FRICTION IN ORTHODONTICS

PREPARED BY/ MOHAMED AL-KHAWLANISUPERVISOR PROF. DR. MAHER FOUDA

Egypt, Mansoura UniversityFaculty of Dentistry

Orthodontics Department

Friction in clinical orthodontics now is receiving much attention because orthodontic companies have decided that low friction is good and are using that concept to market their self-ligating brackets.

Sometimes low friction can be important, as in retractinga tooth along a continuous archwire or in consolidatingspace; sometimes high friction is needed, as in closing loop mechanics, anchorage, and 2-couple systems (torquing arch). Often friction is not an issue, as in a 1-couplesystem (intrusion or extrusion arch) or for repositioningan impacted tooth with a cantilever.

This presentation evaluates friction in the context of resistance to sliding of brackets along an archwire or an archwire through brackets, when friction is just 1 component of the total resistance.

WHAT IS THE FRICTION?

Friction is the resistive force between surfaces that opposes motion. It is not a fundamental force, because it is derived from electromagnetic forces between atoms.

There are 2 types of friction: static and kinetic. Static friction opposes any applied force. Its magnitude is exactly what it must be to prevent motion between 2 surfaces, up to the point at which it is overcome and movement starts. Kinetic friction, which usually is less than static friction, then opposes the direction of motion of the object.

• For all practical purposes, kinetic friction is irrelevant in orthodontic tooth movement because continuous motion along an archwire rarely if ever occurs. In sliding mechanics, we are dealing with a quasi-static thermodynamic process, which means that the process happens slowly and goes through a sequence of states that are close to equilibrium.

• Forces and resistance to sliding change as the tooth moves down the wire, tips, has a biologic response, uprights as bone remodels around the root, and then tips again.

• In orthodontic tooth movement, friction (static or kinetic) results from the interaction of an archwire with the sides of an orthodontic bracket or a ligature. Friction is only a part, and usually a small part, of the resistance to movement as a bracket slides along an archwire.

Kusy and Whitley divided resistance to sliding (RS) into 3 components: (1) friction, static or kinetic (FR), due to contact of the wire with bracket surfaces; (2) binding (BI), created when the tooth tips or the wire flexes so that there is contact between the wire and the corners of the bracket (when a force is applied to a bracket to move a tooth, the tooth tips in the direction of the force until the wire contacts the corners of the bracket, and binding occurs); and (3) notching (NO), when permanent deformation of the wire occurs at the wire-bracket corner interface. This often occurs under clinical conditions.

FRICTION (FR) BINDING (BI) NOTCHING (NO)

FRICTION IN FIXED APPLIANCE TREATMENTWhen teeth slide along an arch wire, force is needed for two purposes: to overcome frictional resistance, and to create the bone remodeling needed for tooth movement. Controlling the position of anchor teeth is accomplished best by minimizing the reaction force that reaches them. Use of unnecessarily heavy force to move teeth creates problems in controlling anchorage. Unfortunately, anchor teeth usually feel the reaction to both frictional resistance and tooth movement forces, so controlling and minimizing friction is an important aspect of anchorage control.

To retract a canine by sliding it along an archwire (in this case with 100-g distal force), conventional wisdom dictates that additional force, beyond what is required to move the tooth, is necessary to overcome friction (in this case also assumed to be 100 g). Some authors suggest that additional frictional force increases loading on anchor molar to value equal to canine retraction force plus frictional force (in this case to 200 g) and, consequently, increases molar anchorage loss.

When sliding mechanics are used, friction occurs at the bracket-wire interface. Some of the applied force is therefore dissipated as friction, and the remainder is transferred to supporting structures of the tooth to mediate tooth movement. Therefore, maximum biological tissue response occurs only when the applied force is of sufficient magnitude to adequately overcome friction and lie within the optimum range of forces necessary for movement of the tooth.

When one moving object contacts another, friction at their interface produces resistance to the direction of movement.The frictional force is proportional to the force with which the contacting surfaces are pressed together and is affected by the nature of the surface at the interface (rough or smooth, chemically reactive or passive, modified by lubricants, etc.). Interestingly, friction is independent of the apparent area of contact. This is because all surfaces, no matter how smooth, have irregularities that are large on a molecular scale, and real contact occurs only at a limited number of small spots at the peaks of the surface irregularities (Figure).

These spots, called asperities, carry all the load between the two surfaces. Even under light loads, local pressure at the asperities may cause appreciable plastic deformation of those small areas.

Friction can be described by the coefficient of friction, which is a constant and is related to the surface characteristics of the material. The coefficient of friction can be described mathematically as the frictional force that resists motion, divided by the normal force that acts perpendicular to the two contacting surfaces. There are two coefficients of friction for a material. One is the coefficient of static friction, which reflects the force necessary to initiate movement, and the other is the coefficient of kinetic friction, which reflects the force necessary to perpetuate this motion. It takes more force to initiate motion than to perpetuate it.

FRICTIONAL FORCES, THEIR ORIGIN, AND CLASSIC FORMULAS

• If a force is applied to a canine from a chain elastic or a coil spring, the tooth will not feel the full force if there is friction in the appliance. What the tooth feels is the effective force (FE), not the applied force (FA):FE= FA – Frictional force (FF)

• When the frictional force is the same as the applied force, the tooth will feel no force from the spring. As long as there is frictional force, effective force is always less than the applied force. Of course, it is the effective force that is relevant for the clinician.

• Where do frictional forces come from? The nature of friction is still being debated between adhesion and interlocking theory, even among modern physicists; however, classic friction theory tells us that forces perpendicular to the archwire are responsible for friction. Figure-a shows a canine sliding along an archwire. For simplicity, all moments are ignored.

