Copyright Eur J Oral Sci 2003 Eur J Oral Sci 2003; 111: 258–262 Printed in UK. All rights reserved European Journal of Oral Sciences ISSN 0909-8836 Human enamel dissolution in citric acid as a function of pH in the range 2.30 £ pH £ 6.30 – a nanoindentation study Michele E. Barbour1,2, David M. Parker3, Geoff C. Allen2, Klaus D. Jandt1,4 1 University of Bristol, Department of Oral and Dental Science, Biomedical Engineering and Biomaterials Science Section, Bristol, UK, 2 University of Bristol, Interface Analysis Center, Bristol, UK; 3GlaxoSmithKline, Consumer Healthcare, Coleford, UK; 4Institut f'r Materialwissenschaft und Werkstofftechnologie, Friedrich-SchillerUniversity Jena, Jena, Germany Barbour ME, Parker DM, Allen GC, Jandt KD. Human enamel dissolution in citric acid as a function of pH in the range 2.30 £ pH £ 6.30 – a nanoindentation study. Eur J Oral Sci 2003; 111: 258–262. Eur J Oral Sci, 2003 The objective of this study was to investigate the dissolution of human enamel in citric acid solutions over a wide range of pH. The in vitro conditions are considered to be relevant to soft drink-induced enamel erosion. Nanoindentation was used to investigate changes in the nanomechanical properties of polished enamel surfaces after exposure to citric acid solutions. Solutions used had 38.1 mmol l)1 citric acid and pH greater than 2.3 but less than 6.3 (2.30 6 pH 6 6.30). Samples were exposed to rapidly stirred, constant composition solutions for 120 s. Statistically significant changes in enamel hardness and reduced elastic modulus were observed after exposure to all solutions. There was an approximately linear dependence of enamel hardness on solution pH for 2.90 6 pH 6 6.30. Below pH 2.90, enamel is thought to have reached the lowest possible hardness value. The reduction in enamel dissolution caused by an increase in pH of a soft drink is likely to be small. Product modification to reduce the erosive potential of drinks may require additional methods such as addition of calcium salts. Soft drinks are well known to cause enamel erosion in situ and in vitro (1). Citric acid is the main acid in many fruit drinks and juices, with typical concentrations of 15–45 mmol l)1 (2), and is also present in confectionery (3). As a result, enamel dissolution in citric acid solutions has been the subject of many in vitro investigations (2, 4, 5, 6). Factors such as pH (2, 4, 5), exposure time (5) and degree of saturation with respect to hydroxyapatite (6) have been investigated. In contrast, citrate has been added to soft drinks to reduce the cariogenic potential of the drink (7), and has been shown to reduce the rate of enamel dissolution when compared to other organic ions at pH 3.5 in vitro (8). It has long been recognized that rate of enamel dissolution increases with decreasing pH for all acids. However, to the authors’ knowledge, no studies have been carried out to investigate thoroughly the dependence of enamel dissolution on pH over a wide range of pH values. This is particularly important in the case of citric acid. Citric acid is a tribasic carboxylic acid and causes enamel dissolution by reaction of hydroxyapatite with acid: Ca10(PO4)6(OH)2 + 2H+ 10Ca2+ + 6PO43– + 2H2O (9). The citrate ion is a chelating ligand, and forms a soluble complex with the calcium ion, promoting further dissolution (8). Chelation is not expected to occur at low Klaus D. Jandt, Institut f'r Materialwissenschaft und Werkstofftechnologie, Friedrich-SchillerUniversity Jena, L1bdergraben 32, D)07743 Jena, Germany Telefax: +49–36–41947732 E-mail: [email protected] Key words: atomic force microscopy; calcium; enamel; hardness; tooth erosion Accepted for publication February 2003 pH, but has been shown to cause an increase in enamel dissolution rate above pH 3.9 (2). The relationship between pH and enamel dissolution has been employed in the design of soft drinks with a reduced erosive potential (10). An increase in pH, often accompanied by addition of calcium and/or phosphate salts, has been shown to reduce the erosive potential of soft drinks in situ and in vitro (11–17). The addition of calcium and, to a lesser extent an increase in pH, however, are associated with a less appealing drink taste (10). A balance between good drink taste and reduced erosive potential is desirable. It is not clear whether the erosive potential of a soft drink could be reduced by a slight increase in pH, sufficiently small that it does not adversely affect the taste of the drink, without addition of the calcium and/or phosphate salts. Alternatively, addition of calcium and/or phosphate may prove sufficient to reduce the erosive potential and an increase