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On the role of electrostatic forces in the adhesion of polymer particles to solid surfaces
On the Role of Electrostatic Forces in the Adhesion Polymer Particles to Solid Surfaces B. V. DERJAGUIN,
I. N. ALE!NIKOVA
Laboraror_x of Surface Phenomena. Institute of Phuical
A&D Yu.
Chemx.nr>. USSR
P.
of
TOPOROV
Acadcm> of Scr~=zces,Moscon~ /US
S R.)
(Rccmed July 4, 1965)
SUMMARY Simultaneous
adheske force after
their
measurements haze been made of the and double electric charge of particles
remora1 from
a metal
surface.
For
action. However, the contribution of the electrostatic forces can be estimated by simultaneously measuring the force of adhesion and the charge of the double layer arising upon contact
the
systems int-estigated, the adhesice force and charge on the particles increase with particle diameter according to a power Imr with an e.xponent close to 2. Such dependence can be explained on the basis of the electrostatic nature of the adhesice forces. A double electric layer exists at the interface between the particles and tire metal sur$ace. A calculation was made of the x&ace density of chargefor the pblyL-in_vI chloride particle-steel system.
INTRODUCI-IOS
Investigations of the adhesion of polymer films to various substrates, including polymers, have shown that in the ease of the adhesion of compatible polymers the Brownian motion of segments of the chain moIecuIes may lead to cold welding of the two polymers in contact As a result, the surface of contact becomes indistinct and the seam acquires an essentially cohesive nature. In all other cases, the strength of the seam depends on the attractive forces between the two bodies. For the most part the main contribution to the work of separation is due to the attractive forces between the opposite shells of the double layer formed on the interiace. The principal limitation to the work required to separate the opposite charges of the double layer is the occurrence of a gas discharge_ In the case of small particles on solid surfaces, adhesion is determined, as a rule, by measuring the force required to remove the particles; in such experiments it is rather difficult to separate the electrostatic and molecular mechanisms of interPonder Techrwiog_a- ElsevierSequoia CA..
EJPERIMENTAL
In view of the great practical interest of the problem, we undertook an experiment to measure the force of adhesion of polymer particles to metallic substrates and the charge of the double layer arising upon contact. The second problem is simplified compared with the case of films by the fact that s hen small particles are removed there is no accompanying gas discharge, and hence no loss of the charge carried off by the particles_ This is due to the small volume of the electric field which arises in the process of detachment of the particles. In order to remove small particles (less than 30 p in diameter) in the direction of the perpendicular to the substrate surface an acceleration of the order of lo’-lo6 g is required. To obtain such accelerations we constructed a special pneumatic adhesiometer’ (Fig. l), in which adhesion of the particles deposited on the plane surface of a target fixed to the end of a cylindrical tube was overcome by the impact of a bullet on the opposite side of the target. The bullet was accelerated by compressed gas_ The acceleration of the target due to the bullet was determined by graphically differentiating the time dependence of the rate of displacement of the free end of the sample. The velocity was determined with a capacitance gauge. To calibrate the adhesiometer we determined the dependence of the target acceleration (the acceleration required to remove the particles) on the speed of the bullet along the tube, measured by means of a photoelectric circuit. By a proper choice of the weight of the bullet and its speed we could regulate the magnitude of
J_ausmne- Pnnted in the NetherIan&
ADHESIOS OF POLYMER PARTICLES I-0 SOLID SUTFACES
Fig 1. Scheme of pneumatic adhesiomercr 1, manometer; 2. high pressore chamber; 3. membrane; 4 bulks; 6, target; 7. block formeasuring spazdof 5ullct; 5, qlindcr 16th compressed ps.