The classic law of friction is also known as Amontons-Coloumb Law and is very simple:

The coefficient of friction is not an inherent property of a material, such as modulus of elasticity. It is a dimensionless property that represents the amount of friction between two materials and is determined by experiment only and not by theory. If the material used at the interface of two materials reduces the coefficient of friction, it is called a lubricant. If it increases the coefficient of friction, it is called an adhesive. For a stainless steel wire and stainless steel bracket in the mouth, an average value for the coefficient of friction (µ) is 0.16. The magnitude of normal force can be unpredictable because of the many variables, including three material interfaces that can be present: wire, bracket, and polymeric O-ring. Suppose a 50-g normal force is applied to a bracket. The frictional force can be calculated, and the effective distal force is 92 g.

FF= Coefficient of friction (µ) × Normal force (FN)

The coefficient of friction is the lowest with stainless steel wires and the highest with beta-titanium wires. Ceramic brackets have higher coefficients than stainless steel, and the high variation is related to design and manufacturing methods. It is often assumed that the smoother the material, the lower is the coefficient of friction; however, the relationship is not so simple. If the forces are high, destructive changes can occur in either the bracket or the wire, changing the subsequent behavior. Examples include wire notching, as depicted in Fig . A tipped tooth can notch a wire, producing effects not easily predicted.

Some surface treatments, such as ion impregnation by nitrogen bombarding, increase the hardness and reduce the coefficient of friction of a wire. Figure below shows a group of beta-titanium archwires; the various colors are produced after titanium nitride particles are distributed in the wire’s surface by ion impregnation.

Colored -TMA wires

Doshi et al (AJO-DO 2011) investigated the static frictional resistance between 3 modern orthodontic brackets—ceramic with gold-palladium slot, ceramic, and stainless steel—and 4 archwires (0.019×0.025-in)—stainless steel, nickel-titanium, titanium-molybdenum alloy (TMA), and low-friction colored TMA. They reported that frictional values for colored TMA were comparable with SS wires and thus seem a good alternative to SS wires during space closure in sliding mechanics.

SEM microphotographs showing A. colored TMA , B. TMA

Vs

BA

SOURCE OF NORMAL FORCESFrictional forces are evident at all stages of orthodontic treatment. They involve any mesiodistal sliding between wire and bracket. This occurs not only with purposeful sliding mechanics such as canine retraction but also in alignment arches where, if the wire cannot slide, buccal or lingual forces can be attenuated.

Friction exists during all movements in which the wire is in contact with the bracket and ligature. During leveling, when a flexible wire is placed in a high canine bracket, the tooth moves downward with the elasticity of the wire. As the curved wire is deactivated, it straightens by sliding through the adjacent brackets, with friction occurring between the wire, bracket, and ligature materials.

Forces perpendicular to the wire can come from a number of sources and in any direction: buccal, lingual, occlusal, or apical (Fig a). In the passive wire, the O-ring produces a lingual force in (Fig b)that can lead to a frictional force. Thus, the ligation method is only one source of friction. Any other forces required for tooth movement, if perpendicular to the archwire, can also lead to friction and in many situations can produce much more friction than the ligature tie.

a b

Of particular importance are forces originating from pure moments or couples. By definition, couples are equal and opposite forces not in the same line of action. Normal forces exist on the wire, although the sum of the forces is zero (Fig below). Moments are used in a first-order direction to rotate teeth, in a second-order direction to change axial mesiodistal inclinations, and in a third-order direction to change buccolingual axial inclinations. A moment (couple) at the bracket is required to give an equivalent force system for full control of a tooth. This moment is one major source of friction with the edgewise appliance.

Some brackets are designed to allow a tooth to tip or rotate. With this type of bracket, this source of friction can be eliminated, but control of tooth movement is lost as a result.

(a) Even in a low-friction self-ligating bracket, frictional force operates at the distal of the bracket in a mesial direction. (b)The frictional force produced a side effect that opened up space,and the crown moved mesially. In clinical situations, forces on the wire are a major source of friction, not just the ligature tie.

CANINE RETRACTION

During canine retraction, the canine rotates distal in, and the crown tips distally. The archwire elastically deforms and, during recovery, prevents or minimizes the rotation (a) and tipping (b) by exerting couples on the teeth. (c and d) The same diagram with the couples (curved arrows in a and b) replaced by two normal forces (arrows) to further show the origin of the frictional force.

To figure out how much frictional force occurs during canine retraction, we must consider the phase of canine retraction as evaluated from both the facial and occlusal views. Four phases can be recognized. After a distal force is placed, the canine may have play between the wire and the bracket, and initially the tooth will display uncontrolled tipping.This is phase I. No moments or normal forces operate in this plane. For now, ligation forces are ignored. The tooth continues to tip more, and the play is eliminated.

Increasing moments are created by the elastically deformed wire, and a controlled tipping phase is produced (phase II). Perhaps we have a tipping center of rotation at the apex. Note that normal forces are produced in phase II as the tipping is being minimized, but only low levels of friction are produced. When the tooth tips some more and a sufficiently high moment is delivered by the wire, translation occurs (phase III).

The greatest frictional forces are produced during translation. During phase IV, as the force is reduced, no more distal sliding occurs, and the axial inclination is corrected. Here, of course, there is a high frictional force that is acceptable because sliding is not desired at this stage (see also Fig 14-9).

In short, frictional force varies depending on the stage of canine retraction: none initially with play and the highest levels during translation. Even with rigid edgewise arches, a retracted tooth will go through these four phases; however, the angle of tip will be smaller. The angle of tip during translation is mainly a function of wire stiffness and the applied distal force. Clinically, it may appear that the tooth has translated in one phase. In reality, however, it has first tipped, then translated, and then finally uprighted. Ligation forces and forces in other planes are considered separately in this .As the bracket width decreases, the friction will increase because the normal force must increase to provide the same amount of moment.

However, the mechanism of narrow brackets (eg, Begg bracket) is different. They produce only a single force and negligible frictional forces because they do not prevent tooth tipping (no control moments) and do not demonstrate phases II, III, and IV of space closure. In Begg treatment, a separate individual root spring is used for tooth uprighting during phase IV.