in pH may be unnecessary. A study of the reduction in enamel dissolution rate afforded by a particular increase in pH of citric acid solutions is therefore desirable. Nanoindentation has recently been used to investigate enamel dissolution rate in situ (14) and in vitro (6). Nanoindentation is very sensitive to changes in the nanomechanical properties of the enamel surface, and has been shown to detect enamel softening due to 40 min Enamel dissolution and pH of exposure to orange juice in situ (14) and 120 s of exposure to citric acid (pH 3.30) in vitro (6). The aim of this study was to investigate the dependence of enamel dissolution rate on pH in citric acid over a wide pH range. The solution compositions and exposure times are considered to have strong relevance for soft drink related erosion (2, 18–21). The objective of this study was to use nanoindentation to determine the hardness and reduced elastic modulus of enamel surfaces after exposure to constant composition citric acid solutions with pH between 2.30 and 6.30. Material and methods Thirty erupted human molars were stored in tap water with thymol after removal of the roots and pulp. Enamel samples were cut from the buccal and lingual sides using a diamond saw. Samples were embedded in epoxy resin (Stycast; Hitek Electronic Materials, Scunthorpe, UK) and the natural surface was polished using 1200 grit silicon carbide paper and 0.25 lm aluminum oxide powder. Care was taken to remove only sufficient enamel to provide a surface large enough for analysis. This resulted in samples with an average area for exposure of 3–4 mm2. Samples were cleaned by ultrasonication in ethanol for 2–3 min before and after polishing. Sixteen solutions were prepared with 38.1 mmol l)1 (8.00 g l)1) citric acid monohydrate (Sigma-Aldrich, Poole, UK) and distilled water. The pH of the solutions was adjusted to values between 2.30 and 6.30 using NaOH as shown in Table 1. The pH was measured using a pH meter (HI 9321 Microprocessor pH meter; Hanna Instruments, Leighton Buzzard, UK) calibrated using standard calibration solutions at pH 4.01 and pH 7.01 (Fisher Scientific, Loughborough, UK). The accuracy of the pH detector was estimated by recording the pH of the calibration solutions between each measurement. The titratable acidity was determined by calculating the charge imbalance of each solution and subtracting the value from that for a solution with pH 7, hence calculating the moles of OH– necessary to Table 1 The pH and titratable acidity values of the citric acid solutions investigated in this study pH Titratable acidity mmol l)1 2.30 2.50 2.70 2.90 3.10 3.30 3.50 3.70 3.90 4.10 4.30 4.70 5.10 5.50 5.90 6.30 112 108 103 97.8 92.3 86.7 81.3 76.1 70.9 65.4 59.6 47.7 36.8 26.3 15.5 6.92 259 adjust the pH of each solution to 7. Titratable acidity is shown in Table 1. Charge imbalance was calculated using a computer program (22). Eight samples were assigned to each solution, and to a control group of samples, giving a total of 136 samples. Samples were randomly assigned to one of the solutions using random numbers generated using atmospheric noise (www.random.org). The control samples were not exposed to any solution prior to nanoindentation, and therefore represented the condition of the enamel before exposure to acid. Each other sample was exposed to 50 ml of the appropriate solution, stirred using a magnetic stirrer operated at 500 r.p.m., for 120 s. After exposure the sample was rinsed in running distilled water for 10 s to remove any citrate, calcium and phosphate ions and stop the dissolution process. Excess water was removed from the surface of the enamel by touching absorbent paper to the edge of the epoxy resin, without touching the enamel surface. The enamel samples were then allowed to dry thoroughly in air before analysis. The study was performed at room temperature, 24.2 ± 0.1C. Solutions were analysed chemically in order to demonstrate that the study was performed under constant composition conditions. Eight enamel samples were exposed to the solution at pH 2.30, which, with the lowest pH, was expected to cause the greatest enamel dissolution, for 120 s at 500 r.p.m. The initial and final pH of the citric acid solution was measured. The citric acid solution was analysed for phosphate content after exposure to enamel (23). The degree of saturation with respect to all phases of calcium phosphate of all solutions was initially zero as the solutions contained no calcium or phosphate. The maximum possible change in degree of saturation was estimated using a computer program (22). Nanoindentation was used to measure the hardness and reduced elastic modulus of the