the critical acceleration. With pressures up to IO atm and bullets weighing up to 100 g it was possible to achieve accelerations of from IO3 to IO6 g_ The adhesiometer was constructed so that adhesion could be measured in wcuo and in controkd atrnospheres The powders were deposited on the surface of the target by spraying from metal nozzks. Since the particles of the powder were heterodisperse, the diameter of each was measured separately. The adhesive force of the particles was determined by the formula F =
ma,
(1)
where E is the mean critical acceleration of particles ofa fned diameter d, and m is the mass of the particle_ The main critical acceleration was defined by the formula
where n(a) = N&7,
155
ticks, and N the number of particles adhering to the target after appIication of the acceIeratior a. In silch a method of determining si and_ respectively_ F_ it is assumed that as a result of experiments with _-dually increasing accelerations the surface of the target can be completely freed from *he particles. In cases when not ail the particles were detached (only SO+Oc/,) si was estimated by extrapolation to the values of u at which N=O_ To measure the charge of individual particles we developed a charge spectrometei. The charges were measured as the particles settled out in a laminar flow in the field of a stepwise condenser_ The particles under investigation entered the measuring part of the chamber of the charge spectrometer (see Fig. 2) in the form of a thin flat jet enveloped by a similarly directed stream of air and settled on the glassslidesattached to theelectrodesofthechamber. The charge of the particles was computed by the formula
where J(s)=!: E(s)dx, h is the coordinate of the point of entrance. _x the coordinate of the point where the particles settled out, II the flow v-elocity11the viscosity of air and E the field in the measuring part of the chamber_ The particles settIed out in the spectrometer at rates between 1 and 1 x 10eJ cm/set/v/cm (for particle diameters rangh-rg from 2 to 50 p)). The error in the determinatron of the charge was 25o/0.
; IV0 is the initial number of par-
Fig. 2 scheme of charge spectrometer_1. cntmncc channel; 2,3, aspiration blocs; 4, fdtcr; 5,6, m-ring eleczrodes; 7. grid for rec@ing jet
A complete analysis of the results was carried out by drawing the distribution function of particles of a given drameter rersus the charge_ After impact of the bullet on the target and separation of the particles, a fraction of the particles delineated by the area of the entrance slit of the spectrometer. entered a chamber set up horizontally directly behind the adhesiometerThe spectrometer chamber was also used to deposit par-ticks with a fried small charge of one sign. To this end we prepared special metal plates which were set up in a definite place in the chamber: the voltage on the ekctrodes and the rate of flow were chosen so that the mzssary number of simikrIy charged particks was deposited (in these experiments the stream of particles was obtained after Poder
TecZmoL
Z(1968.69)
15115S
156
B. V. DERJAGUIN,
I. N. ALEINIKOVA,
spraying from nozzles set up near the entrance of the chamber)_ After the particles were thus deposited, their adhesion to the metal plates was measured with the pneumatic adhesiometer, whiIe the charges of the particles after separation, were again measured with the charge spectrometer. The objects of investigation were polymer powders, mainly of regular spherical shape (polyvinyl chloride, polystyrene, etc. obtained in the process of emulsion polymerization). For the force of adhesion F which is overcome upon removal of a particle we can write F = F,i-Fe
= F--i-
2m2SK
I $
~
(4)
where F,,, is the molecular component; 2-ii~%, is the electrostatic component due to the formation in the zone of contact of a double layer with area Sli and surface density of charge G; the term t&d2 isdue to interaction with its image of the charge 4. homogeneously distributed over the surface of a spherical particle of diameter d. This charge arises as a result of preliminary electrilication of the particles. Table 1 gives the comparative data on the measurements of the charge before and after removal of the particles from the metal (steel 65-G, 10th grade of quality; polyvinyl chloride powder)_ As appears from the table. the charges of individual particles increased approximately lOO-fold after removal_ This result can be explained from our point of view only by assuming the existence of a douhle electric layer on the metal-powder interface_ W IL;: the faces of the double layer are separated they become highly electrified_ We chose such small values of q,, that the component of the adhesive force q$d2 was negligibly small compared with the total force measured and could be disregarded. For example, by means of the charge spectrometer it is possible to deposit on the surface under investigation particles with a charge such that the component 8,/d2 comprises lo- 5lo-’ dyne (for particles of diameter S-20 p). In addition, we measured the possible decrease of the charge with time on particles adhering to a grounded subst-rate (by the dynamical electrometer method). The measurements also showed that the initial charge of the particles decreases fairly rapidly under ordinary atmospheric conditions. The charge q,, was therefore very small, much less than the charge 4 after removal of the pat-ticks. The component of the adhesive force due to the double layer
YU_ P. TOPDROV
2_2s,
since 4 -go then
9 q.
