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Diffusion of Ca2+ ions through neoprene latex films (Ca2+ diffusion through latex films)
Diffusion of Ca 2+ Ions Through Neoprene Latex Films (Ca 2+ Diffusion Through Latex Films) ~ C. W. STEWART, SR. E. I. du Pont de Nemours and Company Elastomer Chemicals Department, Experimental Station, Wilmington, Delaware 19898 Received J u n e 19, 1972; accepted October 2, 1972 A m a t h e m a t i c a l model is developed which predicts the rate at which divalent cations diffuse t h r o u g h a coalescing rubber latex film. Factors which affect the rate of film deposition when a latex comes into contact with a coagulant solution are considered. Experimental results on polychloroprene latices are presented to test t h e theory.
I. INTRODUCTION
divalent cations diffuse through a coalescing latex film and experimental results are presented to test the theory.
Large quantities of elastomers are marketed to the rubber industry in latex form for conversion to a variety of end products. These products require that the latex be stable during compounding operations, have a high solids content to avoid excessive shrinkage, have a relatively low viscosity for processing and be subject to destabilization in a controlled manner such as by evaporation, freezing, filtration, gelation, coagulant dipping or electrodeposition. Furthermore, the usual applications of these latices require that they rapidly form a strong continuous film upon destabilization. Since it is well known that the rate of film formation and the nature of the film produced depend very strongly on the method used for destabilization as well as on the composition of the latex (1, 2), it is of obvious practical importance to understand how various factors control the process of film formation. In this paper, the factors which affect the rate of film formation in latex dipping operations are considered. An approximate mathematical model is developed which predicts the rate at which
II. T H E O R E T I C A L Consider a system which consists of a rubber latex separated from a coagulant solution by a plane harrier. The coagulant is a concentrated water solution of a divalent metal cation M 2+, and occupies the region x < 0. The latex occupies the region x > 0 and is stabilized by a monovalent anionic soap which is permanently adsorbed onto the surface of the latex particle. If the barrier at x = 0 is removed at time t = 0 the M 2+ ions diffuse into the latex and, if the M 2+ salt of the anionic soap is insoluble, an almost immediate coagulation of the latex occurs with the formation of a thin rubber film. The thickness of the coagulated film increases
with time as the M s+ ions diffuse into the latex. The thickness of this film is dependent on the rate of diffusion of M 2+ ions as the latex particles coalesce. Since latices used in coagulant dipping applications are usually of very high solids content, it is assumed that immediately upon coagulation, the latex particles are arranged in
1 Contribution No. 278. 2 D u P o n t ' s registered t r a d e m a r k for its surface active agents. 122
Journal of Colloid and Interface Science. Vol. 43, No. 1, April 1973
Copyright • 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.
DIFFUSION
THROUGH
a close packed structure. Measurements of the degree of volume shrinkage which occurs when coagulated films are completely dried show this to be the case. Let R represent the radius of the monodisperse latex particles, 2b the quantity of soap per unit volume of latex in a close packed structure, a the constant concentration of M s+ in a coagulant solution and ~-(t) the position of the film/latex interface with time t. The coordinate system is chosen so that the interface between the coagulant and the film remains fixed at x = 0. Let ~(x,t) represent the volume fraction of fluid (coagulant and serum) which is trapped in the interstices of the coagulated film, and let c(x,t) represent the concentration of free (unprecipitated) M s+ ions in this fluid. Then the concentration, C(x,l) of free M s+ in the coalescing film is given by:
C(x,l)
=
~(x,t)c(~,t).
E~]
By the usual manner of considering the rate of increase of M s+ ions in an element of volume in the film, it is found that the concentration C(x,t) must satisfy the diffusion equation (3).
123
FILMS
Furthermore, if the diffusion coefficient is assumed to be independent of concentration, then Eq. [2] becomes:
(OC/Ot) = D(O2C/Ox s) 0 < x < ~'. r-s] if contact is established between the coagulant and the latex at time t = 0 and it is assumed that the concentration of M 2+ in the stirred coagulant solution remains constant up to the interface at x = 0, then the boundary conditions are given by:
C(O,t) = a~(O,t)
t >_ O,
[6]
C(x,~)
z > ~.
[.7]
=
o
If the latex is of very high solids content or is gently stirred, diffusion of the latex particles in the region x > ~" can be neglected. Furthermore, since the latex coagulates into a structure of close packed spheres the boundary condition at x = ~'(t) is given by:
-D(OC/Ox)t
=
b(dr/dt),
[.8]
to the same approximation as Eq. E5]. The left side of Eq. [-8] gives the number of M 2+ ions diffusing through a unit area of the plane ~C/~t = (a/ax)[¢D(oc/ax)] o < x < ~- [2] x = ~"in unit time and the right side determines the amount needed to completely precipitate where the material derivative ~C/~I is used to the soap molecules in 1 unit volume. This account for the convection of M s+ ions by the expression also takes into account the fact that moving fluid as the latex particles coalesce and each M s+ requires two monovalent soap moleD is the diffusion coefficient for M s+ ions in the cules for complete precipitation. film. The diffusion coefficient in the coalescing Mathematically, the approximations in Eqs. latex film is related to the diffusion coefficient [5-] and [-8] are equivalent to the assumption of M s+ in the coagulant solution, Do, by the that the volume fraction of the fluid ~(x,t) is expression (4) constant throughout the film and is equal to D = Do~r, [3] ~(0,t), the value that it has at the initial where r is the tortuosity factor for spheres. For boundary. The diffusion of M s+ in this model simplicity, the tortuosity factor in the present is controlled, therefore, by the rate of coamodel is chosen to have the value for close lescence of the latex particles at the interface packing of spheres. between the coagulant and the film. This approximation is valid for polymers which are r = 1.36. [4] used in latex dipping applications since the If the rate of particle coalescence is very particles are usually somewhat crosslinked or slow compared to the diffusion rate of M s+, "gelled," in order to provide coagulated films then the velocity of the fluid in the coalescing with adequate wet gel strength and elasticity. film and the gradient of the volume fraction The solution of the diffusion problem can be can be neglected as a first approximation. obtained (5) by writing down a particular Journal of Colloid and Interface Science, Vol. 43, No. 1, April 1973
124
STEWART r2 shown in Fig. la become hTlportant. The
.............
~.~_°_r_rhighly localized hydrostatic tension or surface pressure in the immediate region of contact between the two particles is given by the equation of Young and Laplace. Ib
la
P , -- P2 = 3 , ( 1 / r , -- 1/r2 + 2 / R ) ,
[10-1
F1G. i. Model for the coalescenceof two spheres. solution of the differential equation [-5.] and boundary conditions [-6.], [-8.] and then selecting an arbitrary constant so that the solution also satisfies the boundary condition [-7.]. The particular solution is obtained from the solution of the diffusion equation in a semi-infinite medium by applying Duhemel's theorem (3).
c(x,t)
=
X
~(0, t - x~/4D#2)e-~'2dv.
[-9]
/2(Dr)½
The time dependence of the volume fraction of fluid in the coagulated film can be obtained from the theory of coalescence of latex particles. Vanderhoff and co-workers (6) have considered the interracial forces involved in latex particle coalescence. They found that the pressure forcing the spheres together is the result of the polymer/water interfacial tension and the small radii of curvature in the region of contact between two particles. The exact problem for the stress distribution and displacements within two viscoelastic spheres which are coalescing as the result of the interfacial tension has not been solved. Furthermore, the usual treatments of surface leveling of fluids (7) are not applicable here since they deal only with the final state of coalescence in which the surface gradient is assumed very small; whereas, only the initial stages of coalescence are of interest in the present model. Therefore, to obtain an approximate expression for the rate of coalescence, consider the schematic diagram of two coalescing latex particles in Fig. 1. As Vanderhoff et al. (6) have pointed out, when two latex particles come into contact and begin to coalesce, two radii of curvature, r, and Journal of Colloid and Interface Science, Vol. 43, Iffo. 1, April 1973
where -/ is the polymer/water interracial tension. It is well known (8) that when two viscoelastic spheres in a fluid medium approach each other under the action of Van der Waals or other forces, the hydrodynamic pressure generated as the liquid is squeezed out is greatest at the center of the contact region. This results in a flattening or dimpling of the spheres before contact is achieved. It is very likely, therefore, that when contact is made, the radius of the contact region, r2 is much larger than the radius r,. Then since r, << R, Eq. [10] can be rewritten as
P* -- P2 = "y/r,.