enamel samples, and was performed in air under ambient conditions. A Hysitron Triboscope nanoindenter (Hysitron, Minneapolis, MN, USA) on a Nanoscope IIIa atomic force microscope (AFM) (Digital Instruments, Santa Barbara, CA, USA) was used to perform nanoindentation. A Berkovich tip with a tip angle of 142 and a tip radius of approximately 100–200 nm was used. The enamel surface was imaged using the nanoindenter tip before each indentation to ensure that the surface was clean and free from damage. Each sample was indented five times in different areas. Hardness and reduced elastic modulus were calculated by the Hysitron software using the method of Oliver & Pharr (24). For each sample, five values of hardness and reduced elastic modulus were obtained. These values were not independent as they were obtained from a single sample. The mean of the five was therefore taken as a single value for each sample. Since the data were found not to be normally distributed, a Kruskal–Wallis test and box-whisker plots were used to identify statistically significant differences within the data at a 95% confidence level. Results The citric acid solution with an initial pH of 2.29 ± 0.01 had a final pH of 2.30 ± 0.01 after 120 s contact with an enamel sample. The accuracy of the pH detector was estimated to be ± 0.01 pH units. The phosphate content after 300 s contact with an enamel sample was below the minimum detection limit of the test and was estimated to 260 Barbour et al. 5 4 Hardness (GPa) hardness (P < 0.00001) and the reduced elastic modulus (P < 0.00001) of samples treated with different solutions and those of untreated enamel at a 95% confidence level. There was no statistically significant difference between the hardness of samples exposed to solutions with 2.30 6 pH 6 2.90. Above this pH there was a linear dependence of hardness on pH, as shown in Fig. 1 (H ¼ 1.08 · pH ) 2.78; R2 ¼ 0.99). There was an increase in reduced elastic modulus with pH for all solutions. The shape of the reduced elastic modulus graph was rather different from that of hardness, however, and fits well to a polynomial, as shown in Fig. 2 (Er ¼ )4.29 · (pH)2 + 50.8 · pH ) 54.0; R2 ¼ 0.93). Untreated enamel Linear fit for pH 3.1 – 6.3 R2 = 0.99 3 2 1 0 2 3 4 5 6 pH Fig. 1. Median hardness of enamel samples exposed to citric acid solutions with 2.30 < pH < 6.30. A linear fit to the data for 3.1 £ pH £ 6.3 is also shown. The triangular point represents the hardness for enamel samples not exposed to any solution. Reduced elastic modulus (GPa) 110 100 90 80 70 Untreated enamel 2nd order polynomial fit for pH 2.3 – 6.3 R2 = 0.97 60 50 40 30 2 3 4 5 6 pH Fig. 2. Median reduced elastic modulus of enamel samples exposed to solutions with 2.30 < pH < 6.30. A second-order polynomial fit to the data for 2.3 £ pH £ 6.3 is also shown. The triangular point represents the reduced elastic modulus for enamel samples not exposed to any solution. be 0 ± 2 lm l)1. The maximum possible change in degree of saturation with respect to hydroxyapatite, assuming approximately stoichiometric dissolution, was therefore £ 0.00005. The hardness (H) and reduced elastic modulus (Er) of untreated enamel were found to be 4.74 ± 0.14 GPa and 104.8 ± 2.8 GPa, respectively. Enamel hardness and reduced elastic modulus as a function of solution pH are shown in Figs 1 and 2. The 95% confidence intervals are indicated by error bars. Each point represents a total of 40 measurements with five measurements from each of eight samples. There was a statistically significant difference between both the Discussion Changes in enamel hardness and reduced elastic modulus as a result of exposure to citric acid solutions were investigated over the pH range 2.30 6 pH 6 6.30 using nanoindentation. Nanoindentation was used for this study because it is extremely sensitive to the early stages of enamel dissolution in situ (14) and in vitro (6). Using this technique it is therefore possible to distinguish enamel dissolution after short exposure times that have a high clinical relevance. The solutions used in this study had citric acid concentrations typical of soft drinks (2). There was no significant change in the pH or phosphate concentration of the solutions over the exposure time. The maximum possible change in degree of saturation with respect to hydroxyapatite was therefore less than 0.00005, which is not expected to cause any change in enamel dissolution (6, 25). The solutions can therefore be considered to have had constant compositions during the exposure time. The solutions were also highly undersaturated with respect to all other phases of calcium phosphate during the exposure time, and