2x(4;40)= K
=
and
25rd’ 9 &,
27E(4-40)2
*d
S,
d
2'
i.e., the contribution of the surface charge to the electrostatic force is negligibly small. A similar conclusion was reached by Krupp’. The main difficulty encountered in interpreting experiments on the adhesion of particles to a solid surface consists in separating the molecular component of the adhesive force from the electrostatic component. Although not offering a general solution of this problem, the experiment on the simultaneous measurement of the adhesive force and the charge after stripping allows us to distinguish the cases when the molecular component is smJ1. In the experiments described, the adhesive force of the particles increased with their size ; the dependence approached a power law with the exponent close to 2 (Fig. 3). It can be shown by simple calculations that this form of dependence of F on the radius of the particles is connected with the character of the measurements on the pneumatic adhesiometer and can be explained on the basis of the electrostatic nature of the adhesive forces- Indeed_ at the moment of impact when the elastic wave emerges on the free (front) surface of the target this surface at first comes into motion with great speed in the direction TABLE
’
CHARGE
,qo)AwJ
OF pOL\-VlSXL
AFrER
dbl
5 008 72
1O6 x 40 (%=4 10~xq(cg.s.c.)
Oo
CHLJXUDE
(q)REMovAJ_mKn1
5
70
d(p)
10 0 16 XI0
8 013 7.4
15
PARTICLES
BEFORE
AsrEEL-*a
15 026 15.0
20 033 48-O
20
FQ. 3. Dependence of adhesionforce of polyvinyl chioridc (0) and polystyrene (0) particks on their diameter to the steel SWEola F=dZ; 0, k=00016 face (h=F/d=l, full cmx-pam dynes/p=. 0 k=OOOOS dy=s//?) Ponder Techrwl., 2 (1968/69)
154-158
ADHESION
OF POLYMEX
PARTICXES
of motion of the bullet and then returns to its initial position_ As a result, before stripping occurs the particles arc subjected to an acceleration pressing them to the surface, whereas after the change in the direction of motion they experience an equally large acceleration tearin g them from the surface_ Let the area of contact of the particles upon impact be determined from I-Iertzk formula s,
= RPiK
P = ma.
(7)
where a is the maximum acceleration at the moment of impact (the “compressing” acceleration). We assume that separation is counteracted by an electrostatic force FC= 2rra’SK. Then at the moment of separation =
F = ma,
6%
where a is the acceleration at separation. equal in magnitude to the accelerarion upon impact In the left-hand part of eqn. (8) we substitute S, from eqn. (6), taking into account eqns (6’) and (7). and determine the dependence of the acceleration of removal on r; this gives us for the adhesive force F = A+?
(for p= I, where p is the density of the particle material). It follows from the preceding considerations, that when adhesion is determined in the main by electrostatic forces, then in measurements with the pneumatic adhesiometer the force F should be proportional to ~_Themolecular component oftheadhesive force in these conditions (preliminary compression) remains proportional to r, and is independent of
8 23
157
SURFACES
the degree of compression, as follows from a previous paper4_ Let us turn to an estimate of the surface density of electrification G in these experiments. The charge of the particles after separation is q = G& (since the original charge q,-, is small)_ From eqn. (8) vve then obtain
G=--.
