___.Most of the studies dedicated to the friction encountered in othodontics focus on the couples metal-metal or metal-ceramic, hard bodies, and only few examine the friction existing between the soft elastomeric ligature and the arch wire. This is unfortunate, as the main culprit in high friction is the elastomeric ligature and the way it is tied. Other studies dealing with the friction stainless steel-polymer focus not on rubber or polyurethane elastomers but on.... Teflon^1,2.
___.A feeling of impotence regarding the possibility to understand the elastomer-ligated bracket pervades from Stoner’s article³:“Because of appliance inefficiency, sometimes applied force is dissipated by friction or improper application and it is difficult both to control and determine the amount of force that is being received by the individual tooth”. The same feeling is shared by Meling et al.⁴: “Ligation with elastomeric or stainless steel ligatures creates additional frictional forces, the significance of which is difficult to forecast as they depend on the material used”. Bazakidou et al.⁵, after showing that the highest frictional forces exhibited by the system elastomer/ stainless steel were 95.8g + 28.4 for the arch wire 0.016” x 0.022” and 83.7g + 17.8 for the 0.017” x 0.025”, noted that “For all brackets, there was no trend noted between mode of ligation and friction”.
Materials and methods
___.Several brackets were tested for the friction generated while a rectangular wire was made to slide through their slots. In some cases, while the wire and the elastomeric ligature were kept constant, the type of ligation differed. The instrument used was a simple coil spring deadened balance in which the friction bracket-ligature worked as a brake: the device was previously reported both as poster and articles^6,7. All the experiments were made in dry state.
___.Study of individual brackets. To relate bracket’s shape to friction, some characteristics of the brackets were taken in account. Among these were the tying perimeter of the elastomeric module stretched around the bracket and the angle formed above the wire by the stretched module. To obtain reliable results, it became necessary to avoid the influence of the gaps formed between the arch wire and the bracket slot, as these may lead to the entrapment of the elastomeric module. The deadened scale used to measure friction is shown in principle in Fig.1: detailing photographs are shown in Fig.2^6,7.
___.One of the objectives of this study was the influence of the angle a formed by the elastomer over the arch wire inserted in the bracket. Fig.3 shows its dependence of the distance of the bracket shape, and Fig.4 the dimension dictating its value, i.e. the distance between the upper edge of the arch wire found at the bottom of the slot and the highest point of the under-the-tie wing area. In this case, various stainless steel brackets were used along with the same couple elastomeric module-rectangular steel arch wire. Both were sold by American Orthodontics; the ligatures (Memory) were delivered as a die-cut chain, gray, short, code 854-253 and the wire was cut from a stainless steel arch (0.0215”x 0.028”). The active part of the scale was a calibrated coil spring that expands only above 100g (M-21 from Midwest Fastener Corp. Kalamazoo, MI). The spring, firmly attached at its upper end, had its lower end mobile and provided with a pointer and a hook. To the latter were attached weights added in a container weighing 100g (tare). During the tests, the straight, rec-tangular wire was ligated in various ways while made to slide through a bracket maintained at the same height. The pre-extension of the module was kept constant the at 1cm.
___.The zero point of the pointer was adjusted to the weight of the tare; as weights were added, the displacement of the pointer D (mm) vs. the force F (g) was recorded. The scale was calibrated first in the absence of any friction. When measuring the resistance opposed by non-ligated brackets, in order to keep the wire into the slot, the first was made to remain inserted by maintaining an angle no higher than 3^o to the vertical. Efforts were made all throughout to assure the verticality of the wire (with the help of a plumb bob). Indeed, both bracket angulation and wire tipping may alter the results. In addition, whenever a new weight was added, the bracket was slightly twisted or moved horizontally to allow the wire to slide at its maximum. In contrast, the bracket torque was easily accommodated by the spring. Prior to each reading, the weight container was balanced till the readings remained constant, in average for five minutes. Up to ten readings were made for each weight addition: the measurement error was maximum 7%.
___.An important source of measuring errors resides, in some cases, in the existence of a gap between the slot and the arch wire at its insertion point, as seen in Fig. 5: Fig. 6 shows an elastomeric ligature being dragged into this gap. To avoid the phenomenon and the resulting increase in friction, a contraption made of wire has been used to keep slightly apart the ligature from the gap, as seen in Fig. 7 and 8.
