Table 1 Ideal properties of an endodontic sealer

Ideal Properties of an Endodontic Sealer

1. Viscosity which enables flow to apex, without extrusion, into lateral canals and dentinal tubules.
2. Mechanical and/or chemical adhesion to root dentine.
3. Mechanical and/or chemical adhesion to gutta-percha or other core material.
4. Particle size distribution to allow flow into lateral canals and tubules but not through apex.
5. Solvent available for easy removal.
6. Insoluble in tissue fluids.
7. Non-toxic.
8. Promotes hard tissue bridge formation.
9. No discolouration of tooth.
10. As radiopaque as the core material.
11. Bacteriostatic or bacteriocidal.
12. Dimensionally stable when set.
13. Minimum setting contraction or expansion.
14. Clinically satisfactory working and setting times.
15. Impervious to bacteria and bacterial toxins.

Restorative

The following rheological studies of restorative materials have been published recently

2010

1. Initial dynamic viscoelasticity change of composites during light curing. Kim MH, Min SH, Ferracane J, Lee IB.
Dent Mater. 2010 May;26(5):463-70. Epub 2010 Feb 18.

A custom-made oscillation rheometer with parallel plate geometry(gap=2mm, frequency 6Hz), measured the increasing viscoelasticity of six commercial restorative composites during light curing at 25C(n=5). The possibility of predicting shrinkage stress relative to the continuously changing shrinkage strain and elastic modulus is discussed. There were great differences in the development of viscoelasticity in each material and in the time taken to reach a particular reference value of complex modulus.


2. Slumping tendency and rheological properties of flowable composites.
Lee IB, Min SH, Kim SY, Ferracane J.
Dent Mater. 2010 May;26(5):443-8. Epub 2010 Feb 18.
Slumping was assessed by measurement of aspect ratios and the complex viscosity by an oscillatory shear test (angular frequency 0.1-100rad/s.

Results Flowable composites demonstrated shear thinning behaviour, resistance to slumping increased with increased complex viscosity and there was significant variation between the five flowable composites.

2009

1. Effect of heat on the flow of commercial composites.
da Costa J, McPharlin R, Hilton T, Ferracane J.
Am J Dent. 2009 Apr;22(2):92-6.
18 conventional resin composites and four flowable composites were
tested at room temperature (23C). The conventional composites were also
tested at 54C and 68C. Thickness/volume (T/V) were compared for the composites
for the three temperatures.
RESULTS: At 23C, the flowable composites T/V were significantly less
than the conventional composites (P < 0.001). The T/V of the conventional composites were not significantly different at all three temperatures (P> 0.05),



2. Rheological properties of experimental Bis-GMA/TEGDMA flowable resin composites
with various macrofiller/microfiller ratio.
Beun S, Bailly C, Dabin A, Vreven J, Devaux J, Leloup G.
Dent Mater. 2009 Feb;25(2):198-205. Epub 2008 Jul 14.

Steady state shear tests over range of 0-30 reciprocal seconds, with cone and plate geometry, diameter 35mm and angle 1 degree, measured viscosity and Newtonian behaviour of unfilled mixtures(n=3). Filled experimental composites were tested with ARES rheometer using parallel plate geometry, diameter 25mm and gap 1mm. Time sweep tests at 0.1 rad/sec followed by frequency sweep test from 100 rad/sec to 0.01 rad/sec measured complec viscosity, storage and loss modulus and tan delta.(n=3) . All tests were carried out at 23C
Results: all unfilled mixtures as well as pure Bis-GMA and pure TEGDMA are Newtonian. Viscosity and shear thinning increased with increasing filler content. These results were compared with spacial organisation of particles using TEM and suggest that modifying chemical and physical surface properties could improve flow and handling performance.

2008

1. Slumping resistance and viscoelasticity prior to setting of dental composites.
Lee I, Chang J, Ferracane J.
Dent Mater. 2008 Dec;24(12):1586-93. Epub 2008 Apr 22.

Dynamic oscillatory test using AR 2000 Rheometer, parallel plate, diameter 8mm, gap 2mm, frequency 0.1-50rad/s, temp 25C tested three commercial compositesand compared with slumping resistance
Slumping resistance index (SRI) varied significantly between the composites and was strongly related to loss modulus.

2. Rheological properties of veneer trial pastes relevant to clinical success.
Chadwick RG, McCabe JF, Carrick TE.
Br Dent J. 2008 Mar 22;204(6):E11. Epub 2008 Feb 15.
Carri-med Rheometer with cone and plate geometry, diamter 20mm, angle 2 degrees, gap 0.07mm tested three shades of three veneer pastes at 25C and 35C (n=3). In this study, the authors have chosen to use yield stress and shear rate index as the outcome measure parameters.
Results: Temperature effects were not shown to be significant for most materials. One material showed significantly greater yield stress, which could affect handling properties.


3. Rheological properties of flowable resin composites and pit and fissure sealants.
Beun S, Bailly C, Devaux J, Leloup G.
Dent Mater. 2008 Apr;24(4):548-55. Epub 2007 Jul 30.
Eight flowable resin composites were tested with ARES Rheometer , parallel plate geometry, gap 1mm, frequency 0.01-100 rad/s, at 23C. Complex viscosity, loss and storage moduli and loss tangent were recorded. Four pit and fissure sealants which are of lower viscosity were tested with cone and plate geometry diameter 50mm, angle 0.02 rad. and frequency 0.1-100 rad/s. The filler weight content was determined by thermogravimetric analysis (TGA) and the morphology of the particles was investigated by scanning-electron
microscopy (SEM).
Results: No correlation was found between the rheological properties and the
filler weight content or the particles' shape.

2007

1. Time-dependent visco-elastic creep and recovery of flowable composites.
Baroudi K, Silikas N, Watts DC.
Eur J Oral Sci. 2007 Dec;115(6):517-21.

Creep behaviour of flowable composites was evaluated in relation to their filler
fraction and the postcure period. Flowables that had the highest percentage of filler produced the lowest creep strain. The creep response decreased with 1 month of preload storage. Clinically, the finding of this study suggests that flowable composites are unsuitable for stress-bearing areas.

Endodontics

Subsequent to the studies reviewed in Table 2, the following recent studies have been published which report findings for flow of endodontic materials. Most of these have used the method described in ANSI/ISO specifications rather than rheological tests.

