
I
Y O
0
0,
0
0.5 0
5
10
15
c p l g dm
20
25
0 .o
0
-3
Figure 1. Osmotic pressures of labeled and unlabeled PVP samples at 33.0 f 0.1 "C. Labeled sample: (0)in water; (0)in 0.1 M NaC1. Unlabeled sample: (0)in water. Polymer concentration cpis expressed in g dm-3.
Determination of the extent of labeling of PVP was carried out as follows by measuring the osmotic pressures. In Figure 1 osmotic pressures of the solutions in water are shown for labeled and unlabeled unfractionated samples. Since the labeled sample carries some number of charges introduced by the dye molecule, the labeled sample exhibits higher osmotic pressures than the unlabeled one. We can assume the osmotic coefficient to be unity because of very low charge density. The osmotic pressure II at a polymer concentration c is given as follows in terms of v, the number of charges per polymer, if the number of univalent counterions per polymer is assumed to be given by v.
0.1
0.2
0.3
t 11dsec
0.5
0.4
+
Figure 2. Transported amount Q of PVP in 80 kg m-3 dextran 2 M salt: PVP concentration, CO,20 kg m-3; (0)NaBr; (A)NaI; (W) NaN03; (A) NaC1; (0)NaSCN; (0)no salt.
Viscosity was measured with an Ubbelohde type capillary viscometer (flow time of water 19.1 s) at 25.0 f 0.01 "C. Reproducibilities of the flow times were within 0.5 s. Density of the solutions was measured with a DMA 60-602 densitometer (Anton Paar) at 25.0 f 0.001 "C or a pycnometer of GayLussac type (25 mL) at 25.0 & 0.05 "C. Visualization and recording of structured flows were done with still photographs. Free liquid boundaries between two solutions were formed in the center of a light absorption cell (1 cm wide and 0.1 cm in depth). The operation was performed manually by gently placing the top solution, dispensed from a syringe through a fine plastic cannula, onto the bottom solution. The experiments were performed in an air-conditioned room at 25 f 1 "C. The boundary was photographed at proper intervals of time under a microscope (Nikon SMZ-2T).
Results We extrapolated linearly in the low concentration region to evaluate Mappas shown in Figure 1. We obtained Mapp= 1.2 x lo5. For the unlabeled neutral polymer in water, II is given as a virial expansion series.
WcRT = 1 N n
+ B,c
(3)
With Mn = 3.2 x 105 from the measurements on the unlabeled sample, we have v = 1.6. The corresponding degree of polymerization DP, is 3.1 x lo3 and DPJv = 2 x lo3. We could conclude that one dye molecule is attached, on the average, per 2000 residues. In Figure 1, the results on the labeled sample in 0.1 M NaCl solution are also shown. The result is close to or identical with that of the unlabeled sample in water, as expected for polyions in the presence of excess salt. This indicates that little or no significant perturbation, such as chain scission, took place during the labeling reaction. Transport experiments were carried out at 25 f 1 "C with Sundelof ~ e l l s . ' ~Each J ~ compartment of the cell is a cylinder of about 1 cm long with a cross sectional area A of about 0.2 cm2. Values of the area A were determined from the diffusion measurements on KN03. Transported amounts Q of PVP were determined from the absorption of the upper solution sampled at a prescribed time. Wavelengths used were 225-300 nm and 633 nm for alkali metal chlorides and sodium salts, respectively. The dextran concentration was kept constant at 80 kg m-3 throughout the present study. PVP concentrations were either 10 or 20 kg m-3 for alkali halide or sodium salt series.
Enhancement of the Transport Rate of PVP by the Addition of Simple Salts. In Figure 2, the transported amounts Q of PVP from the lower to the upper compartment of the Sundelof cell are shown in the presence of 2 M sodium salts together with the result in the absence of the simple salts. In the latter case we have found similar transport characteristics as reported in the original work by Preston and c o - w ~ r k e r s . ~ , ~ As reported preliminarily, significant enhancement of the PVP transport was found for alkali metal chlorides at a concentration of 2 M as seen from Table 1. The transport rate v is defined from the following relation
Q/ACo = vt
(4)
where COdenotes the initial PVP concentration in the lower compartment. Instead of eq 4, we sometimes observed linear relations between Q and t with a positive or a negative intercept on y-axis (Q-axis). Positive intercepts have been noted for solutions of high visc~sities.'~In the cases where plots did not pass through the origin, the transport rates were determined from the slopes of straight lines, as done for the data shown in Figure 6. In Table 1, a summary of the transport rate v is given. The order of enhancement effects exhibited little correlation with the osmotic coefficients of the salt solutions or with their order in the lyotropic series. We can conclude that the different abilities of the salts do not arise from their different thermodynamic properties.