precipitation of these phases on the surface was therefore not thermodynamically favored. There is some disagreement in the literature with regard to baseline values of hardness and reduced elastic modulus of sound enamel. This may be explained by the recent demonstration that hardness and reduced elastic modulus of molar enamel vary from H < 3 GPa and Er < 70 GPa close to the enamel–dentin junction to H > 6 GPa and Er > 115 GPa close to the enamel surface (26). The baseline hardness and reduced elastic modulus of enamel found in this study were 4.74 ± 0.14 GPa and 104.8 ± 2.8 GPa, respectively. Although the information given in previous publications as to the types of teeth used is in some cases scarce, the value for hardness is in agreement with values reported for unerupted molars (6), incisors (27) and primary molars (28) but is higher than other values reported for unerupted molars (14), third molars (29), and molars (30). The value for reduced elastic modulus is in agreement with values reported for unerupted molars (6, 14), incisors (27) and molars (30) but is higher than other values reported for third molars (29), and primary molars (28). The values found in this study are thought Enamel dissolution and pH to be at the higher end of the scale because efforts were made to remove as little enamel as possible from the surface during the polishing procedure. The baseline values for the mechanical properties are therefore close to those for surface enamel. The plateau in hardness of samples exposed to solutions with 2.30 6 pH 6 2.90 seen in Fig. 1 is unlikely to indicate that these solutions do not differ in their erosive potential. It is suggested that there is a minimum possible value of the hardness of softened enamel. If the enamel structure is further weakened by continued exposure to dissolving solutions after this minimum hardness value has been reached, the softened enamel at the surface is removed. The underlying enamel is then exposed to the dissolving solution. As the dissolution proceeds, it is suggested that the hardness approaches a constant value, independent of exposure time, which corresponds to the minimum possible enamel hardness. A similar result was observed in a previous study (6) and also in a microhardness study of enamel dissolution (31). It is suggested, therefore, that the samples exposed to solutions with 2.30 6 pH 6 2.90 had the minimum value of enamel hardness before the net material loss that is observed under these experimental conditions. This assertion is supported by the reduced elastic modulus data. The reduced elastic modulus increased with increasing pH over the range 2.30 6 pH 6 2.90, indicating that there was a difference in the nanomechanical properties of the enamel surfaces exposed to these solutions. It has been shown in investigations of thin films that reduced elastic modulus is sensitive to underlying materials at greater depths than hardness (32, 33). Although these materials have different mechanical properties from enamel, the results may be applicable to the system, as there is a soft layer of enamel overlying hard, sound enamel. Hence, if the enamel close to the surface had the same mechanical properties but the thickness of the softened region was greater for solutions with lower pH, one could expect that the reduced elastic modulus was lower for solutions with lower pH. As the hardness is less sensitive to underlying material, one would expect to see a constant hardness in this region. This greater sensitivity of reduced elastic modulus to underlying material (32, 33) may also explain the difference between the shapes of the hardness and reduced elastic modulus graphs (Figs 1 and 2). An approximately linear dependence of enamel hardness on solution pH for pH values > 2.90 can be seen in Fig. 1. Some studies of the relationship between enamel material loss and pH have indicated a different relationship, including an exponential (5, 12) and other functions (4, 34), in citric and other acids. Comparison of these results is complicated, owing to the different experimental conditions and different parameters measured. The studies described above used exposure times of 30 min to 4 h, compared with the 120 s used in this study. The exposure time used in this study is considered to have a high clinical relevance, as it is comparable to the clearance time for citric acid in vivo (19–21). In addition, the stirring or agitation rate is 261 lower in some of the above studies than in the present study (5, 34), and is unknown in others (2, 4, 12); hence, diffusion of ions close to the enamel surface may play a greater role in these studies than in the present