.
uhere E,. and E2 arc Young3 moduli, v1 and q2 the Poisson coefficients of the bodies in contact, and P the pressure at the contact. We shall assume that
?zG~&
TO SOLlD
10
1.7
15 19
20 31
F
(l@)
2nq
The quantity c is determined by the nature and state of the particle and substrate surfaces and is independent of the radius of the particles, Hence_ if the measurements on particles ofdifferent diameters d show that the ratio F/q is independent of the diameter. then this will also indicate that the electrostatic component of the adhesive force is predominant in the system under investigation. If we calculate G from eqn. (10) for polyvinyl chloride powiier. for example. then it is evident from Table 2 that within the limits of experimental error G is independent of d, and in order of magnitude comprises lo3 cg_s_e. units. This order of magnitude of G is in agreement with the electron theory of adhesion. which assumes the existence of donoracceptor bonding on the interface’_ The compression hypothesis ad\-axed abo\-e can be checked by comparing the magnitudes of SKdetermined by eqns- (6) and (7) and by the equation S, =Zsrq’/F, where F and q are experimentally determined values. For example. for polyvinyl chloride particles of diameter= 10 p the values of SK. determined by taking into account compression and from the experimental vaiues of F and q. are 3x 10m9 cm2 and 2 x 10m8 cm”, respectiveiy- The discrepancy between these two values lies within the limits of experimental error_ It may be explained by the difference between the real values of Young-s moduli and those used in calculating the tabular data.
cOscLusIoss
It follows from the given experiments that: (1) There exists a double layer on the interface between a polymer particle and a metal surface. The polymer particles which are preliminarily weakly eIectrifkd_ after remova in a perpendicular direction, without friction, are strongly charged. (2) In the systems inxstigated, *&e adhesive force eiectric
Po*dtT
Te&d.
2 (196.3,69)154-15s
158
B. V. DERJAGUIN,
I. N. ALEINIKOVA.
and the charge after separation increase with the diameter of the particles in the range of diameters from 2 to 30 fi according to a power law with an exponent close to 2. When we take into account the initia3 compression of the particles in the method of measurement used, as well as the hypothesis of the electrostatic nature of the adhesive forces we find that the results of the experiments are in agreement with a quadratic law of dependence of the adhesive force on the particle diameter_ (3) We carried out calculations for the system polyvinyl chloride particles-metal under the above assumptions. Within the limits of experimental error the surface density of charge is independent of the diameter of the particles and in order of magnitude comprises IO3 c.gs.e. units. This result is in agreement with the assumption of the electrostatic nature of the adhesive forces for this system.
YU.
P. TOPOROV REFERENCES
1 B. V. DLSJAGUIN, Yu. P_ TOPOROV, I. N. Toam, I. N. ~~KOVA AND B. H. P~xcovscx. Jizhknzs~chni~e mareri& i ich primene+e, (J_ lacquer-painting materials and theirapplication), No. 2 (1964) 62; I. N. ~XOVA, P_ A DAAXD Yu. P. TOPOROV. ibid., No 4 (1967) 64. 2 4 V. Km-, I. N. Ax_nsaxov~, G. G. KOTL.Y-SSXYA AND V A. Pucmuw, Tr. Vses Nauchn. k&-d Insr. Medic Obonrd, No 3 (1965) 143. 3 G. Born W_ KLIXG. H_ KRUPP. H. JLXGE _cm G_ SamSTEDE. Z. Angm. P&S_. 16 (1964) 486; H. KRUPP AlD G. SPERUhG, J. Appl. Ph_vs_ 17 (1966) 4176 4 B. V. DERJAGIJIN. Koll. Z_. 69 (1934) 155 5 B V. DERJAGLZSx-cc N. A. I(ROTOVA, AdgezzJo, (Adhesion), Acad Sci Pubi.,Moswm. 1949. B. V.D~AG~XA~P V.P. sWLG.4. D&l. A&d Nauk SSSR. Ii? (1958) 877; It’ (1958) 1049; J_ AppL Ph>s_ 28 (1967) 4609; B. V_ DERJAGUS AXXB N. A. KROTOVA, Research, 8 (1955) 10; Ii2 Inrem. Kongr. Grenzfldchemchr. Sfoffe. K&h, 1960, Vol. 2, Sect B. p_ 39.