From the facial view, frictional forces are developed because the CR is apical to the bracket. In a similar evaluation from the occlusal view, the bracket is labial to the CR and, hence, a distal force will rotate the canine distal in. The archwire prevents or minimizes canine rotation in four phases (Fig 19-16).During phase I, if play exists between the wire and the bracket, the canine is free to rotate. No wire restraining of the rotation occurs; therefore, there is no friction in this phase in the occlusal view. Duringphase II, the tooth continues to rotate; however, the archwire is minimizing the rotation by elastic deformation. Because of the restraining archwire moments, friction increases and finally reaches its maximum during phase III translation. No sliding occurs in phase IV when the rotation is being corrected.

The amount of frictional force from the occlusal view depends on the perpendicular distance of the bracket to the CR. The greater this distance, the larger is the moment rotating the canine and the greater is the moment needed from the archwire to prevent this rotation.

TORQUE AND FRICTIONIt has been seen that moments associated with the prevention of tipping and rotation of a canine can lead to high frictional forces. In addition, third-order moments (ie, torque) can lead to particularly high frictional forces. Figure(a and b)compares two activations on a canine; both have the same moment magnitude of 1,000 g mm, but one is in the bending mode (Fig- a), and the other is in the torsion mode (Fig-b).

The torque produces the largest vertical force of 2,000 g because the distance is small across the wire cross section. Because the normal forces from torque are greater than those from the second-order couple, the friction will be eight times higher in torque than tipping for the same moment. (In this example, the ratio of the moment arms is 4 mm/0.5 mm = 8; hence, the normal force is eight times greater.) For this reason, it is not recommended to use edgewise wires that fully engage the brackets (with possible unwanted torque) for canine retraction. The high friction can potentially make for inefficient or unpredictable retraction. Round or undersized wires are preferable to eliminate possible unwanted torque problems.

BRACKET DESIGN AND FRICTIONLet us consider two bracket design parameters: (1) method of ligation and (2) bracket width. A wire can be placed passively into a bracket, and a ligature or locking mechanism holds it in place. No force is exerted on the tooth, and the tie function is purely restraint (Fig - a). In (Fig –b), the tie mechanism activates the wire, producing an active force for desired tooth movement. Displacing the ligature tie with more force will cause the wire to more fully seat in the bracket. After the wire is fully seated, a greater ligature tie force does not increase the force to move the tooth (Fig -c).

The added perpendicular force will only produce a frictional force that most likely is not required or wanted. This friction from tight ties is sometimes used to keep teeth from sliding. Normal force from metal ligature ties are difficult to control if predictable ligating forces are to be achieved. Elastomeric O-rings can deliver initially higher forces than a lightly tied metal ligature wire.

However, elastomers will undergo degradation (or relaxation) over time, making the ligation force unpredictable; after degradation, their normal forces may be as low as some self-ligating brackets. If one only considers friction from ligation, so-called self ligating brackets do have the advantage of more predictably delivering lighter restraining forces (forces at 90 degrees to the archwire) and, hence, lower friction.

Both active and passive self-ligating systems can produce lower normal forces by ligation alone than elastomeric rings or metal ties. On the other hand, after degradation, elastomers can deliver low tie forces; also, some clinicians are very adept at forming light metal ties. If the frictional forces are known, they can be overridden. It should be remembered that, during treatment, the orthodontist applies forces perpendicular to the arch during wire placement and that it is these forces that can produce the most friction during sliding mechanics; self-ligating brackets are not an exception. The same forces are required for delivering the correct force system with self-ligating brackets as with more traditional brackets; hence, friction is similar.

• WHICH BRACKET PRODUCES THE MOST FRICTION: A WIDE BRACKET OR A NARROW BRACKET DURING RETRACTION?

Narrow brackets may show faster tooth movement initially; therefore, it may be assumed to have less friction, but this concept is wrong. The tooth movement in this case is not directly related to the friction. The reason narrow brackets seem to show initial faster tooth movement during sliding mechanics is due to the play between the bracket slot and the wire in phase I of sliding mechanics (Fig a & b). With the same amount of play (clearance) between the bracket and the wire, the narrow bracket can tip (rotate) more during phase I of space closure. In this phase, the friction comes only from the normal force ligature mechanism. To find the frictional force, we must use a moment (couple) thatproduces vertical forces.

THE FORMULA IS (FF = Μ × N = Μ × 2M/ W)

where FF is frictional force, N is normal force, M is moment at the bracket, and W is bracket width.Figure 19-23 compares two brackets: a narrow 2-mm bracket and a wide 4-mm bracket. Let us suppose both teeth need a counterclockwise moment of 1,000 gmm for translation. The narrow bracket requires equal and opposite 500-g forces (500 g × 2 mm = 1,000 gmm), and the wide bracket needs 250-g forces (250 g × 4 mm = 1,000 gmm). The narrow bracket has twice the frictional force because the normal force is two times that of the wide bracket. Therefore, the wide bracket has less friction during phases II and III of space closure.

Smaller cross-section wires may have more clearance between the wire and the bracket and therefore may have an extended phase I (no friction). Also, these wires have lower wire stiffness and associated lower normal forces during other phases of canine retraction. But remember that the lowerfriction found in small round wires is not caused by the smaller contact area.

OCCLUSAL FORCES, VIBRATION, AND FRICTIONIt could be theorized that vibration in the mouth could relieve some frictional forces. This certainly is a commonly observed phenomenon in laboratory friction. Liew et al has shown a 60% to 85% reduction of frictional force using O-rings and round wire. O’Reilly et al also demonstrated a 19% to 85% friction reduction in both rectangular and round wires.

Different phenomena may operate to reduce the magnitude of friction. The horizontal component of occlusal forces can produce lateral tooth displacement that can loosen the ligature tie or O-ring. Thus, vibration or tooth displacement could be an important factor in eliminating the frictional force from the ligation mechanism.

The frictional forces produced in response to tipping during sliding of a tooth along an archwire are an entirely different phenomenon, because it is the elastically bent wire that produces the normal forces, not the force from ligation.

Occlusal forces may not relieve the friction unless the chewing force is placed in a direction to temporarily reduce the normal force between the wire and the bracket.