2010

1. Marin-Bauza GA, Rached-Junior FJ, Souza-Gabriel AE, Sousa-Neto MD, Miranda CE,
Silva-Sousa YT. Physicochemical properties of methacrylate resin-based root canal sealers.
J Endod. 2010 Sep;36(9):1531-6. Epub 2010 Jul 4.

2. Duarte MA, Ordinola-Zapata R, Bernardes RA, Bramante CM, Bernardineli N, Garcia
RB, de Moraes IG. Influence of calcium hydroxide association on the physical properties of AH Plus
J Endod. 2010 Jun;36(6):1048-51. Epub 2010 Mar 19.

3 Bernardes RA,de Amorim Campelo A,Junior DS, Pereira LO, Duarte MA, Moraes IG, Bramante CM. Evaluation of the flow rate of 3 endodontic sealers:Sealer 26, AH Plus,and MTA Obtura.
Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2010 Jan;109(1):e47-9.

2009

4. Camilleri J. Evaluation of selected properties of mineral trioxide aggregate sealer cement.
J Endod. 2009 Oct;35(10):1412-7.

5. Souza SF, Bombana AC, Francci C, Gonçalves F, Castellan C, Braga RR. Polymerization stress, flow and dentine bond strength of two resin-based root canal sealers.
Int Endod J. 2009 Oct;42(10):867-73.



6. D. Papadogiannis, R.S. Lakes, G. Palaghias, Y. Papadogiannis. Creep and dynamic viscoelastic behavior of endodontic fiber-reinforced composite posts.
Journal of Prosthodontic Research, Volume 53, Issue 4, October 2009, Pages 185-192
In this study, specimens were tested in a torsional creep apparatus and the shear modulus calculated. Dynamic viscoelastic measurements were taken at 21C, 37C and 50C in dry and wet conditions. The loss tangent and storage modulus were calculated

Prosthetics: tissue conditioners

Rheology articles have been published recently on tissue conditioners


2010

1. Viscoelastic behavior of commercially available tissue conditioners under
compression. Dent Mater J. 2010 Aug 7;29(4):461-8. Epub 2010 Jul 23. Saitoh S, Sasaki K, Nezu T, Taira M.

Parallel plate rheometer in compression mode measured hardness, compressive modulus of elasticity, relaxation rate, relaxation time, and modulus of viscosity of water-immersed and non-immersed samples.
Immersion in water increases hardness, compressive elasticity,relaxation time and modulus of viscosity while decreasing the relaxation rate. It is suggested that two of the materials would perform better as functional impression materials while the third would be best as a tissue conditioner.

Blogger comment: no experimental temperature reported for rheological tests.


2. Dynamic mechanical properties of oral mucosa: Comparison with polymeric soft denture liners Mechanical Behaviour of Biomedical Materials (2010) M-H Lacoste-Ferreab, Ph Demonta, J Danduranda, E Dantrasa, D Duranb, C Lacabannea

Porcine oral mucosa was tested in creep recovery and dynamic mechanical tests using parallel plate rheometer in compression mode. Hydrated and dried samples were tested at 37C (n=2)
Soft liners were tested with ARES strain controlled rheometer in torsion rectangular mode. Loss and storage moduli were recorded from –150C to 70 C(n=2)
Adsorbed water has a plasticization effect on the mechanical properties of oral mucosa. Soft liners demonstrate viscoelastic behaviour.

Prosthetics: impression materials

The following articles on impression materials are of interest. Items 2 and 3 are included in Table 2 in previous posting.

2008

1. Effect of temperature on rheological properties of dental interocclusal recording material. Pae A, Lee H, Kim H-S. Korea–Australia Rheology Journal 2008 20:4 221-226

This study used parallel plate geometry with gap size 0.5mm in oscillating mode. Storage modulus and tan delta were recorded at 21 C and 33 C, n=5.
Values of storage modulus were higher at 33 C than at 21C. There were significant differences in G and tan delta recorded for polyether and polyvinylsiloxene materials.



2. Determining the complex modulus of alginate irreversible hydrocolloid dental material. Dental Materials, Volume 24, Issue 11, November 2008, Pages 1545-1548. Shalinie King, Howard See, Graham Thomas, Michael Swain

A Micro-Fourier Rheometer using parallel plates with varying gap size to produce a squeeze effect gave values for loss and storage moduli at 23C. Because of the squeeze mechanism, the MFR can record moduli longer than the controlled stress rheometer beyond the clinical working timeand until the alginate is completely set.

Blogger comment : The material will be setting at mouth temperature clinically so do the results have clinical relevance?

3. Surface detail reproduction of elastomeric impression materials related to
rheological properties. Dent Mater. 2008 Jul;24(7):951-6. Epub 2007 Dec 27.
German MJ, Carrick TE, McCabe JF.

A controlled stress rheometer with cone and plate geometry, gap size 0.7mm measured viscosity and tan delta of materials at 23C every 30s until the amount of set at working time allowed no further measurements(n=5). Flow of the material was also recorded using a shark’s fin test. Hydrophilicity was tested in moist gypsum casts.
Tan delta most accurately reflected flow of materials, the higher tan delta giving most accurate impressions of large detail. For smaller detail, hydrophilicty has better effect on accuracy.

2007

Working time of elastomeric impression materials: relevance of rheological tests. Am J Dent. 2007 Dec;20(6):347-52. Balkenhol M, Kanehira M, Finger WJ, Wastmann B.

Phase angle and storage modulus measured and working time determined according to ISO 4823. Dimensional accuracy was measured at 30s intervals.
For most materials, impression accuracy was constant within the manufacturers' recommended working time whereas phase angle and storage modulus changed
significantly. When determined according to ISO 4823, working
time was longer than operator-assessed working time for all materials investigated.

Adhesion

Does rheology have an effect on adhesion? The following recent article is an interesting introduction



2010

International Journal of Adhesion and Adhesives 30(2010) 393-402
Determining the initial viscosity of 4 dentinal adhesives. Relationship with their penetration into tubuli.
Leforestier E, Darque-CerettiE, Peiti Ch, Bouchard P-O, Bolla M

A Reologica Stresstech Rheometer with Couette geometry for low viscosity material measured viscosity of three three adhesive systems at gap 0.1mm, shear rate of 0-5000 reciprocal seconds and constant temperature of 25C. Parallel plate geometry for a higher viscosity material measured the viscosity of the “dual” adhesive which polymerises in the absence of oxygen. The temperature in this case was varied from 10-37C
Result: The variation in viscosity affects the time for material to penetrate tubuli but at manufacturer’s recommended time of 20 seconds the viscosity effect is not an important decisive factor in its adhesion.