Powder Technol., 2 (1968/69) 15-l-158
I. N. ALE!NIKOVA
Laboraror_x of Surface Phenomena. Institute of Phuical
A&D Yu.
Chemx.nr>. USSR
P.
of
TOPOROV
Acadcm> of Scr~=zces,Moscon~ /US
S R.)
(Rccmed July 4, 1965)
SUMMARY Simultaneous
adheske force after
their
measurements haze been made of the and double electric charge of particles
remora1 from
a metal
surface.
For
action. However, the contribution of the electrostatic forces can be estimated by simultaneously measuring the force of adhesion and the charge of the double layer arising upon contact
the
systems int-estigated, the adhesice force and charge on the particles increase with particle diameter according to a power Imr with an e.xponent close to 2. Such dependence can be explained on the basis of the electrostatic nature of the adhesice forces. A double electric layer exists at the interface between the particles and tire metal sur$ace. A calculation was made of the x&ace density of chargefor the pblyL-in_vI chloride particle-steel system.
INTRODUCI-IOS
Investigations of the adhesion of polymer films to various substrates, including polymers, have shown that in the ease of the adhesion of compatible polymers the Brownian motion of segments of the chain moIecuIes may lead to cold welding of the two polymers in contact As a result, the surface of contact becomes indistinct and the seam acquires an essentially cohesive nature. In all other cases, the strength of the seam depends on the attractive forces between the two bodies. For the most part the main contribution to the work of separation is due to the attractive forces between the opposite shells of the double layer formed on the interiace. The principal limitation to the work required to separate the opposite charges of the double layer is the occurrence of a gas discharge_ In the case of small particles on solid surfaces, adhesion is determined, as a rule, by measuring the force required to remove the particles; in such experiments it is rather difficult to separate the electrostatic and molecular mechanisms of interPonder Techrwiog_a- ElsevierSequoia CA..
EJPERIMENTAL
In view of the great practical interest of the problem, we undertook an experiment to measure the force of adhesion of polymer particles to metallic substrates and the charge of the double layer arising upon contact. The second problem is simplified compared with the case of films by the fact that s hen small particles are removed there is no accompanying gas discharge, and hence no loss of the charge carried off by the particles_ This is due to the small volume of the electric field which arises in the process of detachment of the particles. In order to remove small particles (less than 30 p in diameter) in the direction of the perpendicular to the substrate surface an acceleration of the order of lo’-lo6 g is required. To obtain such accelerations we constructed a special pneumatic adhesiometer’ (Fig. l), in which adhesion of the particles deposited on the plane surface of a target fixed to the end of a cylindrical tube was overcome by the impact of a bullet on the opposite side of the target. The bullet was accelerated by compressed gas_ The acceleration of the target due to the bullet was determined by graphically differentiating the time dependence of the rate of displacement of the free end of the sample. The velocity was determined with a capacitance gauge. To calibrate the adhesiometer we determined the dependence of the target acceleration (the acceleration required to remove the particles) on the speed of the bullet along the tube, measured by means of a photoelectric circuit. By a proper choice of the weight of the bullet and its speed we could regulate the magnitude of
J_ausmne- Pnnted in the NetherIan&
ADHESIOS OF POLYMER PARTICLES I-0 SOLID SUTFACES
Fig 1. Scheme of pneumatic adhesiomercr 1, manometer; 2. high pressore chamber; 3. membrane; 4 bulks; 6, target; 7. block formeasuring spazdof 5ullct; 5, qlindcr 16th compressed ps.