[-Ii]
In general, one might expect r, and, hence, the surface pressure to change with time as the particles coalesce. However, it appears experimentally from electron microscope studies that r, actually remains relatively constant during coalescence and this will be assumed to hold in the present model. To estimate the rate of coalescence due to the localized surface pressure "y/r,, consider the cylindrical section in Fig. lb where it is assumed that a stress (pressure) ~ r = 3'/r, is applied to the lateral surface of the cylinder while the ends are free of stress ~,, = 0. One can easily calculate the displacements which arise from these stresses in an elastic material and it is found, from the theory of linear elasticity (9), that exactly the same displacements can be achieved in the cylinder by applying a uniform stress ~ = -- 3,/r, over the ends of the cylinder while leaving the lateral surface free ~rr = 0. That is, the same displacements can be achieved by applying a force F of magnitude.
DIFFUSION THROUGH FILMS
where B is the constant which is chosen to satisfy boundary condition Eq. [-73 and err denotes the error function. From Eq. [-83, then, the motion of the boundary must follow the integro-differential equation :
By analogy with this example, in order to obtain a first approximation for the coalescence of two spheres, one can assume that the displacements which occur in the region of contact due to the interfacial pressure, Eq. [-11~, are similar to those which occur when two spheres are pressed together with a force given by Eq. [-123. Stewart and Johnson (10) have used this approach to obtain a theoretical expression for the rate of coalescence of two incompressible viscoelastic spheres whose relaxation modulus G(t) can be expressed by an equation of the form a ( t ) = E[-t//31 -,~
t > o,
125
(df/dt) = [2BDa/b@)½] X { [0.26/2(D1)½]exp(-- f2/4DI) --f~;2(D,)~ EmA~/D~2~[-t--f2/4D#232m-1
E131
exp(-- ~2)d~}. where/3 is a suitable unit of time and E and m are experimentally determined constants. They found excellent agreement for polystyrene latices at temperatures near the glass transition region. If one follows this approach, it is found that for polymers whose relaxation modulus can be expressed by Eq. [-131, the volume fraction ~(0,t) is given by (10) v(0,t) = 0.26 -
AtTM,
The form of the integrand makes it necessary to use numerical methods to find a solution of Eq. [-17]. However, for the coagulation of rubber latices with slow coalescence, a solution can be obtained by the method of successive substitutions (11). By this method, it is found that the first two terms in the series which expresses the thickness of the coagulated film with time is given by
[-141
A = 2.22{~,~, sin mzc/8Er~-] •
Am exp (~2/2)F (2m) X t2mWI-2m,~(c~2)/[-O.263[-2m + ½3~½},
~" -- 2~ (Dt)~{ 1 --
[-r (m)r (2m)/r (3m)~}2, [-lS]
where r (m) denotes the gamma function and 13 has been chosen to have the value/3 = 1 hr. The factor (0.26) arises from the assumption that the latex coagulates initially in a close packed structure. Equation [13] is found to be an excellent representation for the relaxation modulus of a number of film forming polymers over a large time scale. When the expression for the volume fraction is substituted into Eq. [-93, a particular solution of the diffusion problem described by Eqs. [-5-], [61 and [-73 is obtained of the form
C(x,t) =
a(0.26)
-- B { a[-0.26]
× /~ x]2(Dt)½
[-17-]
[-18]
where W denotes the Whittaker function (14) and ~ satisfies the equations. exp(a 2) erf(a) =
[-0.26~a/b~r~,
B = 1/err(a).
[-193 ~203
The first term on the right side of Eq. [18] is identical to the result of Hermans (5) for diffusion with precipitation but no coalescence. The second term is, therefore, the first correction due to the slow coalescence of elastomeric latex particles. III. EXPERIMENTAL PROCEDURE
1. Preparationof Latices
erf[-x/2(D@3+ [2aA/rc~] Et --x2/4D#212~e-u~d~} [-16]
A series of polychloroprene latices were prepared by the usual emulsion polymerization technique using K2S202 as catalyst (2). To ensure that the series of polymers would
Journal of Colloid and Interface Science, VoL 43, No. 1, April 1973
126
STEWART
1.2~ o
E
THEORETICAL MAXIMUM
l,(3
/
i
,'7 .2!
[]
o
/'W
"
7
~
~
~
( TI ME) I/2 ( h r ) I/a
FIG. 2. Film thickness as a function of (time)½for polychloroprene latices with a = 1.34 M; 2b = 0.118 M. (©) Polymer A; (0)polymer B; (V1)polymer C; (I)polymer D. exhibit a significantly broad range of viscoelastic behavior the polymerizations were modified with dodecyl mercaptan levels ranging from 0 to 0.3 phr (parts per hundred parts of rubber) and the conversion was varied in the range from 70 to 100k. The sodium salt of rosin acid was used as t h e emulsifier in all polymerizations. The quantity of sodium rosinate used was varied with the final conversion in such a way that the final ratio of rosinate/polymer was the same for each latex. The latices were stablized with 0.01 phr phenothiazine and 0.01 phr 4-tert-butyl pyrocatechol.
2. Rate of Film Formation One end of a thin walled glass tube, 2.5 cm in diameter was covered with an open mesh nylon net 0.005 cm thick. The net was then placed in contact with the coagulant solution and allowed to become saturated. The tube was removed from the coagulant solution, filled with the latex aad then placed back into contact with the coagulant solution. After the desired time interval the net was easily removed from the coagulated latex at the bottom of the tube and the thickness of the film was measured with a thickness gauge. I t was necessary to saturate the net as described above prior to addition of the latex in order to prevent the latex from leaking out of the Journal of Colloid and Interface Science, V o l . 43, N o . 1, A p r i l 1973
tube. This also made it possible to remove the net from the coagulated film. IV. RESULTS AND DISCUSSION Four specially prepared polycholroprene latices were chosen for study. The amount of sodium rosinate used in each polymerization was controlled so that the actual quantity of rosinate in a close packed structure, 2b, would be equal to 2b = 0.118 M. F21] The latices were concentrated by evaporation to a high solids content of 65% by weight and their p H was adjusted to 10.5. At this relatively low p H Ca(OH)2 does not precipitate, while the rosin acid is still almost completely dissociated. Figure 2 shows the film thickness obtained with time when these four latices were brought into contact with a stirred coagulant solution of Ca(NO3)2 in water at a concentration of a = 1.34 M.
[22]
The latex was also gently stirred during film formation although as shown later this was found to be unnecessary. The uniformity and reproducibility of film thickness by this technique was within -4-5%. The relaxation modulus of each polychloroprene polymer was measured by placing a weighted steel ball on a thick film of dried
DIFFUSION THROUGH FILMS polymer and observing the depth of penetration with time. It was found, when the observed penetration was plotted as a function of elapsed time on a log-log scale, that straight lines resulted over times ranging from 10-2 hr to greater than 102 hr. Thus, Eq. [13] is an excellent representation for the shear relaxation modulus of these polymers over a very large time scale of interest. The equations necessary for calculating the relaxation modulus from these data are given by "fang (12). The value of m in Eq. [13-] is determined from the slope of the line and E is determined from the penetration when t --- 1 hr. The values of E and m for the four polymers selected are given in Table I. It is seen that these polymers do represent a very broad range of viscoelastic behavior from "high gel" (polymer A) to a very soft "sol" (polymer D). From Fig. 2 it is seen that the higher the relaxation modulus, as expressed by E and m, the greater the rate of film formation due to diffusion of Ca 2+ through the coagulated film. This is what one would expect, since a low relaxation modulus corresponds to an increased tendency to flow, and allows the particles to coalesce rapidly. As the latex particles coalesce, the cross-sectional area of serum through which the Ca 2+ can diffuse decreases and, for polymers such as I), an impermeable rubber barrier is eventually set up. The diffusion coefficient of Ca 2+ through a 0.118 M sodium rosinate solution was determined directly by dissolving the rosinate in a 20-/0 solution of 1000 cps methyl cellulose and then drawing the viscous solution into capillary tubes. The tubes were placed into the 1.34 M Ca 2+ coagulant solution and the position of the precipitated calcium rosinate boundary was measured with time. The value of the diffusion coefficient Do under these conditions was found to be (5) Do = 5.2 X 10-7 cm2/sec.