Ceramics

There are two recent rheological studies of dental ceramic materials which may be of interest.

2010

Rheological properties of concentrated aqueous fluorapatite suspensions. Albano MP, Garrido LB. 2010. Ceramics International 36 (2010) 1779-1786

Steady state flow was measured over shear range 0.5-542 reciprocal seconds using a concentric cylinder viscometer (Haake VT550,Germany). A yield stress was observed, followed by shear thinning behaviour. The effect of volume fraction on yield stress and limiting viscosity values was demonstrated and related to flocculation mechanism.


2009

Determination of the particle interactions, rheology and the surface roughness relationship for dental restorative ceramics.
Journal of the European Ceramic Society, Volume 29, Issue 14, November 2009, Pages 2959-2967 M. Kes, H. Polat, S. Kelesoglu, M. Polat, G. Aksoy

A commercial dental ceramic powder, IPS Empress 2 veneer powder, was tested as the raw material with slurries produced using different concentrations of electrolyte solutions of sodium chloride and calcium chloride. Apparatus was a Brookfield DV 111+ rheometer (with ULA adapter). Shear rate range was 0-140 reciprocal seconds. Temperature was not reported.
Dental ceramic slurries showed Newtonian behaviour when no electrolytes were present but non-Newtonian in the presence of electrolytes indicating respectively the absence or presence of flocculation. The effect on surface roughness and contact angle was also demonstrated.

Rheological studies of dental materials: prosthetic materials and dental cements

Introduction

The handling, working and setting times, adhesion, and stability of dental materials are dependant on their rheological properties. The values of these and their measurement are, in turn, affected by the temperature, humidity, the type of rheometer and the geometry of the measuring device[1]

Rheological parameters commonly in use in dental material science are viscosity, loss and storage modulus, the loss tangent, known as tan delta (tan δ), in shear stress and elastic modulus in elongational flow. Measurements of creep strain and creep recovery are recorded for creep.
The values of these can be modified for any particular material by the particle size distribution, powder:liquid ratio, particle shape, density, volume fraction and the use of additives[2,3]. These latter can be particular (e.g. superplasticisers) or liquid (surfactants). Also involved in these controlling parameters are particle deformability and particle/particle interaction (i.e. attraction or repulsion) [4]

Rheology is defined as the study of the deformation and flow of matter[5]
In rheological terms, materials are either Newtonian, where viscosity is not affected by shear stress, or non-Newtonian, where stress produces shear thinning (pseudoplastic) or shear thickening (dilatant) behaviour[2,5].
The terms psuedoplastic and dilatant, used in earlier studies, may be misleading and are no longer used. Most materials used in dentistry are non-Newtonian. Rheological behaviour is often classified into established models e.g Bingham, Crosse, which can be used to predict future behaviour of the material in differing conditions[1]. These models are used by theoretical rheologists, the building industry, food technologists and pharmaceutical industries[4]. They are used infrequently in dental studies.

Material category

The studies included in this review are of prosthetics materials and also various categories of dental cements. This review does not include endodontic materials, adhesives used in restorative dentistry, fluoride gels, fissure sealants, dental waxes or ceramics. These subjects form the basis of separate reviews.


Viscometer / rheometer type

The geometry and type of the measuring device is of great importance as these will have an effect on the measurement results[1]. The apparatus used in these studies range from two glass plates[6,-9], penetrometer[10-14], reciprocating rheometer[10,15-20,7], oscillating plates[21-44,11], capillary extrusion[6,45-51] , rotational spindle[52,53], ram and piston[14], cone and plate[54-74,24,47,48,27,43], parallel plates[71-73,75-80,17, 35,44], concentric cylinder[ 80,81,50,72], compression rheometer[6,82], cup and bob[81,], displacement rheometer[83-85,30], Instron Universal testing machine[72], creep measurement[83,86] and sinusoidal vibration[87,88]. Some studies use a shark fin method[89, 62], a laser/magnet apparatus[90,91], squeeze film technique[92] and an indenter apparatus[93]. Other methods described are a flow point test[94] , flexural vibration[95] , an amalgam condenser [96],a modified ADA test[97], a Gilmore needle with a Zwick1440 mechanical testing machine [98] and custom made capsule extrusion [99]

Temperature and humidity

The values of rheological measurements are affected by both temperature and humidity. In the prosthetic studies, ambient or working temperature varies from 10ºC to 30ºC. Mouth temperature varies between 32ºC and 37ºC and one early study of compo impression material was tested at temperatures of 45, 50 and 60º C. In most of the studies humidity is not stated but in three studies humidity was controlled at 50% RH [10,55,27] and in one humidity was controlled also at 15%[27].
The dental cements were tested for ambient or working temperatures of 5, 8, 18 (62º F), 22, 23, 25 and 26ºC. Mouth and higher temperatures quoted varied from 29ºC and 60 º C. Again humidity is usually not stated. In four studies [34,37,42,69], humidity was controlled at 50%. Four studies were controlled at 100% humidity [66-68, 86]. One study was controlled between 40 – 60% [96] while another was controlled at 90% [98]


Study design and statistical analysis

Very few studies adhere to the concept of hypothesis testing and in many studies it would appear that the sample size was one or not stated. However sample sizes of between 2 and 10 are reported. Statistical analysis was carried out in 49 of a total of 94 studies reviewed. Of these 43 showed some statistically significant results. However only 20 studies reported use of an experimental control, although some stated that the apparatus had been calibrated before the start of experiment.


Main findings of each material type

Impression materials

Rheometers quoted as suitable for measuring impression materials are reciprocating, capillary extrusion, oscillating, extrusion from disposable syringes and micro-fourier squeeze film. It is stated that the ideal setting property of an impression material is a long working time followed by a sharp set at mouth temperature. It has been found that the viscosity during setting is highly dependant on the temperature. Manufacturers’ working times have been rendered inaccurate by some of these studies and clinically relevant shear rates for syringe extrusion have been suggested. It is generally considered that tan delta is a suitable measure for setting characteristics of dental impression materials.