the critical acceleration. With pressures up to IO atm and bullets weighing up to 100 g it was possible to achieve accelerations of from IO3 to IO6 g_ The adhesiometer was constructed so that adhesion could be measured in wcuo and in controkd atrnospheres The powders were deposited on the surface of the target by spraying from metal nozzks. Since the particles of the powder were heterodisperse, the diameter of each was measured separately. The adhesive force of the particles was determined by the formula F =
ma,
(1)
where E is the mean critical acceleration of particles ofa fned diameter d, and m is the mass of the particle_ The main critical acceleration was defined by the formula
where n(a) = N&7,
155
ticks, and N the number of particles adhering to the target after appIication of the acceIeratior a. In silch a method of determining si and_ respectively_ F_ it is assumed that as a result of experiments with _-dually increasing accelerations the surface of the target can be completely freed from *he particles. In cases when not ail the particles were detached (only SO+Oc/,) si was estimated by extrapolation to the values of u at which N=O_ To measure the charge of individual particles we developed a charge spectrometei. The charges were measured as the particles settled out in a laminar flow in the field of a stepwise condenser_ The particles under investigation entered the measuring part of the chamber of the charge spectrometer (see Fig. 2) in the form of a thin flat jet enveloped by a similarly directed stream of air and settled on the glassslidesattached to theelectrodesofthechamber. The charge of the particles was computed by the formula
where J(s)=!: E(s)dx, h is the coordinate of the point of entrance. _x the coordinate of the point where the particles settled out, II the flow v-elocity11the viscosity of air and E the field in the measuring part of the chamber_ The particles settIed out in the spectrometer at rates between 1 and 1 x 10eJ cm/set/v/cm (for particle diameters rangh-rg from 2 to 50 p)). The error in the determinatron of the charge was 25o/0.
; IV0 is the initial number of par-
Fig. 2 scheme of charge spectrometer_1. cntmncc channel; 2,3, aspiration blocs; 4, fdtcr; 5,6, m-ring eleczrodes; 7. grid for rec@ing jet
A complete analysis of the results was carried out by drawing the distribution function of particles of a given drameter rersus the charge_ After impact of the bullet on the target and separation of the particles, a fraction of the particles delineated by the area of the entrance slit of the spectrometer. entered a chamber set up horizontally directly behind the adhesiometerThe spectrometer chamber was also used to deposit par-ticks with a fried small charge of one sign. To this end we prepared special metal plates which were set up in a definite place in the chamber: the voltage on the ekctrodes and the rate of flow were chosen so that the mzssary number of simikrIy charged particks was deposited (in these experiments the stream of particles was obtained after Poder
TecZmoL
Z(1968.69)
15115S
156
B. V. DERJAGUIN,
I. N. ALEINIKOVA,
spraying from nozzles set up near the entrance of the chamber)_ After the particles were thus deposited, their adhesion to the metal plates was measured with the pneumatic adhesiometer, whiIe the charges of the particles after separation, were again measured with the charge spectrometer. The objects of investigation were polymer powders, mainly of regular spherical shape (polyvinyl chloride, polystyrene, etc. obtained in the process of emulsion polymerization). For the force of adhesion F which is overcome upon removal of a particle we can write F = F,i-Fe
= F--i-
2m2SK
I $
~
(4)
where F,,, is the molecular component; 2-ii~%, is the electrostatic component due to the formation in the zone of contact of a double layer with area Sli and surface density of charge G; the term t&d2 isdue to interaction with its image of the charge 4. homogeneously distributed over the surface of a spherical particle of diameter d. This charge arises as a result of preliminary electrilication of the particles. Table 1 gives the comparative data on the measurements of the charge before and after removal of the particles from the metal (steel 65-G, 10th grade of quality; polyvinyl chloride powder)_ As appears from the table. the charges of individual particles increased approximately lOO-fold after removal_ This result can be explained from our point of view only by assuming the existence of a douhle electric layer on the metal-powder interface_ W IL;: the faces of the double layer are separated they become highly electrified_ We chose such small values of q,, that the component of the adhesive force q$d2 was negligibly small compared with the total force measured and could be disregarded. For example, by means of the charge spectrometer it is possible to deposit on the surface under investigation particles with a charge such that the component 8,/d2 comprises lo- 5lo-’ dyne (for particles of diameter S-20 p). In addition, we measured the possible decrease of the charge with time on particles adhering to a grounded subst-rate (by the dynamical electrometer method). The measurements also showed that the initial charge of the particles decreases fairly rapidly under ordinary atmospheric conditions. The charge q,, was therefore very small, much less than the charge 4 after removal of the pat-ticks. The component of the adhesive force due to the double layer
YU_ P. TOPDROV
2_2s,
since 4 -go then
9 q.