[-23~
The same value for Do was obtained to within 4-5% when the concentration of sodium rosinate was varied between the limits of 0.06 and 0.18 M while the concentration of the
127 TABLE I
VALUES OF E AND $~ZIN EQ.
EXPERIMENTAL Polymer designation
A B C D
14 FOR
POLYCIILOROPRENE POLYMERS E X 104 (dyn/cm2)
20 11 6.5 0.85
0.03 0.07 0.10 0.20
coagulant solution was varied between 0.7 and 2.0 M. These are the practical limits for variations in soap and coagulant concentrations usually encountered. The constant value of Do within these limited concentration ranges shows that this system is adequately described by the equations derived by Hermans (5) for diffusion with precipitation into a medium which does not itself take part in the diffusion process. From the first term on the right side of Eq. [-18], one would predict that for diffusion of Ca 2+ through close packed nondeformable spheres, the boundary of precipitated calcium rosinate ~" should follow the expression = 2a (Dt)~,
~e ~2 erf(a) = (0.26)a/brc½, D = Do/r
(r = 1.26).
[-24-] [-25-] [-26-]
Equation [25-] takes into account that the volume fraction of serum through which the Ca 2+ can diffuse is (0.26), while Eq. [-26~ accounts for the added distance that the unprecipitated Ca 2+ must travel to pass around the spheres. Equation [-24-] then represents the greatest film thickness that one can expect to obtain when a high solids latex comes into contact with a coagulant. Any coalescence of the latex particles will cause a reduced film thickness. The straight line in Fig. 2 then gives the theoretical maximum film thickness for coagulation of a latex of nondeformable spheres with concentrations of soap and coagulant as in Eqs. [-21] and [-22-], respectively, and diffusion coefficient as in Eq. [-23-]. The value
Journal of Colloid and Interface Science. Vol. 43, No. 1, April 1973
12 8
STEWART
1D '
~
,
,
,
,
,
. . . . . . .
,
,
,
,
,,~,E
fly*
rate of film deposition, the quantity
. . . . .
(2a(Dt)½ -- ~),
[293
as given in Eq. [-183 was calculated for the values of E and m listed in Table I and for values of the remaining variables as given in 7 Eqs. ['21~ to [-28~. These theoretical results ~.0 are shown plotted as a function of time on a log-log scale in Fig. 3, and appear as straight lines with slope (2m q- ½). Experimentally, the quantity in Eq. [29-] is just the hypothetical tDO] , , ,,,rr,I , , ,,Jr,,I , , ,r,,,,I , , ,,,,, .OT 0.I iO 10 lO0 maximum film thickness (the straight line in TIME ( h r ) Fig. 2) minus the observed film thickness (the Fla. 3. The effect of coalescence on film thickness. data points in Fig. 2). This quantity is shown The straight lines represent the theoretical quantity plotted as the data points in Fig. 3. As shown, [-2a(Dt)i -- ~'] in Eq. [i83 for a ~ 1.34 M and 2b = 0.118 M. The data points represent the experimental the agreement between theory and experiment values: (©) polymer A; (@) polymer B; (El) polymer is exact for "high gel" polymers A and B over C; (II) polymer D. the complete time scale studied of 25 hr; whereas, for "medium gel" polymer C the agreement is exact up to 5 hr and for "sol" for a which corresponds to these concentrations polymer D up to 30 rain. i s a = 1.1. It should be pointed out that the agreement The polymer/coagulant interfacial tension between theory and experiment in Fig. 3 is was determined by preparing a very low molec- strongly affected by the choice of the value rl, ular weight fluid polychloroprene. The polymer since it enters Eq. [-18~ as the inverse square. was isolated by drum drying and the interfacial The value chosen in Eq. ]-28~ is of the correct tension was measured by a pendent drop order of magnitude and gives the best fit of method (13). No attempt was made to remove the experimental data, so that any other choice surfactant or other impurities from the polymer would shift the lines in Fig. [-3] uniformly in since these are also present in the coagulated the veritical direction. The important observalatex film. The value for the interfacial tension tions are, however, that the slope of these lines ~, was found to be appears to have the correct value (2m -1- ½) at least during the initial stages of coalescence ~, = 15 dyn/cm. [-27~ and the dependence of film thickness on E -~ is of the correct order of magnitude. Once coaDue to the very small radius of polychlorolescence has proceeded to any significant degree prene latex particles (5 X 10-6 cm), it is very the theoretical result Eq. [-18~ is no longer ditgcult to obtain an accurate value for the applicable as expected. radius of curvature of the contact region rl To determine the effects that variations in between two coalescing particles. From electron the solids content have on the rate of film microscope studies, however, it appears that r~ deposition, the four latices were diluted by is of the order of 0.1 times the radius of the adding distilled water and then the coagulation particles. Therefore, in what follows a value of experiments repeated. It was found that between 65 and 450-/0 by wt, the solids content r~ = 5 × 10 -7 c m [-28~ had no apparent effect on film thickness and identical results were obtained whether or not is somewhat arbitrarily chosen. To compare the theory with experiments on the latices were stirred. Since the quantity 2b the retarding effect that coalescence has on the in Eq. [-21~ is not changed by dilution of the O.I
Journal of Colloid and Interface Science,
Vo.
43,
No.
1, April
1973
DIFFUSION T H R O U G H
latices this means that film formation is controlled in this case solely by the diffusion rate of Ca 2+ through the coagulated rubber film. At percentage of solids below 30% it was found that the rate of film formation increased with decreasing solids content. However, the films that were produced were very soft and spongy and exhibited a very large degree of shrinkage on drying. Therefore, it appears that this surprising result is due to a very loose agglomeration of the latex particles within the coagulated film compared with the approximate close packing of spheres which occurs with a high solids latex. This open structure then allows Ca 2+ to diffuse much more rapidly through the film so that diffusion of the latex particles becomes important. Due to the nature of the films produced under these conditions the increased rate of film formation is of little practical interest. To test the effects of changing the coagulant concentration, the film formation experiments were repeated using latex A and three different concentrations of Ca(NO3)2 coagulant. This latex was chosen since the observed effects should be greatest for a polymer which does not coalesce. The concentrations used and corresponding values of a calculated from Eq. [-19] with 2b = 0.118 M, are a = 0.67 M
a = 0.90,
[30]
a = 1.34 M
a = 1.10,
[31]
a = 2.01 M
a = 1.23.
[32]
Therefore, from Eq. [18], if the coagulant concentration is decreased from 1.34 to 0.67 M one would expect a decrease in the rate of film formation of about 18%; whereas, if the coagulant concentration is increased from 1.34 to 2.01 M the rate of film formation should increase by about 12%. Experimentally, the changes are found to be 14 and 90-/0, respectively. The differences are probably due to a concentration dependence of the diffusion coefficient D which occurs even between such narrow concentration limits as these. To observe the effects on film formation of changing the quantity of emulsifier, the poly-
FILMS
129
Inerization of latex A was repeated using two different levels of sodium rosinate. The polymerizations were carried out in such a way as to keep all other variables, such as the relaxation modulus of the polymers, as identical as possible, although the particle size and size distribution must be significantly affected by changes in emulsifier concentration. Again, this particular latex was chosen to maximize any differences which might occur. The quantity of sodium rosinate, 2b and the corresponding values of a, caiculated from Eq. [19] with a = 1.34M, are 2b = 0 . 0 5 9 M
a=
1.3,
[33]
2b = 0.118M
a = 1.1,
[34]
2b = 0.177M
~ = 1.05.