This suggests once again that friction from the ligation mechanism may not be as important as friction from tooth-moving forces—the forces from the elastically bent wires. One of the main advantages of a self-ligating bracket is that the ligation mechanism produces less normal force in the passive state of the wire. This advantage may be minimized because vibratory forces seem to be successful in reducing friction from conventional ligature ties or O-rings.

FRICTION AND ANATOMICAL VARIATIONPatients could have identical brackets, malocclusions, and wires and still not have the same frictional forces based on anatomical variation in root length and alveolar and periodontal support. only consider the translation phase during canine retraction for the four teeth. To translate the teeth, a force must be placed through theCR (yellow arrows). That force is usually replaced at the bracket level with a force and a couple (red arrows). The magnitude of this couple is the force times the distance from the bracket to the CR. Thus, the greater the M/F ratio, the higher are the vertical normal forces that create the frictional force.

The tooth in Fig- a is a typical tooth with average periodontal support as a reference. The CR is away from the bracket; therefore, a high M/F ratio at the bracket is required. This moment produces much friction, as discussed in this chapter. The teeth in Figs b and c have shorter roots, with their CRs closer to the bracket. Here, the M/F ratios are low with subsequent low frictional force. Root resorption (see Fig c) is certainly unwanted, but it does have the advantage of minimizing the friction produced at the level of the bracket. The tooth from an adult showing alveolar bone loss (Fig d) has the largest distance to the CR and would have the greatest friction during translation. Clinically, the tooth might not move so rapidly by translation, and we would be disappointed in the response. We might blame the poor response on the age of the patient and biologic factors, but perhaps the greater frictional force is the real culprit.

REDUCING FRICTION DURING SPACE CLOSURESpace can be closed using sliding mechanics even if there are frictional forces. The problem with friction is that it makes the force system more unpredictable. There are a number of approaches that can be employed to reduce frictional forces and make the force system more predictable.

We have already discussed bracket design and the use of wider brackets and lower ligation forces. Some cases do not require translation, and then tipping can be allowed. Tipping and suitable rotation such as distal-in canine rotation can require less friction, because less moment requires less frictional force. If the force is placed closer to the CR, it is not necessary for the archwire to produce the anti-tip and antirotation moments, and subsequent friction will be eliminated.

The applied force can be placed more apically by an extension arm or by an equivalent force system at the bracket from an additional wire or spring. Apical levers and lingual placement of the force can readily be utilized. The spring to store and release energy can be part of the canine retraction spring and its apical extension. To eliminate or minimize the friction from canine retraction, rotational forces from a chain elastic or a coil spring can be attached on the lingual surface of the canine (Fig 19-33).

If an auxiliary retraction spring or loop is used, activations can be placed to minimize tipping and rotation during canine retraction three-dimensionally so that the sliding archwire can deliver a smaller frictional force. An archwire is still present to give positive control with minimal friction (Fig 19-34).

En masse space closure requires sliding of the archwire at the posterior brackets. Because the mesial force is buccal to the CR of the posterior teeth, molars tend to rotate mesial in (Fig 19-35).

The use of a buccal archwire can barely prevent this side effect, and friction will be produced. Lingual or transpalatal arches can preserve arch form without producing friction from a wire observed in the occlusal view.Finally, space closure can be accomplished without sliding or friction mechanics by a so-called frictionless spring. In Fig 19-37, canine retraction springs were used. All needed anti-tip and antirotation moments are bent and twisted into the springs.No sliding on an archwire is required. With sliding mechanics, the required moments are obtained by perpendicular normal forces from the archwire inevitably producing friction. With frictionless springs, the same forces and moments may be required and are present, but because no sliding occurs, there is no friction.

FRICTION DURING INITIAL ALIGNMENT AND FINISHING

Frictional forces can be present and influence results at all stages of treatment from leveling to finishing.Two effects that occur with lighter alignment arches merit mention. Frictional forces produce a component of force that is parallel to the archwire.Sometimes this is good and other times bad. The positive effect of mesiodistal forces due to frictionis the opening of space for tooth alignment.

Many patients have moderate crowding, and an increase of arch length is desirable. If the wire is not free to slide, the wire will open space by pushing teeth laterally, causing an increase in arch length.It is a well-known principle that teeth cannot be aligned or rotated unless there is enough space for them. Because there are limitations in the ability of a main archwire to sufficiently increase arch length, auxiliary or secondary wires such as coil springs, intrusion arches, and bypass arches can be used to increase arch length. If there is adequate space, low friction in an archwire is desirable.

The negative effect of friction during leveling is that the wire may not be free to slide mesially or distally through the brackets; therefore, the desired buccal forces are not free to express themselves.

Longitudinal frictional forces prevent deactivation of the wire (Fig-a). Large lateral deflections of the wire that cannot be recovered to the original shape because of friction necessitate removal and reinsertion of the archwire. Friction at the canine and the first molar prevents the wire from fully deactivating (Fig-b). If full deactivation does not occur and the wire does not slide spontaneously, it can be removed and retied. Leaving a wire in place to deactivate it can open space and relieve the offending friction; however, these mesiodistal forces may not be efficient or wanted.

A reverse articulation of the maxillary lateral incisor is treated by a nickel-titanium (Ni-Ti) overlay wire (Fig). If the ligature is too tight, the Ni-Ti wire cannot fully deactivate. It is important to allow sliding at the tie (green arrows in Figs 19-41a to 19-41c). Note that the overlaid Ni-Ti wire has a hook on each side (blue arrows in Figs 19-41a to 19-41c) and that the elastics are activated with light force in the direction of the axis of the wire. The mesiodistal forces to the wire will thereby unlock the friction and will allow full labial force expression to the lateral incisor (Figs 19-41c and 19-41d). Another approach is to remove the Ni-Ti overlay and retie the ligature to eliminate the unwanted longitudinal forces.

Tying of archwires into irregular teeth can either increase the arch length or reduce the arch length, even when identical forces are applied, because of friction. To simplify this explanation, let us consider a cantilever force system with a single force delivered at the free end. Figure 19-42 shows an intrusion arch with a V-bend placed anterior to the molar tube.Its configuration after initial intrusion will also produce flaring of the incisors; however, let us not consider this effect. We could assume that the intrusion force is acting at the CR of the anterior teeth.

