2698
Langmuir 1992,8, 2698-2106
Importance of Dissociated Ions in Contact Charging A. Diaz,’ D.Fehzel-Alexander, D.Wollmann,and J. A. Barker
IBM Almaden Research Center, K93/803,650 Harry Road, San Jose, California 95120 Received May 26, 1992. In Final Form: August 6, 1992 Organic salts are known to affect the contact charge developed between two polymers. When ionomera are present, the charge often increases monotonically with the salt concentration and the charge has been ascribed to the transfer of ions. A model is presented which relates the charge with salt concentration in the polymer blend. In this model, only dissociated ions but not ion pair ions are proposed to tranafer. The model incorporates ion pair dissociation (K1 and ion pair aggregation ( K ) and shows that when ion pair aggregation is minimal, the concentration of dissociated ions scales near linearly with the square root of the concentration of salt in the blend. The linear relationship between the charge and [salt]1/2 is demonstrated. It is further shown that the equilibrated charge which is establbhed is limited by the concentration of dissociated ions on the surface of the polymer and not by the surface provided by the second material.
Introduction When two different materials are contacted and then separated, electrostatic charges of equal magnitude and opposite sign are found on the two surfaces. This phenomenon is known as contact charging.I+ Contact charging between two metals is well described by electron transfer? However, the mechanism of charging between two insulating polymers is not well understood and both electron- and ionlOJ1 transfer have been proposed. Recent studies using polymers containing ions have shown that the ions dominate the charging behavior and the results have been explained by implicating electron,12-14 proton,15-17or transfer. Charge control by ions has been used extensively in dry printing processes, where toner, or electrophotographic “solid ink”, is moved from a storage bin to a specific location on a piece of paper by the application of appropriate electric fields. Protic acidsIMsalts,” and ionomers,12-14~18~1B~21~22~25-~ have been used to control the charge in toners. These materials are
generally blended into a nonionic resin at low concentrations, ca. 2-50 pmol/g. Since charging is a surface phenomenon, the control of the resulting surface composition is important for understanding and controlling the charge. Ionomers are copolymers in which the minor component ! ) is ionic. The incorporation of ionic (typically 10, the line again deviates downward from linearity. [X-I becomes progressively smaller with increasing values of K until it becomes a very small value which does not respond to [MXI. In light of this treatment the charging data for S-O.06 MVP OTs used in Figure 2 has been replotted in Figure 8 using [N-MePy O T S ] ~ / ~ The . reasonable straight line fit suggeststhat dissociated ions are important for charging and they are a small fraction of the total ion content (Kf is small). A similar fit is observed for the charge generated with bare beads; however, the slope is 10% smaller. Likewise, the other ionomers appear to show a straight line fit, although the data are limited. The linear fit suggests that ion pair aggregation is not serious (Kie not big). Since the data fit the model, the fraction of dissociated ions can be estimated from Figures 4 and 6 assuming K is 0.1-1. For the caae where K' is 10-8-10-8, then for [MXI equal to 0.2,[X-I/[MXl is equal to 0.060.0002. Thus, only a small fraction of the ions are dissociated and available for charging. Since the XPS
Langmuir, Vol. 8, No.11,1992 2706
Diusociated Ions in Contact Charging 0.301
I
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Figure7. Plot of [H+]/(IP)1/2against [MX11/2forRequals10-8 and different values of K.
tJP '
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o [Charge Agent], pph 0 [Charge
Agent]"*
Figure 9. (a) Plot of QIMagainst [T-373 and [ T - 3 7 I ~ lin/ ~ S-BMA reain, Modificationof part of Figure 7 from ref 39. (b) Plot of QIMagainst[Me(CLPh)SOTsl and [Me(CLPh)80Tsl1/*, modification of part of Figure 2 from ref 13.
chromium azo complex dye known as T-37.= This dye is poorly miscible in the resin and some of the dye is often present as a dispersion of fine particles. The linearity of the plot improves when the charge is plotted against [T-37W; however, the few number of data points limit our interpretation of the results (the point for the loweet ion concentration was not included in the plot). The plot in Figure 9b is for the charge for methyltria(chloropheny1)phosphonium arylsulfonate in styrene.13 The plot is reasonably linear against [saltW except for the highest concentration point which is off the line. In this experiment, 1pph is ca. 20 pmol/g. A similar result was found in treating the results reported in Figure 1 of ref 14 with the methyltriphenylphosphoniumtosylate. Since only those ions on the surface of the particles are considered available for charging, only avery small fraction of the ions formulated into the blend are effective. Assuming that ions which are in a 10-20 A "skin" along the surface are available for transfer, then the fraction of the ions in the "skin" is estimated from the ratio of the "skin"-bulk volume ratio assuming a spherical geometry for the particle, i.e. 4 ~ r ~ 6 r / ( 4 / 3or ) d(36r)/r. For r equal to 5 pm,the fraction is ca. 0.OOO5-0.001, and 99.9% of the total salt is ineffective for charging. The corresponding surface density of ions, rm, can be estimated from the expression C ~ x 4 ~ r 2 ( 6 r ) p / 4or ~ rCm(6r)p ~, (assuming a sphericalgeometry for the particle). For a blend containing 40 pmol of ions/g, rm is ca. (0.04-0.08) X moVcm2 (for p equal to ca. 1 g/cm3). This is about a percent of a monolayer coverage (ca. (4-6) X lO-'Omol/cm2for a planar surface). This estimate will of course vary with the thickness selected for the "skin" region. To comparethe observed charge levels with the surface ion content, we can use the charge observed with the powder containing 40 pmol/g methylpyridiniumtoluenesulfonate which is 70 pC/g and corresponds to 7 X 1W'O moVg of ions, assuming one charge per ion. Assuming all the charge is on the Surface of the particle, thia corresponds
2 OO
2
4
6
[N-MePy OTs]
8
10
"*
Figure 8. Plot of Q/M against [ i o n ] b ~for ~ /blends ~ of S-co4-MVP OTs (520 pmollg) in S-BMA (rolled against coated irregular beads).