[35]
These values represent the practical limits for this system since at lower levels of emulsifier the latices become unstable and agglomerate during polymerization. At higher levels, the sodium rosinate is in excess. Thus, added soap remains in the serum as micelles which tend to increase viscosity and interfere with coagulation. When the values of ~ given in Eqs. [-33] to [-35] are substituted into Eq. [-18], one finds that as the quantity of rosinate used in the polymerization is decreased from 0.118 to 0.059 M the theory predicts an increase in the rate of film formation of about 18°-/o. Experimentally, the rate of film formation is found to increase about 12%. The discrepancy is probably due to the aforementioned agglomeration and subsequent coalescence which occurs during polymerization at low levels of emulsitier. This agglomeration results in a broader particle size distribution, which leads to tighter packing on coagulation and, consequently, a decrease in the diffusion rate of Ca 2+ through the film. Likewise if the quantity of rosinate is increased from 0.118 to 0.177 M the theory predicts a decrease of 5% in the rate of fihn formation. The change in the film deposition rate is found experimentally to be negligible,
Journal of Colloid and Interface Science, VoI. 43, No. 1, April 1973
130
STEWART
1.50 1.25 TYPE 655
J
J
HIGH GEL
~o1-0
0
~-".5C I
MEDIUM I
-
I
.25
I
2
3
4
(TIME) I/2 (hr) 1/2
FIG. 4. Film thickness as a function of (time)~for three commercialneoprene latices.
since the excess calcium rosinate which precipitates in the serum tends to interfere with coalescence of the particles. The fact that the precipitated excess calcium rosinate in the latex serum can interfere with coagulation and coalescence is also seen by adding 2 phr sodium rosinate to latex D, the "sol" latex described above. One would expect the added emulsifier to cause a slight decrease in rate of film formation as the diffusing Ca 2+ precipitates. However, there is actually observed an increase of more than 50°7o. This increase is most likely due to the hindering of coalescence by excess precipitated emulsifier in the latex serum which must be squeezed from between the particles as they come together. A similar effect is observed when certain emulsifiers other than sodium rosinate are added to the polychloroprene latices. Typical examples of surface active substances which are frequently added to latices to provide additional stability or to improve the overall appearance of dried films are "Aquarex ~ SMO" and "Aquarex 2 WAQ." In general, the added surfactants may be expected to affect film deposition rates either by reducing the polymer/ coagulant interfacial tension or, as is the usual case for anionic surfactants, by precipitating as the calcium salt. Thus, with the addition of anionic surfactants to the latices one observes effects similar to the addition of added sodium rosinate. They have very little effect on non-
coalescing "high gel" latices, whereas, for "sol" latices, the deposition fates are markedly increased as the precipitated soaps inhibit coalescence. As an example, under the conditions described for film formation in Fig. 2, the addition of 4 phr Aquarex WAQ to "sol" latex D causes an increase in the rate of film formation by more than 100%. Again, this increase is due to the precipitated calcium soap which inhibits the thinning and collapse of the intervening liquid film between latex particles prior to and during coalescence. A further example of the unusually large effect that excess surfactant has on film deposition is shown in Fig. 4, where the coagulation experiments were performed on commercially available Du Pont neoprene latices. The latices examined are designated as Types 601A, 650 and 635, and the polymers are reported to be high gel, medium gel and sol, respectively. They are of high solids content, obtained through creaming with ammonium alginate, and they are presently used in coagulant dipping operations. As in the previous experiments, the pH of each latex was adjusted to 10.5 and the concentration of the coagulant was 1.34 M. It is seen from Fig. 4 that the film deposition rates for Types 601A and 650 are of the order that would be expected for high and medium gel polymers, respectively. Type 635, however, produces a film at an extremely fast rate for a sol polymer, which actually
Journal of Colloid and Interface Science, Vol. 43, No. 1, A p r i l 1973
DIFFUSION THROUGH FILMS
approaches the rate of diffusion of Ca 2+ through latex serum. There are two possible reasons for the unusually high rate of film deposition from Type 635 latex, and both are related to the creaming step. First, creaming a latex causes the particles to fluocculate into fairly large nonspherical agglomerates. These agglomerates are unable to pack into a close structure on coagulation, and this increases the rate of diffusion of coagulant through the film as the tortuosity factor decreases. The second, and more important reason for the very fast deposition rate of Type 635 compared with Types 601A and 650 lies in the surfactant added during the creaming step. Types 601A and 650 have a relatively small amount of anionic surfactant added along with the creaming agent, whereas, almost 6 phr anionic surfactant, above the quantity used during polymerization, is added to Type 635. It is not unusual that such a large quantity of additional surfactant can interfere with the coalescence of a sol latex such as Type 635 and make it useful in certain commercial dipping operations where a polymer with very high elongation is desired. When one attempts to produce a coagulated film from Du Pont neoprene Type 735, which is the uncreamed version of Type 635, it is found that after 48 hr in contact with the coagulant, the film thickness remains less than 0.02 cm. This is what one would expect for a "sol" latex which contains no excess surfactant. Changes in the pH of the latices should qualitatively have the same effect as changes in the amount of sodium rosinate used during polymerization. The issue is complicated, however, by the fact that above a pH of 11, Ca(OH)2 precipitates along with calcium rosinate and, since this reduces the Ca 2+ diffusing through the film, the deposition rate is markedly decreased. On the other hand, at a pH below 10, the rosin acid which is now present acts to partially stabilize the latex against coalescence. Therefore, since less cal-
131
cium rosinate now precipitates and the latex is partially stabilized, the rate of fihn deposition increases. To be able to predict quantitatively the effect of pH changes on film deposition rates, therefore, would require a modification of the theory. Since data are available in the literature which shows that the changes are as described above, this subject will not be dealt with further. In conclusion, the theory seems to predict correctly the effects that various factors have on the relative rates of film deposition when polychloroprene latices come into contact with a coagulant. An exceptional case arises when a large quantity of surfactant is present which is in excess of the amount required to completely cover the latex particles. The excess surfactant hinders coalescence, and this has the greatest effect on rapidly coalescing "sol" polymers. REFERENCES 1. CARL,J. C., "Neoprene Latex," pp. 14-16. E. I. du Pont de Nemours and Co., Wilmington, DE, 1962. 2. BLACKLEY, D. C., "High Polymer Latices," pp. 514-540. Palmerton Pubi. Co., New York, 1966. 3. CARSLAW,H. S., A N D JAEGER, J. C., "Conduction of Heat in Solids," pp. 28-32. Oxford Univ. Press, London, 1959. 4. NIELSEN, L. E., J. Macromoh Sci., Chem. 1(5), 929 (1967). 5. HERMANS, J. J., J. Colloid Sci. 2, 387 (1947).
6. VANDEEI~O~'F, J. W., TARKOWSKI, H. L., JENKINS,
7. 8. 9. 10. 11.
12. 13. 14.
M. C., AND BRADFORD, E. B., J. Macromol. Chem. 1(2), 361 (1966). O~CHA~D, S. E., Appl. Sci. Res. Sect. A 11, 451 (1962). TABOR, J., Colloid Interface Sci. 31, 364 (1969). PI~ESCOTT,J. "AppIied Elasticity," pp. 329-332. Dover, New York, (1961). STEWART,C. W., AND JOHNSON, P. R., Macromolecules 3, 755 (1970). DAWS, H. T., "Introduction to Nonlinear Differential and Integral Equations," pp. 83-88. Dover Pub., New York, 1962. YANG, W. H., J. Appl. Mech. 27, 438 (1960). Wv, S., J. Phys. Chem. 74, 632 (1970). !¢VtIITTAKER, E. T., AND WATSON, G. N., "A Course of Modern Analysis," p. 339. Cambridge Univ. Press, London, 1962.