study. Some studies compared solutions with different acids and acid concentrations (12, 34), further complicating interpretation. Some in vitro studies of enamel dissolution have indicated that no enamel or hydroxyapatite dissolution can be detected above certain pH values in both citric and other acids. This pH is reported as 3.8 (34) and 4.4 (4) for enamel, and 5.5 (12) for hydroxyapatite. Other studies, however, indicate that dissolution takes place at pH 6 (35, 36) for enamel, pH 6.5 (37) for fluorapatite, and at pH 7 (38) for hydroxyapatite. All of these studies took place over prolonged exposure times compared with the study presented here. In some studies, pH was kept constant during the experiments (37, 38). This was not done in other studies (2, 4, 5, 12, 34). According to the solubility isotherm of calcium hydroxyapatite, dissolution is thermodynamically favored in the absence of calcium at pH values as high as 8 (39). In addition, chelation by the citrate ion is expected to cause additional dissolution above pH 3.9 (2). It is possible that lack of dissolution above a pH of approximately 4 observed in some previous studies results from the longer exposure times and lower agitation rates (2, 4, 34). Substantial calcium accumulation at the enamel surface or in the dissolving solution and an increase in pH may therefore have prevented or reduced enamel dissolution at these higher initial pH values. This problem is avoided in the present study, as the solution was rapidly stirred (500 r.p.m), had a constant composition, and the exposure time was short (120 s). In terms of soft drink modification, this study indicates that the reduction in enamel dissolution rate arising from a microbiologically and organoleptically acceptable increase in pH of a soft drink is likely to be small, at least in vitro. For example, a pH of 3.8 has been used in a experimental drink with substantially reduced erosive potential (13–17). This experimental soft drink also had an increased calcium concentration relative to typical soft drinks. The results presented here show that an increase from pH 3.30, a typical pH of a soft drink (18), to pH 3.80 would result in an increase in hardness of only about 15% over 120 s exposure, indicating a small reduction in erosive potential. It must be noted that the exposure times in this study are much shorter than the previous studies described (13–17). However, this demonstrates that the addition of calcium and the reduction in titratable acidity may have been largely responsible for the reduction in erosive potential of the experimental drink. This is supported by other studies which have demonstrated a marked reduction in enamel dissolution rate due to addition of calcium and phosphate to acidic solution (25, 40). Acknowledgments – M.E.B. and K.D.J. gratefully acknowledge GlaxoSmithKline for financial support in the form of a PhD studentship. M.E.B. thanks Peter Shellis and Keith Rose for stimulating discussion. 262 Barbour et al. References 1. Zero DT. Etiology of dental erosion – extrinsic factors. Eur J Oral Sci 1996; 104: 162–177. 2. West NX, Hughes JA, Addy M. The effect of pH on the erosion of dentine and enamel by dietary acids in vitro. J Oral Rehab 2001; 28: 860–864. 3. Lussi A, Portmann P, Burhop B. Erosion on abraded dental hard tissues by acid lozenges; an in situ study. Clin Oral Invest 1997; 1: 191. 4. Hughes JA, West NX, Parker DM, van den Braak MH, Addy M. Effects of pH and concentration of citric, malic and lactic acids on enamel, in vitro. J Dent 2000; 28: 147–152. 5. Eisenburger M, Addy M. Evaluation of pH and erosion time on demineralisation. Clin Oral Invest 2001; 5: 108–111. 6. Barbour ME, Parker DM, Jandt KD. Enamel dissolution as a function of solution degree of saturation with respect to hydroxyapatite: a nanoindentation study. J Colloid Interface Sci 2003 (in press.) 7. Duggal MS, Tahmassebi JF, Pollard MA. Effect of addition of 0.103% citrate to a blackcurrant drink on plaque pH in vivo. Caries Res 1995; 29: 75–79. 8. Koulourides TA, Buonocore MG. Effect of organic ions on solubility of enamel and dentin in acid buffers. J Dent Res 1961; 40: 578–593. 9. Dorozhkin SV. Surface reactions of apatite dissolution. J Colloid Interface Sci 1997; 191: 489–497. 10. Grenby TH. Lessening dental erosive potential by product modification. Eur J Oral Sci 1996; 104: 221–228. 11. Tanaka M, Kadoma Y. Comparative reduction of enamel demineralization by calcium and phosphate in vitro. Caries Res 2000; 34: 241–245. 12. Meurman JH, Harkonen M, Naveri H, Koskinen J, Torkko H, Rytomaa I, Jarvinen V, Turunen R. Experimental sports drinks with minimal dental erosion effect. Scand J Dent Res 1990; 98: 120–128. 