Acrylics and resins

Increased viscosity and therefore reduced doughing time is produced by increase in small particles and aesthetic fibres. Shear thickening and thixotropy have been demonstrated and light cured resins have higher viscosity than rubber based materials. Viscosity increases with time, temperature and rotational speed of the apparatus. There may be an induction time before a certain increase in viscosity is reached and this increase is an exponential function of time.


Soft linings/tissue conditioners

Significant difference in rheology of these materials has been found. Gelation can be controlled by presence of ethyl alcohol and polymer molecular weight. Particle size and molar volume also have effect. High values of tan delta and storage modulus improve masticatory function and in a study on dietary effects, corn oil and heptane produced a rapid reduced compliance.

Adhesives

The viscosity of denture adhesives is in the order of 1000000 poise and is affected by the rate of dilution of saliva.


Dental cements

Unset dental composites exhibit a yield stress and on setting are pseudoplastic (i.e. exhibit shear thinning behaviour) and shear dependant (i.e. non-Newtonian). However one study found that composites were dilatant (i.e. shear thickening) while setting. Polymerization rate of composites depends on constituent particle size. There is much discrepancy in the flow of different brands of composites and this affects their handling properties. As would be expected, flowable composites have greater flow but less mechanical strength and are unsuitable for stress bearing areas. Increased filler content increases viscosity and reduces creep strain.
Glass ionomers show power law behaviour and their viscosity may be associated with polymer cross-linking. Mixing glass ionomer orthodontic cements on a chilled slab increases their working time with no effect on the sharpness of set at mouth temperature. The effect of +-tartaric acid varies with concentration: at medium concentration it prolongs working time and sharpens set. Flow properties can be manipulated by cement formulation but also by the geometry of capsule design.
The viscosity of luting cements is shear rate dependant and dual cure setting greatly reduces the working time. The variation in yield stress of temporary pastes has an effect on their handling properties.
Viscosity of cements is affected more by temperature and geometry than shear rate. It is also affected by particle size distribution. Reduced viscosity and increased strength can be achieved by interparticle fillers.

Discussion

This review demonstrates that there has been extensive rheological studies of prosthetic materials and dental cements but there has been great variation in the aim of the studies, the geometry of the apparatus used and the experimental temperatures. With a few notable exceptions, the importance of humidity has not be known or considered. In some cases, this may be because it was felt that within the confined space of certain devices, humidity was not an important factor. The measurement of relative humidity as a percentage of the total humidity possible is however dependant on barometric pressure and height above sea level.
The actual measurement of humidity would be more accurate although the use of the term absolute humidity is no longer recommended.

Study design

For an experiment to be reproducible, the duration of these rheological tests should be stated, as this could vary across a particular range of shear and might give different results. In some studies, different shear rates are used for different materials, which means that the results for the different materials cannot be accurately compared.
Sometimes more than one rheometer or experimental geometry has been used because of the wide range of viscosity of the experimental materials or lengthy setting times. Most modern stress controlled rheometers have a very wide range, so this should no longer a problem. The amount of material required for each test varies from one device to another and can be a factor in choice of rheometer.
Some studies tested different materials at different temperatures, again rendering the results not accurately comparable.
In many of the studies, not all of the results of the reported experiments have been given, only some being quoted as representative. This leads to incompleteness of the data and reduced measurement quality.

Rheological studies are laboratory based and not clinical. In many of these studies, a clinical application or explanation is suggested. There is often a tendency for this to be subjective and not proven.

Table 3 Rheological studies of dental materials 1966-2008


Conclusion

Rheology is a very useful tool for the study of dental materials and has given much information about the intrinsic nature of materials, their properties and behaviour. Many of these excellent studies could be improved by reducing the number of variables, ensuring an adequate sample size followed by suitable statistical analysis and completeness of data reporting.


References

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Rheological studies of endodontic materials: 1. Theory and Basic Equations

Abstract


Rheology is important in endodontics as it affects the flow of materials within the canal, whether material will be extruded, and whether material will enter lateral canals and dentinal tubules. It is necessary to understand some rheological theory before relating it to the practice of endodontics. The purpose of this article is to outline the historical development of rheology, to define some rheological terms, describe various types of flow and the factors affecting flow. Measurement methods will be described and also the possible source of measurement errors. The basic equations commonly used in endodontic and other dental materials will be given with reference to endodontic and dental material literature.



Rheological studies of endodontic materials: 1. Theory and Basic Equations

Rheology is defined as the science of the deformation and flow of matter(1) .
It is of importance in endodontics as it relates to the flow of materials within the root canal system and along the root canal wall. It will have an effect on whether materials extend to the apical foramen without excessive extrusion, whether they flow into lateral canals and enter into the dentinal tubules.

Rheological terms
In the late 17th Century, the deformation of matter was defined by Hooke’s Law for solids and Newton’s Law for liquids.
Hooke’s Law states that “The power of any spring is in the same proportion with the tension thereof” i.e. the strain produced within a solid is proportional to the stress which is applied to it. The constant of proportionality for this law is the elastic modulus, “G”(2).
Newton’s Law for liquids states that “The resistance which arises from the lack of slipperiness of the parts of a liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another”(1). The property referred to here as slipperiness is now known as viscosity. In a Newtonian liquid therefore, the strain within the liquid is directly proportional to the applied stress. The constant of proportionality in this case is the viscosity, “η”.
We now know that there are also liquids, which do not follow Newton’s law and these are known as non-Newtonian fluids. We also know that some materials show a combination of behaviours. Materials can also be compressible, where the density can change, and incompressible, where the density does not change(3). These factors have an effect on the rheology. Under clinical conditions, endodontic materials are incompressible.

Types of flow
Shear flow occurs when the constituent particles or elements flow over or slide along each other.
Extensional (elongational) flow occurs when adjacent elements are pulled away from each other. When this occurs, some elements are also pulled towards each other(2).
If shear and elongation flow are both present in a non-Newtonian fluid, the effects of elongation flow will usually dominate(4).
Both of these flows can be :
Steady when the flow variables are no longer changing with time, as in steady laminar flow, which is flow without turbulence(1).
Dynamic or unsteady when the flow is irregular or intermittent as in start-up flow , end flow, creep and when the motion occurs in steps(3) .
Oscillating when the shear or extensional deformation is performed in, for example, a sinusoidal wave fashion(1).