Because it is a cantilever, the location of the V-bend is not very important. It can be placed at many locations further anteriorly along the intrusion arch to produce identical intrusive forces; yet different configurations would produce varying amounts of horizontal force from the described friction effect during deactivation.

In Fig - a, it is assumed that the wire and the bracket do not have any friction. An occlusal activation force brings the intrusion arch to the level of the incisor brackets; the wire is allowed to freely slide through the molar tube so that the wire just touches the labial of the incisor brackets, exerting no horizontal force. After being tied to the incisors with a ligature, the wire will initially produce only an intrusive force; no labial or lingual (horizontal) forces are possible.

The nature of friction in orthodontics is multi-factorial, derived from both a multitude of mechanical or biological factors. Numerous variables have been assessed using a variety of model systems with nearly equally varying results

Variables affecting frictional resistance in orthodontic sliding mechanics include the following:1. Physical/mechanical factors such as:i) Archwire properties: a) material, b) cross sectional shape/size, c) surface texture, d) stiffness.ii) Bracket to archwire ligation: a) ligature wires, b) elastomerics, c) method of ligation.iii) Bracket properties: a) material, b) surface treatment, c) manufacturing process, d) slot width and depth, e) bracket design, f) bracket prescription (first-order/in-out; second-order/toe-in; third order/torque).iv) orthodontic appliances: a) interbracket distance, b) level of bracket slots between teeth, c) forces applied for retraction.

2. Biological factors such as:a) saliva, b) plaque, c) acquired pellicle, d) corrosion, e) food particles.

Effect of archwire on kinetic friction

Wire material: Most studies have found stainless steel wires to be associated with the least amount of friction. This is further backed up by specular reflectance studies which show that stainless steel wires have the smoothest surface, followed by Co-Cr, ß-Ti, and NiTi in order of increasing surface roughness.

SEM microphotographs of archwires (1000 times magnification): A, SS; B, NiTi; D,TMA.

Kusy & Whitney (1990) investigated the correlation between surface roughness & frictional characteristics. They found Stainless steel to have least coefficient of friction & the smoothest surface. However ß- titanium showed greater friction compared to Ni Ti , though the latter was rougher. Hence they concluded that surface roughness cannot be used as an indicator of frictional characteristics in sliding mechanics.

The reason why ß-titanium has a higher coefficient of friction than Ni-Ti is because of its higher titanium content (79W/W%), which results in increased adherence or cold welding of wire to bracket slot. Frank & Nikolai (1980) found that Stainless Steel had less friction than NiTi at nonbinding angulations but as angulation increased & binding was present, SS showed more friction.

Clinical considerationLarger, stiffer archwires are generally used during final stages of treatment when retaining the tooth position is the objective. The additional resistance to sliding (RS) between the bracket & archwire might further prevent movement of teeth.Loftus et al (AJO 1999) evaluated friction during sliding movement in various bracket-arch wire combinations. They reported that NiTi produced the least amount of frictions followed by SS & ß-Ti in increasing order. As the angulation (& hence binding) of the wire was increased, there was greater increase in frictional forces with SS than with NiTi. They suggested that the flexibility of NiTi may contribute to a decrease in the normal force at the points or contact between bracket & archwire.

Nishio et al (AJO-DO Jan 2004) performed an in vitro study to evaluate frictional forces between various archwires & ceramic brackets. They found that ß-titanium showed the highest frictional force, followed by NiTi & SS wires. They suggest that elastic properties of the wire are secondary & surface texture has more influence on frictional force. Zufall & Kusy (Angle Orthod. 2000) Studied the sliding mechanics of composite orthodontic archwires with a coating of polychloro-p-xylene. The coating eliminated the risk of glass release from the wire. Also frictional & binding coefficients were within the limits outlined by the conventional orthodontic wire-bracket couples.

Wire Size: Several studies have found an increase in wire size to be associated with increased bracket-wire friction. In general, at non-binding angulations, rectangular wires produce more friction than round wires. However, at binding angulations, the bracket slot can bite into the wire at one point, causing an indentation in the wire. However, with a rectangular wire, the force is distributed over a larger area ie. the facio-lingual dimension, resulting in less pressure & less resistance to movement. This may account for the finding of Frank & Nikolai that an 0.020” wire was associated with more friction than the .017 x .025” wire.

Wire stiffness & clearance: Mechanically speaking, orthodontic wires are elastic beams, supported at one or both ends. A force applied on such an elastic beam causes a deflection, which is reversible within elastic limit of the material. Stiffer wires are less springy & deflect less for a given force.Changing the diameter or the cross-sectional greatly changes the stiffness. Doubling the diameter of a wire increases the stiffness by a factor of 16, when supported at one end, & by a factor of 4, when supported between two brackets.Doubling the length of a cantilever beam decreases stiffness by a factor of 8.

During canine retraction in a premolar extraction case the increased inter-bracket span of unsupported wire over the extraction site decreases the stiffness of wire. Retraction force, therefore has a greater chance of deflecting the wire, resulting in buckling. To prevent such deflections, which may increase friction & chances of bracket binding, the diameter of wire should be increased to compensate for decrease in stiffness when interbracket span is greater than normal.

Yet another reason for not using flexible, small-size archwires during sliding canine retraction is that flexible archwires can deflect as the canine crown tips distally, which could result in incisor extusion. This situation can be axacerbated with the use of preadjusted canine brackets with a built-in distal root angulation.For rectangular wires, stiffness is also dependent on cross sectional dimension in the direction of bending. In other words an 017 x 022” wire is more springy in the vertical direction when it is placed edgewise rather than flatwise.

Drescher et al (AJO-DO 1989) stated that friction depends primarily on the vertical dimension of the wire. An 016” stainless steel round wire and an 016 x 022” stainless steel rectangular wire showed virtually the same amount of friction. This was however, lower than that for 018X025” wires. The authors state that for mesiodistal tooth movement, rectangular wire is preferred because of its additional feature of buccolingual root control.