___.To relate the brackets shape to the friction F these oppose when ligated, several characteristics were measured. The perimeter of the under-the tie-wing area was measured directly, with the help of a caliper, while the angle a had to be measured indirectly. Formed above the wire by the stretched module, the angle was measured with a protractor on the image displayed on a screen, Fig. 9, which was previously photographed with a digital camera Nikon Coolpix 950. The variation of this angle can exceed the ratio 2:1, as show in Fig. 10.
___.In addition to measuring the friction caused by the standard circular (single under-the-tie wing peripheral) ligation, we measured also that caused by other types of ligations (crosswise, two superimposed circular ones, a combination of a crosswise and a circular one, as used by some practitioners). Such ligations, presented in Fig. 11, are commonly encountered and were recently reviewed by Faber⁷..
___.Before being tested, both brackets and arch wires were immersed in 50% isopropyl alcohol and dried to avoid the influence of undesirable impurities: the wires were made to slide several times through the ligated bracket while being intermittently rubbed with a cloth with alcohol. This was needed as the particles of elastomer left on the arch during the experiments were observed to increase friction to the point of rendering the measurement inconclusive. When the brackets were ligated and attached to their support, precautions were taken to avoid any interference of the clamping system with the module.
___.Quadrant testing. Series from upper central to second bicuspid brackets (Ormco Diamond, 0.022”, Level Arch prescription) were mounted on supports simulating the shape of half of a jaw. In a first attempt we used Sculpey, a mixture of clay- monomer (Polyform, Estes, Elk Grove Village, IL). After shaping and bonding the brackets using Phase II (Reliance, Itasca, IL), the whole was subjected to heat (250^oF for 30 min). After cooling, stainless steel rectangular wires were ligated in the mock quadrant, Fig. 12-14. The wires were Bonwill Hawley Standard Arch 0.0215” x 0.028” (Highland Metals) and straight 10” pieces 0.021” x 0.025” (G & H Wire Co., Greenwood, IN). In this experiment, the elastomeric modules used (both as chain and as isolated modules) were the same as in the previous experiments. As shown in Fig. 15, an end of the inserted wire was bent and used to hang a container in which water was continuously added from a large separating funnel (1cc=1g). Whenever a displacement of the wire of about 2mm was observed, the corresponding weight (F value) was recorded.
___.In a second experiment, the polymer-clay support was replaced with an adequately cut, common ceramic tile where the quadrant was bonded to its edge, Fig.16. This time, AlastiK^TM chain modules were used (3M Unitek Corp., Deep Black, Code 406-658) along the Bonwill Hawley Standard Arch 0.0215” x 0.028”.
Results
___.The variation of the wire’s hindered displacement it is a measure of the friction encountered. By using the same elastomeric modules and wires but varying brackets, it is possible to measure the influence on friction of the angle a, of the ligating mode, or of the tensile strength of the elastomeric module. In the diagrams which follow, on the ordinate are marked the weights in grams corresponding to the displacement D (mm) of the wire recorded on the abscissa. The friction (F) exhibited by a certain (ligated or non-ligated) bracket is given by the difference between the weight recorded for the bracket-caused deadened movement (F₂) and the one in the absence of any hindrance (F₁) The measurements, made on 5-10 samples, processed using the linear regression method, showed a correlation coefficient larger than 0.96, and a standard deviation lesser than 7%. The mean values obtained lead to almost parallel, straight lines.
___.Angle a. Several twin brackets having a larger ligating perimeter were tested in parallel with two single brackets having a smaller and approximately the same tying perimeter. The result can be seen in Fig. 17, where the values obtained for the twin brackets (shaded, interior area) are comprised between these of the single ones selected (shown in Fig. 10).
___.Ligature mode. Two brackets belonging to the Ormco Diamond series were successively ligated in various ways with American Orthodontics elastomeric modules and subjected to the friction test. The results are shown in Fig. 18 and 19. The friction caused by the various ligating modes is presented in Table 1.
___.Quadrant mode. The five selected brackets belonging to the same series were bonded to two substrates to simulate their position in the mouth. These bonded on the Sculpey polymer clay were successively tested with two types of rectangular wires and the American Orthodontics elastomer in two circular ligating modes (chain and isolated). The results are shown in Table II. The same brackets, bonded this time on the edge of a ceramic tile, were tested only with the arch and the 3M Unitek elastomer tied in the chain mode. The mean friction force recorded Fm was 1955g +117, i.e. in average 391g/bracket, i.e. higher than the average friction obtained in the first quadrant experiment (309g/bracket, from Table II, first raw) and significantly higher than those opposed by the upper central (40g) and the upper bicuspid (65g) when used alone and on the straight portion of the arch wire.