2x(4;40)= K
=
and
25rd’ 9 &,
27E(4-40)2
*d
S,
d
2'
i.e., the contribution of the surface charge to the electrostatic force is negligibly small. A similar conclusion was reached by Krupp’. The main difficulty encountered in interpreting experiments on the adhesion of particles to a solid surface consists in separating the molecular component of the adhesive force from the electrostatic component. Although not offering a general solution of this problem, the experiment on the simultaneous measurement of the adhesive force and the charge after stripping allows us to distinguish the cases when the molecular component is smJ1. In the experiments described, the adhesive force of the particles increased with their size ; the dependence approached a power law with the exponent close to 2 (Fig. 3). It can be shown by simple calculations that this form of dependence of F on the radius of the particles is connected with the character of the measurements on the pneumatic adhesiometer and can be explained on the basis of the electrostatic nature of the adhesive forces- Indeed_ at the moment of impact when the elastic wave emerges on the free (front) surface of the target this surface at first comes into motion with great speed in the direction TABLE
’
CHARGE
,qo)AwJ
OF pOL\-VlSXL
AFrER
dbl
5 008 72
1O6 x 40 (%=4 10~xq(cg.s.c.)
Oo
CHLJXUDE
(q)REMovAJ_mKn1
5
70
d(p)
10 0 16 XI0
8 013 7.4
15
PARTICLES
BEFORE
AsrEEL-*a
15 026 15.0
20 033 48-O
20
FQ. 3. Dependence of adhesionforce of polyvinyl chioridc (0) and polystyrene (0) particks on their diameter to the steel SWEola F=dZ; 0, k=00016 face (h=F/d=l, full cmx-pam dynes/p=. 0 k=OOOOS dy=s//?) Ponder Techrwl., 2 (1968/69)
154-158
ADHESION
OF POLYMEX
PARTICXES
of motion of the bullet and then returns to its initial position_ As a result, before stripping occurs the particles arc subjected to an acceleration pressing them to the surface, whereas after the change in the direction of motion they experience an equally large acceleration tearin g them from the surface_ Let the area of contact of the particles upon impact be determined from I-Iertzk formula s,
= RPiK
P = ma.
(7)
where a is the maximum acceleration at the moment of impact (the “compressing” acceleration). We assume that separation is counteracted by an electrostatic force FC= 2rra’SK. Then at the moment of separation =
F = ma,
6%
where a is the acceleration at separation. equal in magnitude to the accelerarion upon impact In the left-hand part of eqn. (8) we substitute S, from eqn. (6), taking into account eqns (6’) and (7). and determine the dependence of the acceleration of removal on r; this gives us for the adhesive force F = A+?
(for p= I, where p is the density of the particle material). It follows from the preceding considerations, that when adhesion is determined in the main by electrostatic forces, then in measurements with the pneumatic adhesiometer the force F should be proportional to ~_Themolecular component oftheadhesive force in these conditions (preliminary compression) remains proportional to r, and is independent of
8 23
157
SURFACES
the degree of compression, as follows from a previous paper4_ Let us turn to an estimate of the surface density of electrification G in these experiments. The charge of the particles after separation is q = G& (since the original charge q,-, is small)_ From eqn. (8) vve then obtain
G=--.