Journal of Colloid and Interface Science. VoL 43, No. I, April 1973
I. INTRODUCTION
divalent cations diffuse through a coalescing latex film and experimental results are presented to test the theory.
Large quantities of elastomers are marketed to the rubber industry in latex form for conversion to a variety of end products. These products require that the latex be stable during compounding operations, have a high solids content to avoid excessive shrinkage, have a relatively low viscosity for processing and be subject to destabilization in a controlled manner such as by evaporation, freezing, filtration, gelation, coagulant dipping or electrodeposition. Furthermore, the usual applications of these latices require that they rapidly form a strong continuous film upon destabilization. Since it is well known that the rate of film formation and the nature of the film produced depend very strongly on the method used for destabilization as well as on the composition of the latex (1, 2), it is of obvious practical importance to understand how various factors control the process of film formation. In this paper, the factors which affect the rate of film formation in latex dipping operations are considered. An approximate mathematical model is developed which predicts the rate at which
II. T H E O R E T I C A L Consider a system which consists of a rubber latex separated from a coagulant solution by a plane harrier. The coagulant is a concentrated water solution of a divalent metal cation M 2+, and occupies the region x < 0. The latex occupies the region x > 0 and is stabilized by a monovalent anionic soap which is permanently adsorbed onto the surface of the latex particle. If the barrier at x = 0 is removed at time t = 0 the M 2+ ions diffuse into the latex and, if the M 2+ salt of the anionic soap is insoluble, an almost immediate coagulation of the latex occurs with the formation of a thin rubber film. The thickness of the coagulated film increases
with time as the M s+ ions diffuse into the latex. The thickness of this film is dependent on the rate of diffusion of M 2+ ions as the latex particles coalesce. Since latices used in coagulant dipping applications are usually of very high solids content, it is assumed that immediately upon coagulation, the latex particles are arranged in
1 Contribution No. 278. 2 D u P o n t ' s registered t r a d e m a r k for its surface active agents. 122
Journal of Colloid and Interface Science. Vol. 43, No. 1, April 1973
Copyright • 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.
DIFFUSION
THROUGH
a close packed structure. Measurements of the degree of volume shrinkage which occurs when coagulated films are completely dried show this to be the case. Let R represent the radius of the monodisperse latex particles, 2b the quantity of soap per unit volume of latex in a close packed structure, a the constant concentration of M s+ in a coagulant solution and ~-(t) the position of the film/latex interface with time t. The coordinate system is chosen so that the interface between the coagulant and the film remains fixed at x = 0. Let ~(x,t) represent the volume fraction of fluid (coagulant and serum) which is trapped in the interstices of the coagulated film, and let c(x,t) represent the concentration of free (unprecipitated) M s+ ions in this fluid. Then the concentration, C(x,l) of free M s+ in the coalescing film is given by:
C(x,l)
=
~(x,t)c(~,t).
E~]
By the usual manner of considering the rate of increase of M s+ ions in an element of volume in the film, it is found that the concentration C(x,t) must satisfy the diffusion equation (3).
123
FILMS
Furthermore, if the diffusion coefficient is assumed to be independent of concentration, then Eq. [2] becomes:
(OC/Ot) = D(O2C/Ox s) 0 < x < ~'. r-s] if contact is established between the coagulant and the latex at time t = 0 and it is assumed that the concentration of M 2+ in the stirred coagulant solution remains constant up to the interface at x = 0, then the boundary conditions are given by:
C(O,t) = a~(O,t)
t >_ O,
[6]
C(x,~)
z > ~.
[.7]
=
o
If the latex is of very high solids content or is gently stirred, diffusion of the latex particles in the region x > ~" can be neglected. Furthermore, since the latex coagulates into a structure of close packed spheres the boundary condition at x = ~'(t) is given by:
-D(OC/Ox)t
=
b(dr/dt),
[.8]
to the same approximation as Eq. E5]. The left side of Eq. [-8] gives the number of M 2+ ions diffusing through a unit area of the plane ~C/~t = (a/ax)[¢D(oc/ax)] o < x < ~- [2] x = ~"in unit time and the right side determines the amount needed to completely precipitate where the material derivative ~C/~I is used to the soap molecules in 1 unit volume. This account for the convection of M s+ ions by the expression also takes into account the fact that moving fluid as the latex particles coalesce and each M s+ requires two monovalent soap moleD is the diffusion coefficient for M s+ ions in the cules for complete precipitation. film. The diffusion coefficient in the coalescing Mathematically, the approximations in Eqs. latex film is related to the diffusion coefficient [5-] and [-8] are equivalent to the assumption of M s+ in the coagulant solution, Do, by the that the volume fraction of the fluid ~(x,t) is expression (4) constant throughout the film and is equal to D = Do~r, [3] ~(0,t), the value that it has at the initial where r is the tortuosity factor for spheres. For boundary. The diffusion of M s+ in this model simplicity, the tortuosity factor in the present is controlled, therefore, by the rate of coamodel is chosen to have the value for close lescence of the latex particles at the interface packing of spheres. between the coagulant and the film. This approximation is valid for polymers which are r = 1.36. [4] used in latex dipping applications since the If the rate of particle coalescence is very particles are usually somewhat crosslinked or slow compared to the diffusion rate of M s+, "gelled," in order to provide coagulated films then the velocity of the fluid in the coalescing with adequate wet gel strength and elasticity. film and the gradient of the volume fraction The solution of the diffusion problem can be can be neglected as a first approximation. obtained (5) by writing down a particular Journal of Colloid and Interface Science, Vol. 43, No. 1, April 1973
124
STEWART r2 shown in Fig. la become hTlportant. The
.............
~.~_°_r_rhighly localized hydrostatic tension or surface pressure in the immediate region of contact between the two particles is given by the equation of Young and Laplace. Ib
la
P , -- P2 = 3 , ( 1 / r , -- 1/r2 + 2 / R ) ,
[10-1
F1G. i. Model for the coalescenceof two spheres. solution of the differential equation [-5.] and boundary conditions [-6.], [-8.] and then selecting an arbitrary constant so that the solution also satisfies the boundary condition [-7.]. The particular solution is obtained from the solution of the diffusion equation in a semi-infinite medium by applying Duhemel's theorem (3).
c(x,t)
=
X
~(0, t - x~/4D#2)e-~'2dv.
[-9]
/2(Dr)½
The time dependence of the volume fraction of fluid in the coagulated film can be obtained from the theory of coalescence of latex particles. Vanderhoff and co-workers (6) have considered the interracial forces involved in latex particle coalescence. They found that the pressure forcing the spheres together is the result of the polymer/water interfacial tension and the small radii of curvature in the region of contact between two particles. The exact problem for the stress distribution and displacements within two viscoelastic spheres which are coalescing as the result of the interfacial tension has not been solved. Furthermore, the usual treatments of surface leveling of fluids (7) are not applicable here since they deal only with the final state of coalescence in which the surface gradient is assumed very small; whereas, only the initial stages of coalescence are of interest in the present model. Therefore, to obtain an approximate expression for the rate of coalescence, consider the schematic diagram of two coalescing latex particles in Fig. 1. As Vanderhoff et al. (6) have pointed out, when two latex particles come into contact and begin to coalesce, two radii of curvature, r, and Journal of Colloid and Interface Science, Vol. 43, Iffo. 1, April 1973
where -/ is the polymer/water interracial tension. It is well known (8) that when two viscoelastic spheres in a fluid medium approach each other under the action of Van der Waals or other forces, the hydrodynamic pressure generated as the liquid is squeezed out is greatest at the center of the contact region. This results in a flattening or dimpling of the spheres before contact is achieved. It is very likely, therefore, that when contact is made, the radius of the contact region, r2 is much larger than the radius r,. Then since r, << R, Eq. [10] can be rewritten as
P* -- P2 = "y/r,.