Maeda et al.
13428 J. Phys. Chem., Vol. 98, No. SO, 1994
-
TABLE 1: TransDort Rate of PVP in 80 kp m-3 Dextran Solutions at 25 'Cab PVP concentrationkg m-3
CsCl
10 20
45 f 6
(1
NaBr
9.5 f 0.3
The rate is expressed in
m
s-l.
NaI
9.2 f 0.3
Nd03
NaCl
7.6 f 0.2
5.2 f 0.4 5.8 f 0.2
LiCl
no salt
2.6 f 0.2
2.7 f 0.3 2.9 f 0.1
NaSCN
5.0 f 0.3
Salt concentration is 2 M.
TABLE 2: Viscositiee solution
80 kg m-3 dextran(a)' 80 kg m-3 dextran(a) 80 kg m-3 dextran(a) 80 kg m-3 dextran(a) 80 kg m-3 dextran(a) 80 kg m-3 dextran(a) 80 kg m-3 dextran(a) 80 kg m-3 dextran(a) 80 kg m-3 dextran(b)d 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg mv3dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b) 80 kg m-3 dextran(b)
+ 10 kg m-3 PVP + 10 kg m-3 PVP + 2 M LiCl + 10 kg m-3 PVP + 2 M NaCl + 10 kg m-3 PVP + 0.2 M CsCl + 10 kg m-3 PVP + 0.5 M CsCl + 10 kg m-3 PVP + 1 M CsCl + 10 kg m-3 PVP + 2 M CsCl + 20 kg m-3 PVP + 20 kg m-3 PVP + 2 M NaCl + 20 kg m-3 PVP + 2 M NaSCN + 20 kg m-3 PVP + 2 M N d O 3 + 20 kg mT3PVP + 2 M NaI + 20 kg m-3 PVP + 2 M NaI + 20 kg m-3 PVP + 2 M NaBr + 20 kg m-3 PVP + 0.5 M NaBr + 20 kg m-3 PVP + 1 M NaBr + 20 kg m-3 PVP + 0.25 M NaBr + 20 kg m-3 PVP + 0.5 M NaBr + 20 kg m-3 PVP + 1 M NaBr + 20 kg m-3 PVP + 1.5 M NaBr + 20 kg m-3 PVP + 2.5 M NaBr + 20 kg m-3 PVP + 3 M NaBr + 20 kg m-3 PVP + 0.5 M CsCl + 20 kg m-3 PVP + 1 M CsCl
%e?
1.oo 1.93 2.81 2.60 2.06 2.04 1.98 1.77 3.26 4.40 4.76 4.02 5.05 5.05 5.26 2.25 2.45 3.97 4.29 4.75 4.99 5.76 6.16 3.60 3.47
Measured at 25 i 0.05 "C. Relative viscosities are referred to that of the 80 kg m-3 dextran solution. Estimated error was f l % . Lot MOF3306. Lot MlE5640.