.
uhere E,. and E2 arc Young3 moduli, v1 and q2 the Poisson coefficients of the bodies in contact, and P the pressure at the contact. We shall assume that
?zG~&
TO SOLlD
10
1.7
15 19
20 31
F
(l@)
2nq
The quantity c is determined by the nature and state of the particle and substrate surfaces and is independent of the radius of the particles, Hence_ if the measurements on particles ofdifferent diameters d show that the ratio F/q is independent of the diameter. then this will also indicate that the electrostatic component of the adhesive force is predominant in the system under investigation. If we calculate G from eqn. (10) for polyvinyl chloride powiier. for example. then it is evident from Table 2 that within the limits of experimental error G is independent of d, and in order of magnitude comprises lo3 cg_s_e. units. This order of magnitude of G is in agreement with the electron theory of adhesion. which assumes the existence of donoracceptor bonding on the interface’_ The compression hypothesis ad\-axed abo\-e can be checked by comparing the magnitudes of SKdetermined by eqns- (6) and (7) and by the equation S, =Zsrq’/F, where F and q are experimentally determined values. For example. for polyvinyl chloride particles of diameter= 10 p the values of SK. determined by taking into account compression and from the experimental vaiues of F and q. are 3x 10m9 cm2 and 2 x 10m8 cm”, respectiveiy- The discrepancy between these two values lies within the limits of experimental error_ It may be explained by the difference between the real values of Young-s moduli and those used in calculating the tabular data.
cOscLusIoss
It follows from the given experiments that: (1) There exists a double layer on the interface between a polymer particle and a metal surface. The polymer particles which are preliminarily weakly eIectrifkd_ after remova in a perpendicular direction, without friction, are strongly charged. (2) In the systems inxstigated, *&e adhesive force eiectric
Po*dtT
Te&d.
2 (196.3,69)154-15s
158
B. V. DERJAGUIN,
I. N. ALEINIKOVA.
and the charge after separation increase with the diameter of the particles in the range of diameters from 2 to 30 fi according to a power law with an exponent close to 2. When we take into account the initia3 compression of the particles in the method of measurement used, as well as the hypothesis of the electrostatic nature of the adhesive forces we find that the results of the experiments are in agreement with a quadratic law of dependence of the adhesive force on the particle diameter_ (3) We carried out calculations for the system polyvinyl chloride particles-metal under the above assumptions. Within the limits of experimental error the surface density of charge is independent of the diameter of the particles and in order of magnitude comprises IO3 c.gs.e. units. This result is in agreement with the assumption of the electrostatic nature of the adhesive forces for this system.
YU.
P. TOPOROV REFERENCES
1 B. V. DLSJAGUIN, Yu. P_ TOPOROV, I. N. Toam, I. N. ~~KOVA AND B. H. P~xcovscx. Jizhknzs~chni~e mareri& i ich primene+e, (J_ lacquer-painting materials and theirapplication), No. 2 (1964) 62; I. N. ~XOVA, P_ A DAAXD Yu. P. TOPOROV. ibid., No 4 (1967) 64. 2 4 V. Km-, I. N. Ax_nsaxov~, G. G. KOTL.Y-SSXYA AND V A. Pucmuw, Tr. Vses Nauchn. k&-d Insr. Medic Obonrd, No 3 (1965) 143. 3 G. Born W_ KLIXG. H_ KRUPP. H. JLXGE _cm G_ SamSTEDE. Z. Angm. P&S_. 16 (1964) 486; H. KRUPP AlD G. SPERUhG, J. Appl. Ph_vs_ 17 (1966) 4176 4 B. V. DERJAGIJIN. Koll. Z_. 69 (1934) 155 5 B V. DERJAGLZSx-cc N. A. I(ROTOVA, AdgezzJo, (Adhesion), Acad Sci Pubi.,Moswm. 1949. B. V.D~AG~XA~P V.P. sWLG.4. D&l. A&d Nauk SSSR. Ii? (1958) 877; It’ (1958) 1049; J_ AppL Ph>s_ 28 (1967) 4609; B. V_ DERJAGUS AXXB N. A. KROTOVA, Research, 8 (1955) 10; Ii2 Inrem. Kongr. Grenzfldchemchr. Sfoffe. K&h, 1960, Vol. 2, Sect B. p_ 39.
Powder Technol., 2 (1968/69) 15-l-158