13. Finke M, Jandt KD, Parker DM. The early stages of native enamel dissolution studied with atomic force microscopy. J Colloid Interface Sci 2000; 232: 156–164. 14. Finke M, Hughes JA, Parker DM, Jandt KD. Mechanical properties of in situ demineralised human enamel measured by AFM nanoindentation. Surf Sci 2001; 491: 456–467. 15. Hughes JA, West NX, Parker DM, Newcombe RG, Addy M. Development and evaluation of a low erosive blackcurrant juice drink in vitro and in situ 1. Comparison with orange juice. J Dent 1999; 27: 285–289. 16. West NX, Hughes JA, Parker DM, Newcombe RG, Addy M. Development and evaluation of a low erosive blackcurrant juice drink 2. Comparison with a conventional blackcurrant juice drink and orange juice. J Dent 1999; 27: 341–344. 17. Hughes JA, West NX, Parker DM, Newcombe RG, Addy M. Development and evaluation of a low erosive blackcurrant juice drink 3. Final drink and concentrate, formulae comparisons in situ and overview of the concept. J Dent 1999; 27: 345–350. 18. Feldman M, Barnett C. Relationships between the acidity and osmolality of popular beverages and reported postprandial heartburn. Gastroenterology 1995; 108: 125–131. 19. Bashir E, Lagerlof F. Effect of citric acid clearance on the saturation with respect to hydroxyapatite of saliva. Caries Res 1996; 30: 213–217. 20. Bashir E, Ekberg O, Lagerlof F. Salivary clearance of citric acid after an oral rinse. J Dent 1995; 23: 209–212. 21. Millward A, Shaw L, Harrington E, Smith AJ. Continuous monitoring of salivary flow rate and pH at the surface of the 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. dentition following consumption of acidic beverages. Caries Res 1997; 31: 44–49. Shellis RP. A microcomputer program to evaluate the saturation of complex solutions with respect to biominerals. Computer Appl Biol Sci 1988; 4: 373–379. Chen PS, Toribara TY, Warner H. Microdetermination of phosphorus. Anal Chem 1956; 28: 1756–1758. Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 1992; 7: 1564–1583. Margolis HC, Zhang YP, Lee CY, Kent RL jr, Moreno EC. Kinetics of enamel demineralisation in vitro. J Dent Res 1999; 78: 1326–1335. Cuy JL, Mann AB, Livi KJ, Teaford MF, Weihs TP. Nanoindentation mapping of the mechanical properties of human molar tooth enamel. Arch Oral Biol 2002; 47: 281–291. Fong H, Sarikaya M, White SN, Snead ML. Nanomechanical properties profiles across dentin–enamel junction of human incisor teeth. Mater Sci Eng C 2000; 7: 119–128. Mahoney E, Holt A, Swain M, Kilpatrick N. The hardness and modulus of elasticity of primary molar teeth: an ultramicroindentation study. J Dent 2000; 28: 589–594. Habelitz S, Marshall SJ, Marshall GW jr, Balooch M. Mechanical properties of human dental enamel on the nanometre scale. Arch Oral Biol 2001; 46: 173–183. Willems G, Celis JP, Lambrechts P, Braem M, Vanherle G. Hardness and Young’s modulus data determined by nanoindentation technique of filler particles of dental restorative materials compared with human enamel. J Biomed Mater Res 1993; 27: 757–755. Davidson CL, Hoekstra IS, Arends J. Microhardness of sound, decalcified and etched tooth enamel related to the calcium content. Caries Res 1974; 8: 135–144. Tsui TY, Pharr GM. Substrate effects on nanoindentation mechanical property measurement of soft films on hard substrates. J Mater Res 1999; 14: 292–301. Lim YY, Chaudri MM, Enomoto Y. Accurate determination of the mechanical properties of thin aluminium films deposited on sapphire flats using nanoindentation. J Mater Res 1999; 14: 2314–2327. Rytomaa I, Meurman JH, Koskinen J, Laakso T, Gharazi L, Turunen R. In vitro erosion of bovine enamel caused by acidic drinks and other foodstuffs. Scand J Dent Res 1988; 96: 324–333. Gray JA. Kinetics of the dissolution of human dental enamel in acid. J Dent Res 1961; 41: 633–645. Higuchi WI, Mir NA, Patel PR, Becker JW, Hufferren JJ. Quantitation of enamel demineralization mechanisms III. A critical examination of the hydroxyapatite model. J Dent Res 1969; 48: 396–409. Christoffersen J, Christoffersen MR, Johansen T. Kinetics of growth and dissolution of fluorapatite. J Crystal Growth 1996; 163: 295–303. Christoffersen J, Christoffersen MR, Kjaergaard N. The kinetics of dissolution of calcium hydroxyapatite in water at constant pH. J Crystal Growth 1978; 43: 501–511. Anderson P, Hector MP, Rampersand MA. Critical pH in resting and stimulated whole saliva in groups of children and adults. Int J Paediatric Dent 2001; 11: 266–273. Margolis HC, Moreno EC. Kinetics of hydroxyapatite dissolution in acetic, lactic and phosphoric acid solutions. Calcif Tissue Int 1992; 50: 137–143.
© Copyright 2026 Paperzz