Viscosity. It was reported that the transport of PVP in dextran solutions increased with temperature, and this was well explained by the corresponding change of the viscosity? Viscosity is thus a factor influencing the transport rate. We have measured the viscosities of various solutions, and the results are shown in Table 2. Flow times of 80 kg m-3 dextran solutions of two samples were 69.3 and 76.0 sec. Flow times of 80 kg m-3 dextran 10 kg m-3 PVP and 80 kg mP3 dextran f 20 kg m-3 PVP were 133.3 and 246.4 s. When the transport rates v were plotted against the viscosities, little correlation was found. For five sodium salts, both the viscosities and the rates became large in their presence. For a series of different CsCl concentrations, on the contrary, viscosity decreased with CsCl concentration when it was higher than 0.5 M while the rate v increased with it. Little systematic dependence of the rate on the viscosity of the medium is thus apparent as far as the salt enhancement effect is concemed. Density. We have measured the densities of the solutions of different compositions. In Figure 3 the transport rates v are plotted against the density of the solution e of the lower compartment for 2 M salts. Although data points scatter significantly, a kind of correlation is clearly seen between v and 4. In Figure 3 the data corresponding to different CsCl concentrations are also included; the 2 M CsCl point [e = 1.275, v = (45 f 6 ) x ms-'1 is located outside the displayed region. Significant deviation of the data corresponding to both 1 and 2 M CsCl and 2 M NaI from that of other salts has led us to note that density alone can not explain the effect of salts. This was pointed out previously.** Since CsCl solutions exhibit anomalously low viscosities, a correction of the transport rate for a change of viscosity is suggested. In Figure 4 the transport rates corrected for viscosity (qrelv) are plotted against the density
+
i
D
i
0
,O
. > F
55
tt
m
o 1
8
* 1 .1
1.05
1. 1 5
1 .25
1 .2
1 .3
D e n s i t y I l o 3 k g m'3 Figure 3. Dependence of transport rates v on the densities of the
solutions in the lower compartment: (0,O) no salt; (B) CsCl at 0.2, 0.5, 1.0 M; (e)2 M Lick (V) 2 M Nd03;(0) 2 M NaSCN; (A, A) 2 M NaCl; (0)2 M NaBr; (box with a plus in it) 2 M NaI. Filled and open symbols refer to PVP concentrations of 10 and 20 kg m-3, respectively.
Tu
20 L
i
0 u)
I
E c
. >
FE
LO 7
10
i
v
I
&
D
i
A
1
1.1
1.05
1.15
Density I
1.2
1.25
1.3
l o 3 k g ma3
Figure 4. Correlation between the density and transport rate corrected for the viscosity. qreldenotes the ratio of the viscosity to that of 80 kg m-3 dextran solution without PVP and salt. Symbols refer to the same solutions as in Figure 3.
e. Here relative viscosities refer to the viscosity of the solution
+
(80 kg m-3 dextran 20 kg m-3 PVP), which is taken tentatively as a reference. Figure 4 shows a better correlation between rrepand than between v and e. It is to be noted that in Figure 4 filled symbols refer to the solutions of 10 kg m-3 PVP while other symbols refer to those of 20 kg m-3 PVP. The effect of PVP concentration now shows up significantly, which will be confirmed later. With the correction for the viscosity, convergence of the data was improved significantly, including CsCl data (1 and 2 M). However, deviation of the data on 2 M NaI from the suggested correlation was not improved. Effects of Salt Concentrations. We have examined above mainly the effects of different kinds of simple salts at a fixed concentration of 2 M. Since we have arrived at the understanding that the main cause for the enhancement effect is a mechanical rather than thermodynamic, it is pertinent to consider
Polyvinylpyrrolidone in Dextran Solutions
J. Phys. Chem., Vol. 98, No. 50, 1994 13429 50
5
4
O
E
. €
d
I
I
1
I
I
I
40
R
'0 0
a E
3
30 0
c '0
oo
r
4 +
;20
2
z
e
"
e
I
O
0 0
3
2
1
t 1 1 0 ~sec
Figure 5. Effect of CsCl concentration on the transport of PVP in 80 kg m-3 dextran solutions. CsCl concentration (M): (0)0.35; (0)0.6; (A) 1.0; (A) 1.25; (0) 1.5. 3.5
O
0
~
0
I
1
I
I
I
I
0.5
1
1 .5
2
2.5
3
0
3.5
C I M Figure 7. Dependence of the transport rate v of PVP in 80 kg m-3 dextran solutions on salt concentration C: (0,H) CsC1; (0,O) NaBr. Filled and open symbols refer to PVP concentrations of 20 and 10 kg
m-3, respectively.
1
I
I
I
I
1
1
I
I
120
1
I
I
I
,
I
I
e 2.5
e
E E
0 0
. 2
yo .