[-Ii]
In general, one might expect r, and, hence, the surface pressure to change with time as the particles coalesce. However, it appears experimentally from electron microscope studies that r, actually remains relatively constant during coalescence and this will be assumed to hold in the present model. To estimate the rate of coalescence due to the localized surface pressure "y/r,, consider the cylindrical section in Fig. lb where it is assumed that a stress (pressure) ~ r = 3'/r, is applied to the lateral surface of the cylinder while the ends are free of stress ~,, = 0. One can easily calculate the displacements which arise from these stresses in an elastic material and it is found, from the theory of linear elasticity (9), that exactly the same displacements can be achieved in the cylinder by applying a uniform stress ~ = -- 3,/r, over the ends of the cylinder while leaving the lateral surface free ~rr = 0. That is, the same displacements can be achieved by applying a force F of magnitude.
DIFFUSION THROUGH FILMS
where B is the constant which is chosen to satisfy boundary condition Eq. [-73 and err denotes the error function. From Eq. [-83, then, the motion of the boundary must follow the integro-differential equation :
By analogy with this example, in order to obtain a first approximation for the coalescence of two spheres, one can assume that the displacements which occur in the region of contact due to the interfacial pressure, Eq. [-11~, are similar to those which occur when two spheres are pressed together with a force given by Eq. [-123. Stewart and Johnson (10) have used this approach to obtain a theoretical expression for the rate of coalescence of two incompressible viscoelastic spheres whose relaxation modulus G(t) can be expressed by an equation of the form a ( t ) = E[-t//31 -,~
t > o,
125
(df/dt) = [2BDa/b@)½] X { [0.26/2(D1)½]exp(-- f2/4DI) --f~;2(D,)~ EmA~/D~2~[-t--f2/4D#232m-1
E131
exp(-- ~2)d~}. where/3 is a suitable unit of time and E and m are experimentally determined constants. They found excellent agreement for polystyrene latices at temperatures near the glass transition region. If one follows this approach, it is found that for polymers whose relaxation modulus can be expressed by Eq. [-131, the volume fraction ~(0,t) is given by (10) v(0,t) = 0.26 -
AtTM,
The form of the integrand makes it necessary to use numerical methods to find a solution of Eq. [-17]. However, for the coagulation of rubber latices with slow coalescence, a solution can be obtained by the method of successive substitutions (11). By this method, it is found that the first two terms in the series which expresses the thickness of the coagulated film with time is given by
[-141
A = 2.22{~,~, sin mzc/8Er~-] •
Am exp (~2/2)F (2m) X t2mWI-2m,~(c~2)/[-O.263[-2m + ½3~½},
~" -- 2~ (Dt)~{ 1 --
[-r (m)r (2m)/r (3m)~}2, [-lS]
where r (m) denotes the gamma function and 13 has been chosen to have the value/3 = 1 hr. The factor (0.26) arises from the assumption that the latex coagulates initially in a close packed structure. Equation [13] is found to be an excellent representation for the relaxation modulus of a number of film forming polymers over a large time scale. When the expression for the volume fraction is substituted into Eq. [-93, a particular solution of the diffusion problem described by Eqs. [-5-], [61 and [-73 is obtained of the form
C(x,t) =
a(0.26)
-- B { a[-0.26]
× /~ x]2(Dt)½
[-17-]
[-18]
where W denotes the Whittaker function (14) and ~ satisfies the equations. exp(a 2) erf(a) =
[-0.26~a/b~r~,
B = 1/err(a).
[-193 ~203
The first term on the right side of Eq. [18] is identical to the result of Hermans (5) for diffusion with precipitation but no coalescence. The second term is, therefore, the first correction due to the slow coalescence of elastomeric latex particles. III. EXPERIMENTAL PROCEDURE
1. Preparationof Latices
erf[-x/2(D@3+ [2aA/rc~] Et --x2/4D#212~e-u~d~} [-16]
A series of polychloroprene latices were prepared by the usual emulsion polymerization technique using K2S202 as catalyst (2). To ensure that the series of polymers would
Journal of Colloid and Interface Science, VoL 43, No. 1, April 1973
126
STEWART
1.2~ o
E
THEORETICAL MAXIMUM
l,(3
/
i
,'7 .2!
[]
o
/'W
"
7
~
~
~
( TI ME) I/2 ( h r ) I/a
FIG. 2. Film thickness as a function of (time)½for polychloroprene latices with a = 1.34 M; 2b = 0.118 M. (©) Polymer A; (0)polymer B; (V1)polymer C; (I)polymer D. exhibit a significantly broad range of viscoelastic behavior the polymerizations were modified with dodecyl mercaptan levels ranging from 0 to 0.3 phr (parts per hundred parts of rubber) and the conversion was varied in the range from 70 to 100k. The sodium salt of rosin acid was used as t h e emulsifier in all polymerizations. The quantity of sodium rosinate used was varied with the final conversion in such a way that the final ratio of rosinate/polymer was the same for each latex. The latices were stablized with 0.01 phr phenothiazine and 0.01 phr 4-tert-butyl pyrocatechol.
2. Rate of Film Formation One end of a thin walled glass tube, 2.5 cm in diameter was covered with an open mesh nylon net 0.005 cm thick. The net was then placed in contact with the coagulant solution and allowed to become saturated. The tube was removed from the coagulant solution, filled with the latex aad then placed back into contact with the coagulant solution. After the desired time interval the net was easily removed from the coagulated latex at the bottom of the tube and the thickness of the film was measured with a thickness gauge. I t was necessary to saturate the net as described above prior to addition of the latex in order to prevent the latex from leaking out of the Journal of Colloid and Interface Science, V o l . 43, N o . 1, A p r i l 1973
tube. This also made it possible to remove the net from the coagulated film. IV. RESULTS AND DISCUSSION Four specially prepared polycholroprene latices were chosen for study. The amount of sodium rosinate used in each polymerization was controlled so that the actual quantity of rosinate in a close packed structure, 2b, would be equal to 2b = 0.118 M. F21] The latices were concentrated by evaporation to a high solids content of 65% by weight and their p H was adjusted to 10.5. At this relatively low p H Ca(OH)2 does not precipitate, while the rosin acid is still almost completely dissociated. Figure 2 shows the film thickness obtained with time when these four latices were brought into contact with a stirred coagulant solution of Ca(NO3)2 in water at a concentration of a = 1.34 M.
[22]
The latex was also gently stirred during film formation although as shown later this was found to be unnecessary. The uniformity and reproducibility of film thickness by this technique was within -4-5%. The relaxation modulus of each polychloroprene polymer was measured by placing a weighted steel ball on a thick film of dried
DIFFUSION THROUGH FILMS polymer and observing the depth of penetration with time. It was found, when the observed penetration was plotted as a function of elapsed time on a log-log scale, that straight lines resulted over times ranging from 10-2 hr to greater than 102 hr. Thus, Eq. [13] is an excellent representation for the shear relaxation modulus of these polymers over a very large time scale of interest. The equations necessary for calculating the relaxation modulus from these data are given by "fang (12). The value of m in Eq. [13-] is determined from the slope of the line and E is determined from the penetration when t --- 1 hr. The values of E and m for the four polymers selected are given in Table I. It is seen that these polymers do represent a very broad range of viscoelastic behavior from "high gel" (polymer A) to a very soft "sol" (polymer D). From Fig. 2 it is seen that the higher the relaxation modulus, as expressed by E and m, the greater the rate of film formation due to diffusion of Ca 2+ through the coagulated film. This is what one would expect, since a low relaxation modulus corresponds to an increased tendency to flow, and allows the particles to coalesce rapidly. As the latex particles coalesce, the cross-sectional area of serum through which the Ca 2+ can diffuse decreases and, for polymers such as I), an impermeable rubber barrier is eventually set up. The diffusion coefficient of Ca 2+ through a 0.118 M sodium rosinate solution was determined directly by dissolving the rosinate in a 20-/0 solution of 1000 cps methyl cellulose and then drawing the viscous solution into capillary tubes. The tubes were placed into the 1.34 M Ca 2+ coagulant solution and the position of the precipitated calcium rosinate boundary was measured with time. The value of the diffusion coefficient Do under these conditions was found to be (5) Do = 5.2 X 10-7 cm2/sec.