As the stiffness of a beam is dependent on the support at both ends of the beam, during canine retraction, the premolar and lateral incisor brackets should be tied tightly to archwire. This will increase the stiffness of the wire as well as increase friction in the premolar bracket, thus minimizing anchorage loss.

An adequate clearance should be provided between the bracket and the wire to prevent binding. The clearance or play in the second order, i.e., tipping, depends on a combination of slot size, bracket width, and archwire size.

Third order play for rectangular wires in an 0.018 inch slot range between 16.7 for 0.016× 0.016 inch wire, to 4.5º for 0.017x0.025 inch wires. For the 0.022 inch slot, third order play ranges between 27.4º for the .016 × 0.022 inch wire to 2º for 0.0125×0.028 wire. Since rectangular wires produce significantly higher friction than round wires, the authors recommend the use of 0.018 inch wires in the 0.022 inch slot during space closure and canine retraction. The round wire results in less friction, and the 0.018 inch diameter provides adequate stiffness, reducing the buckling tendency of the wire.

Marques et al (Angle Orthod. 2010), investigated the debris, roughness and friction of stainless steel archwires following clinical study. S.S rectangular wires exposed to the intraoral environment for 8 weeks. They showed a significant increase in the degree of debris and surface roughness, causing an increase in friction between the wire and bracket during the mechanics of sliding.

SEM images (200×) showing debris on the wires. (A) Score 0. (B) Score 1. (C) Score 2. (D) Score 3.

EFFECTS OF BRACKET MATERIAL AND DESIGN ON KINETIC FRICTIONOrthodontists today have a multitude of options when it comes to selecting a bracket. In the edgewise design itself, there are choices in slot size, bracket width, number of wings, presciption in preadjusted designs, ligation capabilities, and bracket material. The most popular bracket material remains stainless steel; however, conventional cast S.S has met its competitor in the sintered variety.

Effect of Bracket on Frictiona. Bracket material : Angle used a gold prototype of edgewise brackets over 75 years ago. In 1933, Dr. Archie Brusse presented a table clinic on the first stainless steel appliance system. Since then SS brackets have displaced gold. Because they were stiffer & stronger, SS brackets could be made smaller, in effect increasing their esthetics via their reduced dimension. Their frictional characteristics were so satisfactory that they are today’s standard of the profession. However, conventional cast stainless steel has met its competitor in the sintered variety.

SINTERED STAINLESS STEEL BRACKETS :

Stainless steel, cobalt-chromium, nickel-titanium, and B-titanium archwires were ligated with elastomeric ligatures into sintered stainless steel brackets (Mini-Taurus, Rocky Mountain Orthodontics, Denver, CO); Miniature Twin (Unitek Corp, Monrovia, CA) and conventional stainless steel brackets. The friction of sintered stainless steel brackets was approximately 40% to 45% less than the friction of the conventional stainless steel brackets. The authors attribute this difference to differences in surface texture of the brackets, but they do not provide any evidence of this.

The technology of sintering, the process of fusing individual particles together after compacting them under heat & pressure allows each bracket to be premolded in a smooth streamlined manner. The SS particles are compressed in a contoured, smooth, rounded shape as opposed to the older casting procedure in which the milling or cutting process left sharp, angular brackets, which were bulky and rough.

Investigations comparing these two varieties with various archwire sizes at the Univ. of Oklahoma revealed that for most wire sizes, sintered stainless steel brackets produced significantly lower friction than cast SS brackets. (up to 38.44% less friction.) This difference in frictional forces could be attributed to smoother surface texture of sintered S.S material.

CERAMIC BRACKETSWith ceramic brackets, most of the wire size and alloy combinations with both 0.018 and 0.022 inch slot sizes demonstrated significantly higher frictional forces than with S.S brackets. This difference in friction between St.St and ceramic brackets may be attributed to characteristics of the ceramic bracket material or slot surface texture.Highly magnified views have revealed numerous generalized small indentations in the ceramic bracket slot, while the S.S bracket appeared relatively smooth.

Monocrystalline ceramic brackets are derived from large single crystals of alumina, which are milled into the desired shape and dimensions by ultrasonic cutting, diamond cutting, or a combination of both techniques.Polycrystalline ceramic brackets have also been observed under SEM to possess very rough surfaces, which actually scribed grooves into the archwires.

The monocrystalline allumina brackets were observed to be smoother than polycrystalline ones, but their frictional characteristics were comparable.The combination of metal archwires and ceramic brackets produce high magnitude of frictional forces; therefore, greater force is needed to move teeth with ceramic brackets compared with St.St brackets in sliding mechanics. Since ceramic brackets on anterior teeth are often used in combination with St.St brackets and tubes on the premolar and molar teeth, retracting canines along an archwire may result in greater loss of anchorage because of the higher frictional force associated with ceramic than steel brackets. Greater caution in preserving anchorage must be exerted in such situations.

Clinical significance: Since ceramic brackets on anterior teeth are often used in combination with stainless steel brackets and tubes on premolar and molar teeth, retracting canines along an archwire may result in greater loss of anchorage because of higher frictional force associated with ceramic than steel brackets. Greater caution in preserving anchorage must be exerted in such situation.

PLASTIC BRACKETS Plastic brackets first appeared in around 1970, and these were injection molded from an aromatic polymer called polycarbonate. These were meant to be esthetic but were subject to stains & odors. Moreover these plastic brackets deformed plastically under load & showed creep with time.

About 10 years passed before the first ceramic brackets were developed. In spite of their superior esthetics, their frictional properties are far inferior to stainless steel. Highly magnified views have revealed numerous generalized small indentations in the ceramic bracket slot, while S.S brackets appear relatively smooth. Single crystal ceramic brackets are derived by milling large single alumina crystals into the derived shape & size via ultrasonic or diamond cutting or a combination of these two processes. Polycrystalline ceramic brackets are sintered together using special binders to fuse the particles together. Laser speculance & SEM have shown monocrystalline brackets to be smoother than polycrystalline ones, but their frictional characteristics were comparable.