Viscosity and Elasticity

Viscosity of a fluid is defined as the resistance to external deformation, which is a constant for Newtonian fluid at a given temperature or, for non-Newtonian fluids, depends on the flow rate.
Elasticity is the reversible behaviour of a solid after removal of external stress or strain. An ideal elastic substance will return to its “equilibrium state” when the stresses are removed(5) .
However, there is also viscoelastic behaviour for solids showing both viscosity and elasticity and elastico-viscosity for liquids showing both kinds of behaviour.

Linear and Non-Linear
Both Hooke’s Law for solids and Newton’s Law for liquids are linear laws in that there is direct proportionality between stress and strain (Hookes’ Law) or shear rate (Newton’s Law) within the materials (Fig 1).

Fig.1 An Example of Newtonian Flow (click on image to enlarge)

Viscoelasticity or elastoviscosity for these materials would also be linear.

Many materials however do not exhibit this kind of behaviour and a graph drawn of their stress versus strain would often appear curved. This behaviour would then be described as non-linear. One example of non-linear, non-Newtonian behaviour is shear thinning, where the viscosity reduces with increasing strain rate in steady flow i.e. it becomes easier to flow. Another less common occurrence is shear thickening, where there is increased viscosity with increasing strain rate, i.e. it becomes more difficult to flow (Fig 2).

Fig.2 Viscosity v Shear Rate




The terms pseudoplastic (shear thinning) and dilatant (shear thickening) were used previously but are now considered to be misleading, as they are not all-inclusive(6). This is because, for example, there is not always an increase in volume (dilatancy) when shear thickening is present. Most materials used in endodontics are fairly complex and would be expected to show non-linear, non-Newtonian behaviour.(Fig 3)

Fig 3 Shear thinning behaviour of an endodontic sealer






Thixotropy is a time-dependant decrease in apparent viscosity under constant shear stress or shear rate followed by a gradual recovery when the shear stress or shear rate is removed(1). It results from the structural breakdown of the material under stress6 . This may be an important property of some dental materials but many studies to demonstrate thixotropy show a varying stress and strain as well as time. The change cannot be attributed to time alone and a false positive for thixotropy is obtained(7). A more accurate representation of thixotropy could be shown by a graph of viscosity against time at a constant stress, which is then discontinued at time, t (Fig 4).

Fig.4 Thixotropy




The hysteresis loop demonstrates structural breakdown of a material, where stress and shear rate are varying(6)(Fig 5). The down curve shows that the material requires time to re-structure after the stress is discontinued, or is not rebuilding at all(6).

Fig.5 Hysteresis Loop





For many years, some fluids appeared to have a yield stress. It appeared that for some very shear thinning materials, there was no flow taking place at stresses below the yield stress(2). In fact now with modern controlled stress rheometers, very low rotation rates can be achieved and it has been demonstrated that some flow is actually taking place. However for some other materials there may be a low shear rate below which the materials may not appear to flow(6).
A Bingham body has the behaviour of a solid up to the yield stress after which it starts to flow and the rate of shear is directly proportional to the shear stress minus the yield stress (1,3). This property is important in some foods e.g spreading with a knife(3) and is also important when we want a dental material to remain static until instrumented .


Factors affecting flow.

All materials will show variation in flow with varying temperature and varying pressure(2). Increasing the temperature will enable constituent particles to move more rapidly relative to each other and so make the material flow more easily. A similar effect can be achieved by varying the particle size distribution of the material, by having the particles more spherical and by the addition of a superplasticiser to the continuous phase. The more concentrated the material or the greater its density the greater the viscosity and therefore there is reduction in flow.
Increasing pressure also produces reduced flow. Humidity, which affects atmospheric pressure, will also affect flow unless steps are taken to minimise this effect. Flow of materials is very much affected by the geometry of the container, measuring device or machinery surrounding the material.
It follows therefore that the flow of endodontic materials will be affected by the geometry of the delivery system, the geometry of the root canal and the physical conditions within the canal. Significant effects on the rheology of endodontic materials will be found also from their chemical composition, the molecular weight of macromolecules, their molecular weight distribution and the molecular architecture(3). There is a critical molecular weight for polymer entanglement and the effect on the rheology of polymeric materials alters above and below this value(3).

Measurement
Many viscometers are available for the measurement of viscosity(8), which are used as a scale for comparison with materials measured by the same apparatus at the same flow conditions. Some simple measurements can be made using flow cups and a viscosity-related measure given as the volume of material flowing through the flow cup for a specific time. However, flow between two plates, according to the requirements of EN ISO 6876:2002(9), is the method most recorded in endodontic studies(10,11,12,13,14,15,16).
Pressure can be exerted to a material within a capillary tube and the amount of material extruded in a specific time will give a value related to viscosity(17,18). The volumetric flow and velocity of a material under pressure will also give a value related to viscosity(19). These values will vary with varying angles of the flow cup or internal dimensions of the capillary so the specifics of geometry must always be quoted. The values will also vary with the temperature. Great care must be taken in comparing the results of studies using apparatus with different geometries or different temperatures.
Other geometries which could be used for measurement of material flow properties are rotating vane, ram and piston and concentric cylinders.
Controlled stress rheometers are now available which measure not only viscosity but also normal stresses, loss and storage moduli and tan delta . These rheometers can begin at very low stress and run for very long periods of time (e.g. until a material has set), and achieve very high levels of shear stress and shear rate depending on the viscosity of the material. The results are often given as the log value as the stress and shear rate may be of vastly differing magnitude. These rheometers are also temperature controlled.
In these controlled stress rheometers, the geometry may be cone and plate (Fig 6 ), parallel plate and re-entrant (reversed) cone and plate. Choice of instrument often depends on the particle size of the material, requiring a minimum gap size, and whether it is of high or low viscosity.

Fig.6 Cone and Plate Geometry



Note that only with cone and plate geometry is the applied shear stress the same throughout the entire testing sample, and results are therefore most accurate(20).

Other modern rheometers available are capillary rheometers and concentric cylinder rheometers. In the capillary rheometer, the stress within the material varies from zero at the centre to a maximum at the capillary wall. So a mathematical model has to be constructed for calculating viscosity. The stress varies also within concentric cylinders but if the gap is small enough, it can be assumed that the stress is uniform.