1.5
0,
e
0.5
rl I
0
"
0
,/
-
, . I
1
20
, 2
3
I
1
,
4
5
6
+
+
+ 124(C/M)
for C I2 M
(5)
g(Nal3r) = 1031 -I- 77(C/M)
for C I3 M
(6)
g(CsC1) = 1027
+
Viscosities of the solutions of 80 kg m-3 dextran 10 kg m-3 PVP CsCl and 80 kg m-, dextran 20 kg m-3 PVP NaBr were also measured and varied nonlinearily with C for both CsCl and NaBr. Relative viscosities referred to 80 kg m-,
+
e
OB" ,
,
I
7
the effect of salt concentration. We have examined it on three salts, CsC1, NaBr, and NaSCN. The results are shown in Figures 5 and 6 . In the case of CsCl, linearity between Q and time t held for the entire time range examined. On the contrary, positive or negative intercepts were observed in the case of NaBr, although the linear relation was confirmed. The different behavior between CsCl and NaBr is related to the difference in their viscosities. Shearing motion accompanied by rotating the upper dome of the SundelGf cell against the lower one is suggested to give a perturbation to the transport. Mixing of the upper and the lower solutions may be induced at zero time. Densities of the solutions of 80 kg m-3 dextran 10 kg m-3 PVP CsCl and 80 kg m-, dextran -I- 20 kg m-3 PVP NaBr were found to be linear in salt concentration C and well described with the following relations where 4 is expressed in kg m-,.
+
-
8p@,
t 1 1 0' sec Figure 6. Effect of NaBr concentration on the transport of PVP in 80 kg m-3 dextran solutions. NaBr concentration (M): (0)0; (0)0.5; (A)1.5; (A) 1.75;(m) 2.5; (0)3.0.
+
4
e
1
+
Den8lty 1
lo3 kg
m-'
Figure 8. Summary of the salt enhancement effects on PVP transport in 80 kg m g 3dextran salt solutions. Filled and open symbols refer to PVP concentrations of 10 and 20 kg m-3, respectively. Open triangle refers to 2 M NaI.
+
dextran solution rrelwere well described with the following functions of C given in molarity,
rrel(CsC1)= 1.94
+ 0.57,C - 0.74,C2 + 0.209C3 for C I2 M (7)
grel(NaBr) = 3.40,
+ 2.16,C - 1.01,C2 + 0.20@ for C I3 M (8)
The transport rates are compared in Figure 7 as function of the salt concentration C for CsCl and NaBr. The concentration dependence was very small in the case of NaSCN and is not shown in the figure. A big difference is seen between the two curves, since CsCl solutions are denser but less viscous than NaBr solutions at the same concentration. In Figure 8 all transport rates after correction for the difference of viscosity are plotted against the density 4 for both different salts at 2 M as well as for different salt concentrations of CsCl and NaBr. As a reference, dextran solution without PVP was chosen to normalize the viscosities of solutions of different PVP concentrations. Densities of 0.5 and 1 M CsCl
Maeda et al.