Zirconia brackets: • In order to overcome the problem of brittleness & low fracture resistance associated with ceramic brackets, Zirconia brackets were offered as an alternative. But these were found to have friction coefficients equal to or greater than ceramic brackets. They also showed surface changes consisting of wire debris and surface damage to brackets after sliding of arch wires.

SLOT MODIFICATIONS TO REDUCE FRICTION

Friction from the slot is especially a problem in case of ceramic and plastic brackets. To reduce friction some manufacturers have replaced the slot with metal usually stainless steel, titanium, gold and niobium (Figure 4.14)

Metal lined ceramic Brackets: • In the last few years, it has been recognized that ceramics have desirable esthetics but other materials have superior frictional characteristics. Consequently, as stainless steel and a gold liner have now been placed in a polycrystalline Alumina bracket. • These metal inserted products capitalize on the best of both worlds, namely, pleasing esthetics and competitive frictional characteristics, both in the presence & absence of saliva.

Frank & Nikolai (1980) found that frictional resistance increased in a NON LINEAR manner with increased bracket angulation. • Ogata et al (AJO DO 1994) also noted that as second order deflection increased, frictional resistance was found to increase for every bracket-wire combination evaluated by them. The friction increased appeared in 2 phases: • With lower deflections: - A smooth sliding phase appeared in which friction increased in an approximately linear manner. • As deflection increased further: A binding phase occurred in which friction increased at a higher, non-linear rate.

Clinical Significance: • For patients requiring maximum anchorage protection, complete leveling of the arch prior to using sliding mechanics is imperative. This will reduce the force required for retraction of the teeth because the frictional resistance will be decreased.

Articolo & Kusy (AJO-DO 1999) studied the resistance to sliding as a function of five angulations (0 , 3 , 7 , 11 , 13 ) using a different combinations, of SS, monocrystalline, or polycrystalline ceramic brackets against SS, NiTi or -Ti archwires. When the couples were in the passive configuration at low angulation, all stainless steel wire bracket couples had the least resistance to sliding. When angulation was >3 , active configuration emerged and binding quickly dominated, with RS increasing over 100 fold. • Under these conditions, couples of SS had the highest RS. While couples of the more compliant alloys such as NiTi had the least.

3 d) The role of third order torque: • When torque is applied to the wire, its projected size is larger than the actual size of the wire. This further decreases the clearance between the archwire & the bracket and contributes to frictional resistance to sliding.

Kusy (AJO-DO 2004) evaluated the onset of binding for 3 scenarios • Second order angulation alone. • Third order torque only. • Combination of second order angulation & third order torque. • He found that each wire-slot combination has a common maximum torque angle, independent of bracket width. He suggests that the use of a metric 0.5mm slot might have some advantages with regard to torquing. Wires can be used that apply lighter forces while maintaining angulation and torque capabilities, which were once possible only with larger wires.

•Greater interbracket width allows the

longer lengths of wire between brackets larger amounts of deflection, thus greater flexibility and more initial arch leveling.

•The effect of bracket width and interbracket width on friction appears unclear as indicated by Frank and Nikolai who found interbracket distance to have little effect on frictional resistance.

LIGATION: The fourth wall of Bracket slot

Wires once inserted into the slot should remain within the slot till next appointment. As the edgewise bracket slot has three fixed walls, so there is a fair chances that the wire will come out of the slot opening until or unless a mechanism is present that make up the fourth wall of the slot and prevent the wire from coming out. This fourth wall is traditionally been provided by ligatures.

Traditional wire ligatures were used to keep the wire within the slot. For many decades thin stainless steel wires were used as ligatures which provide durable, cheap and effective ligation. Though stainless steel ligature are stillused but due to increased chair side time which is on the average 11 minutes to tie these ligature, steel ligatures are taken over by elastic ligatures.

Elastic ligatures are mostly used in contemporary orthodontics for ligation of wire within the slot. Elastic ligatures though provide very good ligation at the time of insertion have a rapid force decay rate and almost half of the force is lost in the first 24 hours. They also get discolor with time so increases esthetic concern of the patients. To overcome these problems associated with steel and elastic ligatures self-ligating brackets were introduced. Though the history of self-ligating bracket is very old starting back to 1935 but they have only gained much popularity in the last decade .

Self-ligating brackets are available in all type of materials in which conventional brackets are available. Self-ligating brackets are of two types depending upon the type of ligation they provide.1. Active self-ligating brackets (Figure A).2. Passive self-ligating brackets (Figure B).Active self-ligating brackets are one in which ligating clip is occupying some of the slot space.This clip is flexible and caries some energy. While the passive self-ligating clip doesn't cover the slot space and is usually hard. So an active clip will push a rectangular wire into the slot and in some grossly displaced teeth round wire is also pushed in, while a passive clip will simply prevent the wire whether round or rectangular from coming out of the slot.

Too much have been written on self-ligating brackets and its proposed benefits in different orthodontic books. In following text only evidence based findings would be given.Oral hygiene A systematic review by Nascimento found no evidence of self-ligating brackets related to less formation of streptococcus mutans colonies as compared to conventional brackets. So claims by manufacturers that these brackets are more hygienic are not evidence based.Treatment time and initial painA systematic review by Celar found no evidence that self-ligating brackets are related with less initial pain, less number of visits and less treatment time than conventional brackets.

Friction resistanceEhsani in a systematic review concluded that self-ligating brackets show less friction resistance on round wires if used on well aligned arches but there is no evidence of decrease friction resistance on rectangular wires. A low level of evidence suggested that there is no clinically significant difference in terms of friction resistance between active and passive self-ligating brackets on SS wires.

Torque ExpressionArchambault found that active stainless steel self-ligating brackets show less wire play than passive self-ligating brackets. So there would be more torque expression from active self ligating brackets than passive self-ligating brackets.