Experimental Sources of Error

Wall slip
When measuring particulate sample, very smooth internal walls of a capillary or the very smooth surface of a cone and plate apparatus can result in a thin, particle free layer of material at the surface or apparatus/material interface. This leads to increase in overall flow rate and subsequently to reduce the measurement reading of apparent viscosity. This error can be avoided by using a textured surface with certain roughness. In practical terms, this particle free layer may affect the flow and adhesion of endodontic materials at very smooth walls or gutta percha points.
Secondary flows
These may occur in a very dense material, when the density has a greater effect than viscosity on the flow. They result in readings which are higher than would be expected. In pipe or capillary flow, proper laminar flow does not occur until after a sufficient length has been traversed. At the entrance and exit, therefore, there may be exhibited transit flow behaviour, which would give false readings. Inertial effects depend on the density and velocity of a material and, if these are high, will cause turbulent flow, giving false readings for viscosity
Zero errors
Rheometers need to be properly set to zero by testing with a standard viscosity material, usually a Newtonian liquid. It is also advisable to calibrate them regularly with a standard Newtonian liquid.



Basic Equations used in endodontic and material studies




Viscosity (eta) is equal to shear stress (tau) divided by shear rate (gamma dot). Rheological studies, therefore, are involved with determining shear stress and shear rate to obtain a value of viscosity. For Newtonian fluids, viscosity is constant and independent of flow rate. For non-Newtonian materials, the viscosity is not constant(7).

In capillary flow, the shear stress at the capillary wall (τw) is given by




where ΔP is the change in pressure along the capillary wall, r is the capillary internal radius and L is the length of the capillary.

The shear rate at the capillary wall is given by



where Q is the volumetric flow rate and r is the capillary radius.

From the shear stress and shear rate at the capillary wall, the apparent viscosity (ηa) is calculated.



For non-Newtonian fluids, shear stress (τ-tau) is not a linear function of shear rate (ẙ-gamma dot) and for many of them, can be described by the power law



where k and n are constants.

From this power law shown above, the shear stress at the capillary wall (τw) is given by

  Therefore 

Plotting log τw versus ẙw gives a line with slope of “n”.

When n = 1, the material is Newtonian. If n>1, the material is shear thickening and if n<1>

For Newtonian materials    

For non-Newtonian materials, where n does not equal 1, Rabinowitch’s correction can be used (3,22). The true shear rate at the capillary wall is then given by

From equation above, apparent viscosity at capillary wall (ηa) is then given by







The equations above are also suitable for a capillary extrusion rheometer(17).

Similarly, the viscosity of material flow in a ram and cylinder extrusion viscometer with an exit tube can be given by



where α is the capillary radius and P is the pressure which is given by the force recorded divided by the ram area(23) .

In a rotational viscometer with spindle geometry, the shear stress may be calculated from the measured torque



where S is the shear stress, m is the torque, R is the spindle radius and h is the depth of immersion of the spindle. The slope of the log angular velocity of the spindle(omega) vs log shear stress (S) then gives the reciprocal of the power law exponent (n). As before if n=1 , the material is Newtonian , if n>1 it is shear thickening and if n<1>Flow through an orifice , for example a flow cup, or from a wide tube to a narrower tube, will give values for extensional or elongational viscosity (25) so that  



where lambda is the elongational viscosity, eta is the shear viscosity, P0 is the pressure drop through the orifice and ẙ is the shear rate which will depend on the flow rate and the radius of the orifice.

Phase Volume or Volume Fraction(phi), defined as the ratio of the particulate volume and the total volume of sample(1), affects the rheological properties of suspension fluids and relates to the zero-shear viscosity by



where k1 is a constant related to material density and k2 represents a crowding factor(26) .

Modern rheometers are programmed to readily give readings of rheological properties over a wide range of shear rate and temperature. These include shear and elongational viscosity, first and second normal forces, storage modulus, loss modulus, tan delta and torque. However these commercial rheometers are very expensive and where research funds are limited, the equations shown above will give adequate results from  laboratory based, custom-made apparatus as shown(Fig 7) (19).

Fig 7 A Custom-made Capillary Rheometer


Conclusion
Rheology is a difficult but fascinating subject. Dentistry can gain much from theoretical rheologists. Knowledge of dental rheology can guide formulation design of dental materials, improve their handling properties and their long term effectiveness. A subsequent article in this series will discuss further the experimental methods, the results and clinical applications of rheological studies of endodontic materials.



References

1. Barnes HA, Hutton JF, and Walters K (2001). 'Introduction to Rheology.' (Elsevier: Amsterdam.)
2. Barnes HA (2000). 'A Handbook of Elementary Rheology.' (University of Wales Institute of Non-Newtonian Fluid Mechanics: Aberystwyth, Wales.)
3. Morrison FA (2001) “Understanding Rheology” (OUP:Oxford)
4. Petrie CJS (1979) Elongational flows : aspects of the behaviour of model elasticoviscous fluids (Pitman:London)
5. Frederickson AG(1964) “Principles and Applications of Rheology” Prentice –Hall: New York
6. Tattersall GH and Banfill PFG(1983) “ The Rheology of Fresh Concrete” (Pitman Books Ltd:London)
7. Whorlow RW (1992) “Rheological techniques” Prentice-Hall:Gale
8. Barnes HA (2002). 'Viscosity.' (University of Wales, Institute of Non-Newtonian Fluid Mechanics, Aberystwyth: Aberystwyth,Wales.)
9. EN ISO 6876:2002 International Standard (2002) Dental root canal sealing materials.
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11. Ørstavik D (1982). Seating of gutta-percha points:effect of sealers with varying film thickness. Journal of Endodontics 8, 213-218.
12. Ørstavik, D. (1983). Physical properties of root canal sealers: measurement of flow, working time, and compressive strength. International Endodontic Journal 16, 99-107.
13. Siqueira, F. J., Jr., Fraga, R. C., and Garcia, P. F. (1995). Evaluation of sealing ability, pH and flow rate of three calcium hydroxide-based sealers. Endodontics and Dental Traumatology 11, 225-228.
14. Siqueira JF Jr, Favieri A, Gahyva SM, Moraes SR, Lima KC and Lopes HP (2000) Antimicrobial activity and flow rate of newer and established root canal sealers. Journal of Endodontics 26(5):274-7
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Rheological studies of endodontic materials: 2. Ideal properties and clinical applications.