13430 J. Phys. Chem., Vol. 98, No. 50, 1994 TABLE 3: Effects of Molecular Weight of PVP on the Transport Rate" transport rate/lW7 m s-' Mnb 2 M CsCl 0.61 M CsCl 0.2 M CsCl 0M 5.8 x 105 68 f6 14 f 3 3.9 f 0.5 4.0f0.5 42 f 3 9.6 x 10" 45 f 6 13 f 2 2.7 f 0.2 2.7 f 0 . 3 3.2 x 105 unfractionated Dextran, 80 kg m-3; PVP, 10 kg m-3. Number average molecular weight of PVP. solutions at 20 kg m-3 PVP were calculated according to the relation Q (kg m-3) = 1031 124(C/M). Densities of 0.5 and 1 M NaBr at 10 kg m-3 PVP were calculated according to the relation (kg m-3) = 1027 77(C/M) Filled and open circles refer to 20 and 10 kg m-3 PVP, respectively. It is suggested that the transport rate multiplied by the viscosity is a unique function of the density irrespective of the kind and the concentration of the salt. It is interesting that the effect of PVP concentration becomes significant as the density of the solution increases. In Figure 8 only one data point (a filled triangle) deviates from the curve. The data were obtained with the solutions containing 2 M NaI. Effect of the Molecular Weight of PVP. Effects of the molar weight of PVP were examined with fractionated samples. The results are summarized in Table 3 together with those on the unfractionated sample. We see that longer chains are transported more rapidly. It is interesting to note that in 2 M CsCl the low molecular weight sample (Mn = 9.6 x lo4) exhibits a similar transport rate to that of the unfractionated sample of a higher molecular weight (Mn = 3.2 x lo5). Phase Separation. Although all the solutions examined in the present study were stable against phase separation, we found phase separation under a variety of conditions. In the case of 10 kg m-3 PVP 80 kg m-3 dextran CsCl, solutions were stable up to 2 M CsCl, but 10 kg m-3 PVP 135 kg m-3 dextran CsCl solutions phase separation when CsCl concentration was higher than 0.5 M. In the case of 20 kg m-3 PVP 80 kg m-3 dextran, the critical salt concentrations for the phase separation were 25-28 mM for Na2S04, 1.5-1.6 M for NaC104, and 2.7-2.8 M for NaNO3 at 25 "C. Structured Flow. The rapid transport of PVP in dextran solutions has been shown to be coupled with the formation of a structured flow called 'fingering', which is a kind of dissipative structure. The flow pattern was monitored in a rectangular Tiselius electrophoresis cell (cross section of 2 cm x 0.2 cm).lV2 The spatiotemporal-averaged measurements in the Sundelof cell were imagined to be accompanied by coherent finger structure. We have observed the flow patterns in the presence of various salts using a rectangular cell for light absorption (cross section of 1 cm x 0.1 cm). Examples of flow patterns in the presence of 2 M different salts obtained under identical conditions are shown in Figure 9 together with the result on the no added salt solution. Since both onset time and growth speed of the fingerlike structure differed for different salts, the flow patterns differed when compared at a given time as shown in Figure 9. In Figure 9, the finger-like flow pattern develops well in NaNO3 (B) while, in the solution without added salt, growth of the pattern had not developed. In the late stage, the flow pattern became unstable: merging and/or meandering of structured flow occurred, as seen in the case of NaBr in Figure 9A. One of the characteristics concerning the flow patterns was the thickness of the fingers or the periodicity of up-going and down-going fingers. In the absence of the salts, the thickness or width of the finger was about 0.3 mm. In the presence of 2 M salts, the width was 0.46 f 0.06 mm for NaCl, NaSCN, NaNO3, and NaBr. Little difference was found among these salts. In this
+ +
+
+
+
+
+
(A)2M NaBr
(B) 2M NaNO3
(C) 2M NaSCN
@) No salt
+iomm+
Figure 9. Flow patterns of the solutions 80 kg m-3 dextran + 20 kg m-3 PVP (blue dye labeled) 2 M salt. Time after the formation of the initial boundary was 25 min.
+
way, the finger-like structure becomes wider or thicker in 2 M salts than in their absence. The onset time, the time before the appearance of fingers, was about 5 min for 2 M NaCl, NaNO3, and NaBr, while it was about 10 min in their absence. The average velocities of the growing fingers were about 9.5 and 5.9 mm h-' for 2 M NaNO3 and NaBr, while it was about 4.5 mm h-' for no added salt solutions. We have determined the range for critical PVP concentrations required for the formation of the structured flow. Since detection of the flow was not easy at PVP concentrations lower than 2 kg m-3, we used labeled dextran. Detection was carried out by observing downward fingers of labeled dextran: upper solution (80 kg m-3 labeled dextran salt)/lower solution (80 kg m-3 unlabeled dextran unlabeled PVP salt). In the no added salt system and 2 M LiC1, the critical PVP concentration was 1.0-2.0 kg m-3, while it was 0.5-1.0 kg m-3 for 2 M NaCl. In 2 M CsCl, the structure was still observed at 0.5 kg m-3. A correlation is suggested between the critical PVP concentration for a given kind of salt and the enhancing power of the salt on the transport rate.