[-23~
The same value for Do was obtained to within 4-5% when the concentration of sodium rosinate was varied between the limits of 0.06 and 0.18 M while the concentration of the
127 TABLE I
VALUES OF E AND $~ZIN EQ.
EXPERIMENTAL Polymer designation
A B C D
14 FOR
POLYCIILOROPRENE POLYMERS E X 104 (dyn/cm2)
20 11 6.5 0.85
0.03 0.07 0.10 0.20
coagulant solution was varied between 0.7 and 2.0 M. These are the practical limits for variations in soap and coagulant concentrations usually encountered. The constant value of Do within these limited concentration ranges shows that this system is adequately described by the equations derived by Hermans (5) for diffusion with precipitation into a medium which does not itself take part in the diffusion process. From the first term on the right side of Eq. [-18], one would predict that for diffusion of Ca 2+ through close packed nondeformable spheres, the boundary of precipitated calcium rosinate ~" should follow the expression = 2a (Dt)~,
~e ~2 erf(a) = (0.26)a/brc½, D = Do/r
(r = 1.26).
[-24-] [-25-] [-26-]
Equation [25-] takes into account that the volume fraction of serum through which the Ca 2+ can diffuse is (0.26), while Eq. [-26~ accounts for the added distance that the unprecipitated Ca 2+ must travel to pass around the spheres. Equation [-24-] then represents the greatest film thickness that one can expect to obtain when a high solids latex comes into contact with a coagulant. Any coalescence of the latex particles will cause a reduced film thickness. The straight line in Fig. 2 then gives the theoretical maximum film thickness for coagulation of a latex of nondeformable spheres with concentrations of soap and coagulant as in Eqs. [-21] and [-22-], respectively, and diffusion coefficient as in Eq. [-23-]. The value
Journal of Colloid and Interface Science. Vol. 43, No. 1, April 1973
12 8
STEWART
1D '
~
,
,
,
,
,
. . . . . . .
,
,
,
,
,,~,E
fly*
rate of film deposition, the quantity
. . . . .
(2a(Dt)½ -- ~),
[293
as given in Eq. [-183 was calculated for the values of E and m listed in Table I and for values of the remaining variables as given in 7 Eqs. ['21~ to [-28~. These theoretical results ~.0 are shown plotted as a function of time on a log-log scale in Fig. 3, and appear as straight lines with slope (2m q- ½). Experimentally, the quantity in Eq. [29-] is just the hypothetical tDO] , , ,,,rr,I , , ,,Jr,,I , , ,r,,,,I , , ,,,,, .OT 0.I iO 10 lO0 maximum film thickness (the straight line in TIME ( h r ) Fig. 2) minus the observed film thickness (the Fla. 3. The effect of coalescence on film thickness. data points in Fig. 2). This quantity is shown The straight lines represent the theoretical quantity plotted as the data points in Fig. 3. As shown, [-2a(Dt)i -- ~'] in Eq. [i83 for a ~ 1.34 M and 2b = 0.118 M. The data points represent the experimental the agreement between theory and experiment values: (©) polymer A; (@) polymer B; (El) polymer is exact for "high gel" polymers A and B over C; (II) polymer D. the complete time scale studied of 25 hr; whereas, for "medium gel" polymer C the agreement is exact up to 5 hr and for "sol" for a which corresponds to these concentrations polymer D up to 30 rain. i s a = 1.1. It should be pointed out that the agreement The polymer/coagulant interfacial tension between theory and experiment in Fig. 3 is was determined by preparing a very low molec- strongly affected by the choice of the value rl, ular weight fluid polychloroprene. The polymer since it enters Eq. [-18~ as the inverse square. was isolated by drum drying and the interfacial The value chosen in Eq. ]-28~ is of the correct tension was measured by a pendent drop order of magnitude and gives the best fit of method (13). No attempt was made to remove the experimental data, so that any other choice surfactant or other impurities from the polymer would shift the lines in Fig. [-3] uniformly in since these are also present in the coagulated the veritical direction. The important observalatex film. The value for the interfacial tension tions are, however, that the slope of these lines ~, was found to be appears to have the correct value (2m -1- ½) at least during the initial stages of coalescence ~, = 15 dyn/cm. [-27~ and the dependence of film thickness on E -~ is of the correct order of magnitude. Once coaDue to the very small radius of polychlorolescence has proceeded to any significant degree prene latex particles (5 X 10-6 cm), it is very the theoretical result Eq. [-18~ is no longer ditgcult to obtain an accurate value for the applicable as expected. radius of curvature of the contact region rl To determine the effects that variations in between two coalescing particles. From electron the solids content have on the rate of film microscope studies, however, it appears that r~ deposition, the four latices were diluted by is of the order of 0.1 times the radius of the adding distilled water and then the coagulation particles. Therefore, in what follows a value of experiments repeated. It was found that between 65 and 450-/0 by wt, the solids content r~ = 5 × 10 -7 c m [-28~ had no apparent effect on film thickness and identical results were obtained whether or not is somewhat arbitrarily chosen. To compare the theory with experiments on the latices were stirred. Since the quantity 2b the retarding effect that coalescence has on the in Eq. [-21~ is not changed by dilution of the O.I
Journal of Colloid and Interface Science,
Vo.
43,
No.
1, April
1973
DIFFUSION T H R O U G H
latices this means that film formation is controlled in this case solely by the diffusion rate of Ca 2+ through the coagulated rubber film. At percentage of solids below 30% it was found that the rate of film formation increased with decreasing solids content. However, the films that were produced were very soft and spongy and exhibited a very large degree of shrinkage on drying. Therefore, it appears that this surprising result is due to a very loose agglomeration of the latex particles within the coagulated film compared with the approximate close packing of spheres which occurs with a high solids latex. This open structure then allows Ca 2+ to diffuse much more rapidly through the film so that diffusion of the latex particles becomes important. Due to the nature of the films produced under these conditions the increased rate of film formation is of little practical interest. To test the effects of changing the coagulant concentration, the film formation experiments were repeated using latex A and three different concentrations of Ca(NO3)2 coagulant. This latex was chosen since the observed effects should be greatest for a polymer which does not coalesce. The concentrations used and corresponding values of a calculated from Eq. [-19] with 2b = 0.118 M, are a = 0.67 M
a = 0.90,
[30]
a = 1.34 M
a = 1.10,
[31]
a = 2.01 M
a = 1.23.
[32]
Therefore, from Eq. [18], if the coagulant concentration is decreased from 1.34 to 0.67 M one would expect a decrease in the rate of film formation of about 18%; whereas, if the coagulant concentration is increased from 1.34 to 2.01 M the rate of film formation should increase by about 12%. Experimentally, the changes are found to be 14 and 90-/0, respectively. The differences are probably due to a concentration dependence of the diffusion coefficient D which occurs even between such narrow concentration limits as these. To observe the effects on film formation of changing the quantity of emulsifier, the poly-
FILMS
129
Inerization of latex A was repeated using two different levels of sodium rosinate. The polymerizations were carried out in such a way as to keep all other variables, such as the relaxation modulus of the polymers, as identical as possible, although the particle size and size distribution must be significantly affected by changes in emulsifier concentration. Again, this particular latex was chosen to maximize any differences which might occur. The quantity of sodium rosinate, 2b and the corresponding values of a, caiculated from Eq. [19] with a = 1.34M, are 2b = 0 . 0 5 9 M
a=
1.3,
[33]
2b = 0.118M
a = 1.1,
[34]
2b = 0.177M
~ = 1.05.