A review of rheological studies of endodontic materials 1970-2008


Abstract

Rheology is studied extensively in the food and pharmaceutical industries, in construction, oil and manufacturing industries. It can lead to better understanding of the flow of endodontic materials and help in the development of new materials. Having considered the main points of rheological theory and some of their practical applications, the aim of this paper is to review the existing literature on the rheology of endodontic materials, with emphasis on geometry, temperature and humidity. Study design and statistical analysis will also be considered. The effect of rheology on the ideal properties of endodontic materials will be discussed followed by a review of specific rheological studies of endodontic materials. The main clinical and statistical findings will be reported. Some topics for further research are suggested as well as some rheology-related questions which still need to be addressed.


Introduction

Rheology as a subject was first introduced by Professor Eugene Bingham of Lafayette College, Indiana, USA. It is defined as the study of the flow and deformation of matter(1). The American Society of Rheology was founded in 1929 and the British Society of Rheology, founded in 1940, has members now whose scientific background is in mathematics, physics, engineering and physical chemistry(1). As well as purely scientific study, there are many practical applications of rheology in the fields of food technology, construction industry, pharmaceuticals, paints and printing, polymer processing, haemodynamics, Formula 1 motor racing lubricants and manufacturing engineering, to name just a few(1). The field is open now for advances in endodontic rheology.

In a previous article, an overview was given of the fundamental concepts and theory of rheology. In this article, the rheological properties of endodontic sealers will be discussed, with reference to relevant literature. Studies of the rheology of endodontic materials will be reviewed. Finally some suggestions are made for further studies.


Rheology and the properties of endodontic sealers

The required properties of an endodontic sealer, which might be considered ideal, are listed in Table 1. Several of them are related to rheology.

Table 1 Ideal Properties

1. Suitable viscosity
The sealer should have a viscosity which will enable it to flow to the apex without being extruded. If it is too viscous, it may not flow as far as the apex and if the viscosity is very low it may seep through the apex. The sealer should also flow into lateral canals and into dentinal tubules. The sealer viscosity, combined with pressure applied during insertion, will need to be great enough to overcome the resistance of residual material in lateral canals and the resistance of the interdentinal fluid. The optimum viscosity is as yet unknown.

2. Adhesion of the material to root dentine.
It has been shown that the debonding of soft polymer adhesive systems is related to their viscoelastic properties, in particular to the values of tan delta(2). Also known as the loss tangent , this is defined as the ratio of the loss modulus (liquid-like behaviour) to the storage modulus( solid-like behaviour) of viscolesatic behaviour as measured in oscillatory shear flow. These moduli are affected by the number of molecular entanglements or cross–linkings of polymeric material and by entanglement molecular weight(3). Further study on the effect of entanglement molecular weight on the values of tan delta may help to determine an optimum formulation for adhesive materials(2).
A study of a dentine adhesive system used in a standard peeling test found that bond fracture was related to the Young’s modulus (i.e. the ratio of extensional stress and extensional strain rate) of the test membrane(4).
Steady flow will ensure that the material flows continuously along the surface of the root dentine rather than intermittently and will give closer adaptation to the canal wall(5).

3. Adhesion to gutta percha or other core material
Adhesion to gutta percha or other core material will also depend on
rheology. Of some importance may be the smoothness of the surface of the gutta percha point, but this has not been tested as yet.
The effect of heat and length of time of heating on the adhesion of polysulphone material to glass fibres and steel wire has been studied. Maximum adhesion was found when there was still some plasticity rather than rididity of the interfacial layer, and this was related to the number of cross-linkings present. Above a certain point increased cross-linking produced more rigidity at the interface and reduced adhesion(6).

4. Particle size distribution
The size distribution of particles suspensed in the sealing material is an important factor in determining its rheological properties. As well as the viscosity, the maximum particle size relative to the size of the apical foramen , the size of lateral canals and the size and number of dentinal tubules per unit area will determine whether material will flow into these areas. Addition of silica fume of different particle sizes improved the rheological properties and wettability of certain adhesive systems. The viscosity and contact angle increase with increasing particle surface area. The addition of fumed silica also increased the peel strength of some adhesive joints(7).
Varying the powder:liquid ratio of sealers alters the volume fraction of the mixed material. It has been shown that increasing the powder:liquid ratio of ZnO/eugenol sealers decreases the flow (8,9). Concrete rheological literature also supports this finding(10).

11. Bacteriostatic or bacteriocidal
One study(11) suggested that antimicrobial activity may be related to flow rate of sealers while a later study showed that flow does not affect the bacteriocidal effect of sealers(12).


13. Minimum setting contraction or expansion
Shrinkage stress of light-cured dental resins has been found to be related to their viscosity and glass transition temperature(13).

14 Clinically satisfactory working and setting times
Rheology will affect the working and setting times of materials. and oscillating rheometry has for many years been the method to determine working and setting times(14). With modern stress controlled rheometers, analysis of loss and storage modulus may give a more accurate measure of working times. Various parameters can be used to determine setting time(15).



Studies of endodontic materials

While rheological studies of other dental and commercial materials are extensive, the literature on the rheology of endodontic materials is fairly limited (Table 2).

Table 2 Rheological Studies of Endodontic Materials 1970-2008


Various geometries are used and there is variation in temperatures, humidity and the time of experimental procedure. Often the stress or shear rate of the applied force to produce the flow of material is not specified or not applicable and in many of the studies viscosity is not calculated or measured (16,17,18,19).

One early study compared the flow of 10 sealers under vacuum in a capillary pipette(20). This geometry was chosen to simulate an ultrafine canal. Variation in flow was demonstrated for the sealers, which may be related to particle size. However one material (Klorperka) showed erratic behaviour probably due to the evaporation of chloroform under vacuum.
Another early study compared the flow of sealers on a vertical glass plate at two temperatures(21). However two levels of humidity were used in this study, so that accurate comparison of results from both temperatures is not possible.

Because viscosity is difficult to measure, viscosity-related measures are often used. ISO specification EN ISO 6876-2002(22) for endodontic sealers uses the measurement of the diameter of material flowing between two glass plates under a specified weight for a specified time. In this method, 0.05 ml of material is placed between glass plates 40 mm square and 5 mm thick, a weight of 100g is placed on top of the upper plate for 10 min and the diameter of the resultant compressed disc of sealer is measured. To comply with ISO 6876 this disc diameter should be not less than 20 mm. This method is described in several studies(23,14, 24-31,8).