+
+
+
Conclusions (1) Rapid transport of polyvinylpyrrolidone (PVP) in dextran solutions was found to be further accelerated when a simple salt was added to both upper and lower compartments of a diffusion cell at the same concentration. (2) The enhancement effect increased with the salt concentration in all examined cases: CsCl, NaBr, and NaSCN. (3) The transport rates at 2 M were in the following order: CsCl >> NaCl > LiCl no salt; NaBr NaI > NaNO3 > NaCl > NaSCN > no salt. (4) The enhancement effect was correlated with densities of the solutions. The correlation was further improved when the transport rates were multiplied with the viscosity. (5) The effect was not correlated at all with the osmotic coefficients or lyotropic numbers of the salt solutions (in the absence of the polymers). The effect depended on but was not simply correlated with the viscosity. (6) Critical PVP concentrations for the formation of structured flow at 2 M were in the following
-
-
Polyvinylpyrrolidone in Dextran Solutions order, CsCl < NaCl < LiCl, and were well correlated with the enhancement effect of these salts. (7) In the presence of salt, structured flow appeared earlier and its development was faster than in the no added salt case.
Discussion Finger-like structures in solution have been observed in other systems, in particular, double diffusive systems where counter diffusions of two low-molecular-weight substances are in~ o l v e d . ' ~ - Comper '~ et al. have proposed a mechanism in terms of the hydrostatic instability rather than hydrodynamic one as the cause for the Occurrence of the structured flow in the matrixgradient systems consisting of polymers.8J1 Density inversion which triggers the instability is reached mainly as a result of large cross-diffusional flux of the matrix component caused by the diffusion of the gradient component.8-11*20,21Conditions for the density inversion to occur in diffusion experiments have been examined e ~ t e n s i v e l y . ~The ~ - ~significant ~ extent of cross diffusion is considered to arise mainly from the excluded volume effect and the hydrodynamic frictional e f f e ~ t . Comper ~ and Preston have succeeded in directly demonstrating the cross diffusion between dextran and albumin under the condition where density inversion did not occur.8 As to cross diffusion between polymeric solutes, the entanglement effect should be taken into account in addition to the excluded volume effect and the frictional one. In semidilute polymer solutions, the entanglement effect is discussed in terms of the cooperative diffusion c o n ~ t a n t . In ~ ~addition . ~ ~ to the hydrostatic model just described, two other mechanisms have been examined:lOJ1the osmotic model and the hydrodynamic model. The hydrostatic model is to be applied to the step of the onset of the flow or to the transition from diffusion regime to flow regime. The total phenomenon undoubtedly consists of many steps. The flow grows to form flow structure, and stabilization and growth of the structure need other mechanisms. As to the osmotic model, Comper and Preston have questioned its validity as a probable mechanism leading to density inversion.1° According to their argument, the main diffusion constant of PVP should equal the cross diffusion constant of dextran if the osmotic model is valid. This expected relation was not found experimentally. As to the hydrodynamic instability, fluxes of the two polymer components are described with equations consisting of terms including the velocity of the solution in addition to those representing diffusive motion.20 The fluid velocity is given by the Navier-Stokes equation, where kinematic viscosity and hence density of the solution e, rather than the difference AB between the upper and the lower solutions, play a role. In this respect, the present salt effect may be related to the hydrodynamic instability through its effect on the density. When the enhancement effect of salt reported in the present study is concerned, it is pertinent to consider separately the effect on the two steps: the initiation step (onset of the flow) and the structured flow. The transport rates, a central property measured in the present study, are related to the properties of the final structured flow and are contributed from the effects on both steps. The effect on the initiation step is clearly indicated, since the critical PVP concentrations for the occurrence of the structured flow depended on the kind of salt. The effects of a salt on the cross diffusion constants of the two polymer components will be examined on both excluded volume and frictional interactions. The effect on the excluded volume interaction between the two polymer components is expected to be small. This expectation is partly supported by the result12 that the coil dimension of PVP was not influenced by the
J. Phys. Chem., Vol. 98,No. 50, I994 13431 addition of a salt at 2 M in the cases of three salts, LiCl, NaCl, and CsC1, while these salts showed quite diverse effects on the transport rates of PVP. Since viscosities vary with the kind and the concentration of salt, as shown in Table 2, frictional coefficients are influenced by the presence of a salt. In this respect cross diffusion constants may be affected by salt through a change in viscosity of the medium. We have shown that the salt effect is well correlated with the densities of the solutions. Accordingly the essential part of the salt effect is expected to operate on the steps after density inversion occurs. In the present study we have measured mainly the transport rate to evaluate the salt effect. The enhanced transport rates are expected to be related to the growth speed of fingers. We anticipate that the friction in the boundary layers between up-going and down-going fingers affects the velocity in the centers of both fingers. For thin fingers the velocities will be small. The relationship between the density of the solution and the characteristics of the fingers (such as their thickness and growth rate) is to be clarified. We have observed flow patterns and extracted several properties characterizing them. However, we can not combine them with the data on the transport experiment in a quantitative way because these two types of measurements were carried out using cells of different geometries: circular and rectangular cross sections.