CLINICAL NOTES

Steel ligatures though largely have been taken over by elastic ligatures are still used in cases where there is a need to express more torque i-e lower arch in growth modification cases, impacted canines and cases in which teeth are palatally or buccally displaced. Steel ligature are also a reliable mechanism of ligation in rotated teeth, piggy back mechanics and surgical cases. Steel ligatures are also used on teeth undergoing translation because if wisely ligated they offer less friction as compared to elastic ligatures.

Edwards et al (BJO 1995) compared the frictional forces produced when elastomeric modules were applied conventionally or in a “figure of –8” configuration, stainless steel ties or Teflon coated ligatures were used for archwire ligation. The “figure of 8” modules appeared to create the highest friction. There was no significant difference in mean frictional force between the conventional module and the St.St ligature, but the Teflon coated ligature had the lowest mean frictional force. Dowling et al (BJO 1998) investigated the frictional forces of differently colored modules & found the clear modules to exhibit significantly lower friction than other modules. This study however was carried out in absence of saliva.

Khambay et al (EJO 2004) compared the effect of elastomeric type and stainless steel ligation on frictional resistance and these were further compared with self ligating Damon II brackets. There was no consistent pattern in the mean frictional forces across the various combinations of wire size, type, and ligation method. The polymeric coated module did not produce the lowest mean frictional force. The introduction of a 45 bend into the module (Alastik Easy-to-use) reduced mean frictional force to that of a St.St ligature when using 19 x 25” SS wire. The use of metal ligatures with 7 turns produced the lowest friction confirming the findings of Bazakidon et al (AJO-DO 97). They concluded that the use of passive self ligating brackets is the only may of almost eliminating friction.

Thorstenson & Kusy (AJO 2002): investigated the RS for 3 self ligating brackets with passive slides (Activa, Damon & Twinlock) and 3 self ligating brackets with active clips (In-ovation, SPEED, Time), with second order angulation, in dry and saliva states. They reported that for second order angulations c, the RS of self ligating brackets is small to non-existent regardless of saliva state, thus facilitating siding mechanics, but compromising root position. The RS of brackets with active clips was higher being in range of 1247CN (dry state) and (22-54CN) wet State, respectively. • They reported that in the active state ( > c), the rate of binding is similar, regardless of presence of passive slide or active clip. • According to them “The desire to minimize the RS should be moderated by the necessity to control tooth

Henao & Kusy (Angle orthod. 2004) compared the frictional resistance of conventional & self ligating brackets using various archwire sized. They reported that self ligating brackets exhibited superior performance when coupled with smaller wires used in early stages of orthodontic treatment. However when larger 016 x 022” and 019 x 025” AW were tested, the differences between self ligating & conventional brackets were not so evident. This shows that self ligating brackets have the ability to maintain low frictional resistance only up to a certain size of archwire. It also emphasizes the importance of leveling and alignment before using larger wires & sliding mechanics.

Ion Implantation• Greenberg and Kusy coated orthodontic arch wires with a

polymer composite and a polytetrafluorethylene-based coating (Teflon, Dupont Co.) and preliminary results showed a reduction in the coefficients of friction. Unfortunately, the surface coatings tended to stain, peel off or crack on bending.

• As the titanium content of an alloy increases, its surface reactivity increases and the surface chemistry is a major influence on frictional behavior.12 Thus, -titanium, at 80% titanium, has a higher coefficient of friction than nickel-titanium at 50% titanium, and there is greater frictional resistance to sliding (“stick-slip” phenomena) with either than with steel.

• A solution to this is to alter the surface zone of the titanium wires by implantation of ions into the surface, thereby altering the surface chemistry.

• Implantation of boron or phosphorus into steel produce an amorphous, “glassy” structure on the surface of steel which is free from the grain boundaries of a steel surface and is impervious to pitting corrosion.

• Kusy and Andrews tested stainless steel, cobalt-chromium, nickel-titanium, and ß-titanium archwires against simulated brackets (stainless steel cylinders). In addition to control samples, the polished flats of these cylinders were implanted with N+, N+/Cr+, N+/C+, C+, Ti+/ C+, Ti+/N+, and Ti+ ions. Each arch wire was drawn in an Instron Universal Testing Machine, at 1 cm/min between flats of two cylinders at 34°C in saliva. The stainless steel control cylinders/brackets yielded lower μk values than ion implanted cylinders. This unexpected result may be because the optimal ion distributions for wear resistance were too penetrating for frictional reduction and in addition subjected to low stress, no wear regimes.

wet and dry environmentone would think that saliva acts as a lubricant, but unfortunately, the literature is divided with regards to saliva’s role in reducing friction between orthodontic wires and brackets. No differences were measured in friction levels between trials with saliva and those without saliva. When human saliva is present, frictional forces and coefficients may increase, decrease, or not change depending on the arch wire alloy tested. The greatest differences between dry and wet states occurred with ß-titanium (TMA) archwires, in which the kinetic coefficients of friction in the wet state were reduced to 50% of the values in the dry state. At this point they were comparable to nickel-titanium but still higher than stainless steel.

BIOLOGIC VARIABLES : SalivaIt is suggested that saliva or a saliva substitute serves as an excellent lubricant in the sliding of the bracket along the wire. Baker et al (AJO-DO 1987) using an artificial saliva substitute found a 15% to 19% reduction in friction. • Kusy et al (Angle Orthod 1991): found that saliva could have lubricous as well as adhesive behavior depending on which archwire-bracket combination was under consideration. Stainless steel wires showed an adhesive behavior with saliva & a resultant increase in the coefficient of friction in the wet state. The kinetic coefficients of friction of the -Ti archwire in the wet state were 50% of the values of the dry state. This probably occurred because saliva prevented the solid to solid contact between the -Ti archwires and SS brackets, & thus prevented the slipstick phenomenon from occurring. (The slip-stick phenomenon occurs when -Ti wire slides through SS brackets & the TiO2 layer breaks down, adheres & breaks away)

•Therefore, especially in adult patients, a

history of xerostomia or reduced salivary flow, oral radiation therapy, or anticholinergic medication should be noted as possible factors in varying the force levels necessary to more teeth.