Discussion
___.All the tests was performed with the help of a simple and inexpensive but accurate device, a deadened coil spring scale the principle of which has been validated since R. Hooke’s (1635-1703) time. The related assembly and the procedure can be duplicated elsewhere, in contrast with the use of expensive universal testing machines type Instron.
___.Most previous works dedicated to the study of the sliding mechanism were focused on the loss of force occurring between the arch wire (made of stainless steel, beta titanium, Nitinol, etc.) and the bracket (made of stainless steel, polycarbonate, alumina or zirconia). While hard surfaces exhibit a relatively low coefficient of friction, well below 1, softer and especially rubbery materials exhibit, when in contact with the first ones, coefficients of friction as high as 4, as seen in Table III⁸ . In other words, the actual responsible for hindering the wire in its sliding is the elastomeric ligature.
___.Interestingly, the famous scientist Joseph (1733-1804) who described its first use, that of erasing pencil marks, coined the word “rubber” from the verb “to rub”, which is a translation of the Latin “frictio”.
___.The lack of published work in this field may be due to the discrepancies caused by several causes. The first is that microscopic particles of elastomer easily adhere to the wire: if not removed by rubbing, these can alter the results. The second is the entrapment of the elastomeric module into the gap formed at the insertion point of the wire into the slot. In most cases, these gaps are intentionally made by manufacturer to help arch wire insertion (chamfered slots). While when using a single ligature the module can be kept it from being caught with the help of a device, in all the other cases the entrapment is unavoidable. A related third reason is the use of elastomeric modules which have a rectangular instead of a circular cross section: due to their sharp edges, the first are by far more prone to be entrapped than the second.
___.Physics teaches that friction is proportional with the pressure exerted by a surface on another, in our case of the mo-dule on the wire. This pressure is proportional with the angle formed over the wire by the module, which is nothing but a measure of its intensity. To avoid the likely influence of the tension existing in the module, i.e. its degree of stretching, we have used brackets having a similar tying perimeter.
___.From the examination of the data presented, it becomes obvious that in order to offer less friction, brackets should be single instead of twins and exhibit a proper relation between their limiting dimensions (see Fig.4). In an experiment using single brackets having a similar tying perimeter, the high friction exhibited by some of these (CAT or Stage IV) was traced to the high value of a (Fig.17 and 10a), in sharp contrast with the low friction exhibited by the Ortho-Organizer single bicuspids (Fig. 17 and 10b).
___.The indiscriminate use of cross- or multiple ligatures can double the friction encountered when using the common single, circular ones. As shown in Fig. 18 and 19, these can actually double or even triple the friction harming the anchorage point. The relatively low values of the friction which were obtained only when using single, circular ties. The phenomenon is due to the use of the contraption shown in Fig 7 & 8 which prevents the entrapment of the modules in the gap formed at the insertion point of the wire into the slot. Similar experiments performed with the two elastomeric chains used, one weaker (“Memory” from American Orthodontics) and one stronger (“AlastiK” from Unitek) have shown a significantly increased friction generated by the last ones. As elastomers become weaker in time (ozone attack), older ligatures, as those which have a circular cross section, generate lower friction.
___.The testing of the two quadrants shows that when interconnected, brackets generate a significantly higher friction per unit than when alone, as these may not be perfectly in line, irrespective of the efforts to the contrary. A wire curvature such as the one exhibited by the Bonwill Hawley Standard arch increases with almost 1½ the friction generated by a similar, straight one.
Conclusion
___.The system resulting from the connection of a wire that slides through one or more brackets (which were fastened to adequate supports) to a weighed coiled spring is, in effect, a deadened scale. This simple system allows a do-it-yourself measurement of the friction encountered by the wire when tied with an elastomeric module to a bracket slot. If precautionary measures are taken, the system allows an evaluation of a variety of parameters influencing sliding. Among these measures are the need to remove the rubber particles which adhere to the wire and to prevent the module to be dragged in the chamfered slots purposely made to ease the arch wire insertion.
___.Sharp angles made by the ligature module while bending over the sliding wire are associated with high friction. Complex ligatures, such as the double or crosswise ones, oppose a resistance to sliding which may be the double or even the triple of the one encountered when a simple, circular tying is used. Weaker or older ligatures lead to lower friction, but also are easier to break.
___.Fastened to a support, interconnected brackets generate a significantly higher friction per unit than when alone as a result of their slight non-linearity and the wire’s curvatures (arches increase friction with almost 1½, when compared to the straight wires).

References
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