Acknowledgment. We thank Mr. T. Gotoh for discussion.
This work was partly supported by a Grant-in-Aid (No. 06835017) from the Ministry of Education, Science and Culture, Japan.
References and Notes (1) Preston, B. N.; Laurent, T. C.; Comper, W. D.; Checkley, G. J. Nature 1980,287, 499. (2) Comper, W. D.; Preston, B. N.; Laurent, T. C.; Checkley, G. J.; Murphy, W. H.J. Phys. Chem. 1983,87, 667. (3) Laurent, T. C.; Preston, B. N.; Sundelof, L.-0. Nature 1979,279, 60. (4) Laurent, T.C.; Preston, B. N.; Comper, W. D.; Checkley, G. J.; Edsman, K.; Sundelof, L.-0. J . Phys. Chem. 1983,87, 648. (5) Preston, B. N.; Comper, W. D.; Laurent, T. C.; Checkley, G. J.; Kitchen, R. G. J . Phys. Chem. 1983,87, 655. (6) Preston, B. N.; Comper, W. D.; Checkley, G. J.; Kitchen, R. G. J. Phys. Chem. 1983,87, 662. (7) Comper, W. D.; Checkley, G. J.; Preston, B. N. J. Phys. Chem. 1984,88, 1068. ( 8 ) Comper, W. D.; MacDonald, D. M.; Preston, B. N. J . Phys. Chem. 1984,88, 6031. (9) Comper, W. D.; Van Damme, M.-P. I.; Checkley, G. J.; Preston, B. N. J. Phvs. Chem. 1985,89,128. (10) Comper, W. D.; Checkley, G. J.; Preston, B. N. J . Phys. Chem. 1985,89,1551. (11) ComDer. W. D.: Williams. R. P. W.: Checklev. .. G. J.:. Preston. B. N. j . Phys. them. i987,91,993. (12) Maeda. H.: Mashita, T.: Sasaki, S. Chem. Let?. 1991,635. (13) Newman, S. A.; Comper, W. D. Development 1990,110, 1. (14) Jirgensons, B. J . Polym. Sei. 1952,8, 519. (15) Sundelof, L.-0. Anal. Biochem. 1982,127, 282. (16) Laurent, T. C.; Preston, B. N.; Sundelof, L.-0.; Van Damme, M.-P. Anal. Biochem. 1982,127,287. (17) Turner, J. S. Annu. Rev. Fluid Mech. 1974,6 , 37. (18) Tumer, J. S.J . Geophys. Res. 1978,83,2887. (19)Tumer, J. S. Annu. Rev. Fluid Mech. 1985,17, 11. (20) McDougall, T. J.; Turner, J. S. Nature 1982,299,812. (21) McDougall, T. J. J. Fluid Mech. 1983,126, 379. (22) Wendt, R.P. J . Phvs. Chem. 1962,66, 1740. (23j Vitagliano, v.; ~artOrio,R.; spaduzzi, D.; Laurentino, R. J. solution Chem. 1977,6 , 671. (24) Vitagliano, P. L.; Volpe, C. D.; Vitagliano, V. J. Solution Chem.
1984. 13.549. (25) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Come11 University Press: Ithaca, NY, 1979;W.1.4. (26) Comper, W. D.; Preston, B. N. Adv. Polym. Sei. 1984,55, 105.