[35]
These values represent the practical limits for this system since at lower levels of emulsifier the latices become unstable and agglomerate during polymerization. At higher levels, the sodium rosinate is in excess. Thus, added soap remains in the serum as micelles which tend to increase viscosity and interfere with coagulation. When the values of ~ given in Eqs. [-33] to [-35] are substituted into Eq. [-18], one finds that as the quantity of rosinate used in the polymerization is decreased from 0.118 to 0.059 M the theory predicts an increase in the rate of film formation of about 18°-/o. Experimentally, the rate of film formation is found to increase about 12%. The discrepancy is probably due to the aforementioned agglomeration and subsequent coalescence which occurs during polymerization at low levels of emulsitier. This agglomeration results in a broader particle size distribution, which leads to tighter packing on coagulation and, consequently, a decrease in the diffusion rate of Ca 2+ through the film. Likewise if the quantity of rosinate is increased from 0.118 to 0.177 M the theory predicts a decrease of 5% in the rate of fihn formation. The change in the film deposition rate is found experimentally to be negligible,
Journal of Colloid and Interface Science, VoI. 43, No. 1, April 1973
130
STEWART
1.50 1.25 TYPE 655
J
J
HIGH GEL
~o1-0
0
~-".5C I
MEDIUM I
-
I
.25
I
2
3
4
(TIME) I/2 (hr) 1/2
FIG. 4. Film thickness as a function of (time)~for three commercialneoprene latices.
since the excess calcium rosinate which precipitates in the serum tends to interfere with coalescence of the particles. The fact that the precipitated excess calcium rosinate in the latex serum can interfere with coagulation and coalescence is also seen by adding 2 phr sodium rosinate to latex D, the "sol" latex described above. One would expect the added emulsifier to cause a slight decrease in rate of film formation as the diffusing Ca 2+ precipitates. However, there is actually observed an increase of more than 50°7o. This increase is most likely due to the hindering of coalescence by excess precipitated emulsifier in the latex serum which must be squeezed from between the particles as they come together. A similar effect is observed when certain emulsifiers other than sodium rosinate are added to the polychloroprene latices. Typical examples of surface active substances which are frequently added to latices to provide additional stability or to improve the overall appearance of dried films are "Aquarex ~ SMO" and "Aquarex 2 WAQ." In general, the added surfactants may be expected to affect film deposition rates either by reducing the polymer/ coagulant interfacial tension or, as is the usual case for anionic surfactants, by precipitating as the calcium salt. Thus, with the addition of anionic surfactants to the latices one observes effects similar to the addition of added sodium rosinate. They have very little effect on non-
coalescing "high gel" latices, whereas, for "sol" latices, the deposition fates are markedly increased as the precipitated soaps inhibit coalescence. As an example, under the conditions described for film formation in Fig. 2, the addition of 4 phr Aquarex WAQ to "sol" latex D causes an increase in the rate of film formation by more than 100%. Again, this increase is due to the precipitated calcium soap which inhibits the thinning and collapse of the intervening liquid film between latex particles prior to and during coalescence. A further example of the unusually large effect that excess surfactant has on film deposition is shown in Fig. 4, where the coagulation experiments were performed on commercially available Du Pont neoprene latices. The latices examined are designated as Types 601A, 650 and 635, and the polymers are reported to be high gel, medium gel and sol, respectively. They are of high solids content, obtained through creaming with ammonium alginate, and they are presently used in coagulant dipping operations. As in the previous experiments, the pH of each latex was adjusted to 10.5 and the concentration of the coagulant was 1.34 M. It is seen from Fig. 4 that the film deposition rates for Types 601A and 650 are of the order that would be expected for high and medium gel polymers, respectively. Type 635, however, produces a film at an extremely fast rate for a sol polymer, which actually
Journal of Colloid and Interface Science, Vol. 43, No. 1, A p r i l 1973
DIFFUSION THROUGH FILMS
approaches the rate of diffusion of Ca 2+ through latex serum. There are two possible reasons for the unusually high rate of film deposition from Type 635 latex, and both are related to the creaming step. First, creaming a latex causes the particles to fluocculate into fairly large nonspherical agglomerates. These agglomerates are unable to pack into a close structure on coagulation, and this increases the rate of diffusion of coagulant through the film as the tortuosity factor decreases. The second, and more important reason for the very fast deposition rate of Type 635 compared with Types 601A and 650 lies in the surfactant added during the creaming step. Types 601A and 650 have a relatively small amount of anionic surfactant added along with the creaming agent, whereas, almost 6 phr anionic surfactant, above the quantity used during polymerization, is added to Type 635. It is not unusual that such a large quantity of additional surfactant can interfere with the coalescence of a sol latex such as Type 635 and make it useful in certain commercial dipping operations where a polymer with very high elongation is desired. When one attempts to produce a coagulated film from Du Pont neoprene Type 735, which is the uncreamed version of Type 635, it is found that after 48 hr in contact with the coagulant, the film thickness remains less than 0.02 cm. This is what one would expect for a "sol" latex which contains no excess surfactant. Changes in the pH of the latices should qualitatively have the same effect as changes in the amount of sodium rosinate used during polymerization. The issue is complicated, however, by the fact that above a pH of 11, Ca(OH)2 precipitates along with calcium rosinate and, since this reduces the Ca 2+ diffusing through the film, the deposition rate is markedly decreased. On the other hand, at a pH below 10, the rosin acid which is now present acts to partially stabilize the latex against coalescence. Therefore, since less cal-
131
cium rosinate now precipitates and the latex is partially stabilized, the rate of fihn deposition increases. To be able to predict quantitatively the effect of pH changes on film deposition rates, therefore, would require a modification of the theory. Since data are available in the literature which shows that the changes are as described above, this subject will not be dealt with further. In conclusion, the theory seems to predict correctly the effects that various factors have on the relative rates of film deposition when polychloroprene latices come into contact with a coagulant. An exceptional case arises when a large quantity of surfactant is present which is in excess of the amount required to completely cover the latex particles. The excess surfactant hinders coalescence, and this has the greatest effect on rapidly coalescing "sol" polymers. REFERENCES 1. CARL,J. C., "Neoprene Latex," pp. 14-16. E. I. du Pont de Nemours and Co., Wilmington, DE, 1962. 2. BLACKLEY, D. C., "High Polymer Latices," pp. 514-540. Palmerton Pubi. Co., New York, 1966. 3. CARSLAW,H. S., A N D JAEGER, J. C., "Conduction of Heat in Solids," pp. 28-32. Oxford Univ. Press, London, 1959. 4. NIELSEN, L. E., J. Macromoh Sci., Chem. 1(5), 929 (1967). 5. HERMANS, J. J., J. Colloid Sci. 2, 387 (1947).
6. VANDEEI~O~'F, J. W., TARKOWSKI, H. L., JENKINS,
7. 8. 9. 10. 11.
12. 13. 14.
M. C., AND BRADFORD, E. B., J. Macromol. Chem. 1(2), 361 (1966). O~CHA~D, S. E., Appl. Sci. Res. Sect. A 11, 451 (1962). TABOR, J., Colloid Interface Sci. 31, 364 (1969). PI~ESCOTT,J. "AppIied Elasticity," pp. 329-332. Dover, New York, (1961). STEWART,C. W., AND JOHNSON, P. R., Macromolecules 3, 755 (1970). DAWS, H. T., "Introduction to Nonlinear Differential and Integral Equations," pp. 83-88. Dover Pub., New York, 1962. YANG, W. H., J. Appl. Mech. 27, 438 (1960). Wv, S., J. Phys. Chem. 74, 632 (1970). !¢VtIITTAKER, E. T., AND WATSON, G. N., "A Course of Modern Analysis," p. 339. Cambridge Univ. Press, London, 1962.
Journal of Colloid and Interface Science. VoL 43, No. I, April 1973