Significant and non-significant variations in flow rate were demonstrated for different sealers. It was found that there was variation in restriction of seating of gutta percha points for different sealers(24). However a satisfactory recommended flow rate has not as yet been established(27) and clinical effectiveness depends on other factors as well as flow(26). Aged eugenol gives an improved flow rate which may affect adhesion(28) but this study also had variation in P:L ratio as well as age of eugenol, so again results for flow cannot be accurately compared.

A custom made capillary apparatus(8) gave viscosity related measures of volumetric flow and velocity for six sealers. It was found that the flow of sealers increased with increased applied strain and with reduced capillary internal diameter. This conforms with basic rheological behaviour for capillary or pipe flow(1). It was found that the effect of variation of P:L ratio varied with change in strain rate(8).

Capillary extrusion rheometers(16,18) (i.e. not flow within the capillary) have demonstrated that sealers are shear dependant but an ideal flow rate has not yet been determined. Extrusion through a bore(29) has shown that flow rates and working times were all similar for the tested sealers and they satisfied requirements of ISO specifications.

A rheometer with rotating spindle geometry(17) measured viscosity and showed that viscosity of sealers increases with time (because the material is setting) and decreases with increasing speed. An oscillating rheometer(14) showed variation in flow of sealers and was used to determine their working times.

Pressure and heat applied via a wire rod did not produce flow of gutta percha into lateral canals until a temperature of 47ºC is reached(32). A controlled stress rheometer, with cone and plate geometry(33) showed that increase in sealer viscosity produces increased intercanal pressure, which increases on cone insertion.

Using the ARES controlled stress cone and plate rheometer, the effect of temperature on the viscosity of sealers was investigated(19). It was found that most sealers had reduced viscosity with increased temperature and all sealers except Ketac-endo were shear thinning at 37ºC.

Temperature
ISO standard for flow of endodontic sealers does not specify a temperature for the procedure, but it is an important factor in determining and comparing flow in materials. In the studies reviewed, the authors based in Britain(8) and Sweden(14,24) have quoted 23ºC as ambient temperature, while those in US quote 25ºC(16,18). Where mouth temperature is quoted, it is always 37ºC and it is advisable that this should continue to be the experimental mouth temperature for future work in this area. It should be noted however, that in the rheological studies of other dental materials, such as impression materials, the experimental temperature used is often less than 37ºC, as it is felt that the material does not in fact reach body temperature.

Humidity
Humidity is often not considered in these studies, although it may affect the experimental results, and where it is, there is discrepancy in the humidity level reported. There is some debate as to whether relative or absolute or specific humidity should be used. It is felt now that relative humidity should not be used because of the variation caused by altitude and atmospheric pressure. The term absolute humidity has been discontinued.

Shear Rate
For some of these studies, shear rate is not applicable although it could be calculated from force of gravity, density of material and rate of movement of material on vertical glass plates. It could also be calculated using the applied force in the two plate experiment.
In other studies, using modern rheometers, which are stress controlled, the shear rate is known. However, there is variation in shear rate reported which makes accurate comparison of the studies difficult.

Viscosity
Many of these studies do not measure viscosity, using instead viscosity related measures as indicators of flow. However the newer stress and temperature controlled commercial rheometers give values of viscosity as well as other rheological parameters.

Sample size and control
These endodontic studies generally have adequate sample size and 8 out of 20 studies have used a control material. This is in good comparison to rheological studies of other dental materials, where many have a sample size of only one.

Statistical analysis
Earlier studies did not include a statistical analysis apart from one correlation study(14) but since 1995, most studies have had statistical analysis giving statistically significant results.

Future studies: in vitro and clinical
Many topics related to the flow of endodontic materials could be addressed in future studies.
1. Rheological characterisation of various endodontic materials.
2. Rheological studies using model systems which simulate clinical geometries and conditions
3. Clinical studies to test hypotheses of the effectiveness of materials in different flow categories: rate of insertion, force applied, surface geometry, preparation technique, intracanal conditions




Questions still to be addressed
1. We know that flow is affected by temperature. We need to determine how quickly sealers and other endodontic materials reach mouth temperature from ambient temperature.
2. How quickly is heat transferred via gutta percha points into sealer material in warm condensation and touch and heat techniques.
3. A quantitative study is required to determine the effect of change in humidity on the rheological properties of endodontic materials with reference to different types of rheometers, with different geometries. Does change in humidity have a significant effect on flow properties. A suitable level of humidity could be suggested for further studies.
4. For the study of the rheology of dental materials, it is necessary initially to use a wide range of shear and extensional stresses to understand the nature and behaviour of these materials. This is the rheometric characterisation of the material. On the other hand, to understand the clinical application of these materials and how their use is affected by their rheology, clinically relevant levels of shear need to be determined. How much force is applied, what is the rate of insertion, how do these change on moving from a syringe to a narrowing applicator or from insertion to lateral compaction. What is the effect of secondary flows and turbulence. Therefore, after rheometric characterisations , suitable model systems need to be developed to study the materials in clinical situations.
5. Viscosity is a very sensitive parameter and can range from very small e.g. 10000 to very large e.g. 1000000 so that log values are often used. It has been shown that it is affected by the shape of the measuring device i.e. its geometry and by temperature and humidity. Many studies do not calculate or measure viscosity. Future studies should attempt to give values of viscosity for endodontic materials at specific temperatures and in specific geometries. It would be useful if future studies adhered to temperatures of 25ºC and 37ºC.
6. Rheological properties also include elasticity, loss modulus, storage modulus and tan delta. These also affect the flow and are related to the working and setting times of the materials. These are not considered in the ISO specifications for endodontic sealers but could give a more accurate indication of when the material is changing from liquid-like behaviour to solid-like behaviour and how this affects their handling and sealing properties.
7. More work needs to be done on the flow of gutta percha points. The
temperatures achieved within the canal in warm condensation techniques should be studied.

Conclusion
It is necessary to distinguish between the rheometric characterisation of materials, with suggested clinical implications, and hypothesis based studies of rheological behaviour in clinical situations. More rheometric characterisation studies should be published to contribute to the literature on dental rheology and to inform further rheological study of endodontic materials in the clinical situation.



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