results indicated that the surface ion content matches the bulk, C m = I'm,this is also the level of ion dissociation on the surface. This suggests that the equilibrium amount of ion transfer between the powder and the beads is controlled by the powder and not by the amount of surface area provided by the beads. More specifically, the charge is controlled by the dissociated ions on the powder surface. This agrees with the results in Figure 3 for the powders with higher ion content. The slope in the figure reduces significantly with increasing ion content in the powder but is still finite with the highest ion content powder measured. In practice, it may never be zero unless charge contributions from trace ions and/or moisture on the surfaces are eliminated. This conclusion also implies that the same beads could be reused (equilibrated) many times over with fresh powder (mix, roll, and blow-off) and they willcontinue to accept ions and be charged to a comparable level until the surface of the beads begins to saturate with ions. The results in Table I11 bear this out; i.e., the beads recovered from a powdedbead mixture after charging and removal of the powder could be charged to a comparable level with fresh powder for at least 10 reloadings. The charging data from two literature reports are plotted against the square root of the charge additive concentration. These are shown in Figure 9. The charging data in Figure 9a are for S-BMA containing low amounts of a
~
~~
(39)Gutierrez, A. R.;Dim, A.; Baird, B. Langmuir 1991, 7, 1923.
2706 Langmuir, Vol. 8, No.11, 1992 to 12 X 10-14 mol/cm2,which is 0.02-0.03 of the calculated surface ion density ((4-8) X 10-12mol/cm2). This estimate is within the fraction of dissociated surface ions estimated from Figures 5 and 6, Le., 0.06-0.0002. From the fraction of the surface ions involved in the charging process, 0.020.03, and the plots in Figures 4 and 5, a value for the ion pair dissociation constant, Kf, of ca. lo4 is estimated for the surface MX (assuming K = 0.1-1). To complete this analysis, the dissociation constants of these salts in this polymer remain to be measured. We can, however, make a general comparison of the estimated Kf with literature values for the dissociation constants of organic salts in aprotic solvents. The dissociationconstants of BQN+ salts are ca. lo-" in benzene (D= 2.3), ca. 1o"J in anisole (D= 4.3), and ca. loW4in THF (D= 7.4).36 While this treatment may be fairly generalfor ionomers, extension of this treatment to molecular salts and protic acids introduces other complications. With molecular salts, total ion transfer is greater and involves the transfer of both ions in the ion pair. This does not lead to a net charge and only contaminates the second surface. With protic acids, ion pair dissociation is probably not necessary for the proton to transfer because of its high mobility.
Conclusions Powders of styrenebutyl methacrylate containing styrene-co-methylpyridinium toluenesulfonate develop a positive charge against metal beads (bare and polymer coated). The positive charge correlates with the sign of the cation bonded to the ionomer, and the beads acquired the sign of the mobile anion. This result in combination with the previously reported observation of the mobile ion on the beads after rolling and removing the powder makes a good case for ion transfer for charging. Thus the sign of the charge on the powder is determined by which
Diaz et al. ion is immobilized. A model is presented which describes the charge as being controlled by the concentration of dissociated ions on the polymer surface. This model is based on charge resulting from the transfer of "free" ions on the polymer surface. This model incorporates ion pair association (K1and ion pair aggregation ( K ) and the ratio of the dissociated ions to the bulk ion content is related for several values of Kf and K. The model shows that a linear relationship is observed between charge and [ion] lI2 when ion pair aggregation is not serious with these materials, which would be the case, for example, with salts which are compatible with the resin or at low salt concentrations. This square root dependenceis provided by our results and by some charging data in the literature. The model also indicatesthat the charge attained is limited by ion pair dissociation on the powder surface and not the amount of surface provided by the beads. In line with this,beads which were recovered from the charging mixture and reused in charging experimentswere found to develop the same charge levels several times over. This limitation to the magnitude of the charge will, of course, change when there are not enough ions to dominatethe charging process. The charging behavior with ordinary salts is different from the ionomers. The charge-[salt] plots show a charge increase to a maximum level and then a decrease with higher salt concentrations. The maximum occurs at low salt concentrations and both ions transfer to the beads.
Acknowledgment. The authors wish to thank Dave Dreblow and Michael Ngo for their assistance with the technical aspects of this work. Registry No. (2-MVP OTs) (S)(copolymer), 143773-96-0; (4-MVP OTs) (S)(copolymer), 126726-54-3; (BuMa) (S)(copolymer), 25213-39-2; Fe, 7439-89-6.
