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L050 2 u 8 | mo chIRCIDanDmpGS—p.“ This is to certify that the ‘ thesis entitled TEMPERATURE DEPENDENCY OF THE EQUILIBRIUM SORPTION ISOTHERM AND ITS'UTILITY IN SHELF LIFE SIMULATION OF A PACKAGED MOISTURE SENSITIVE PHARMACEUTICAL TABLET presented by Chong Hyun Lee has been accepted towards fulfillment of the requirements for M. S. ‘19?!” in Packaging 041W ack R. Giacin Major professor Date November 112 1987 07,539 _ MS U i: an Aflinnativc Action/Equal Opportunity Institution TEMPERATURE DEPENDENCY OF THE EQUILIBRIUM SORPTION ISOTHERM AND ITS UTILITY IN SHELF LIFE SIMULATION OF A PACKAGED MOISTURE SENSITIVE PHARMACEUTICAL TABLET BY Chong Hyun Lee A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1987 ABSTRACT TEMPERATURE DEPENDENCY OF THE EQUILIBRIUM SORPTION ISOTHERM AND ITS UTILITY IN SHELF LIFE SIMULATION OF A PACKAGED MOISTURE SENSITIVE PHARMACEUTICAL TABLET BY Chong Hyun Lee A modified B.E.T. equation was applied and was found to accurately predict the effect of temperature on the equilibrium sorption isotherm of a packaged moisture sensi- tive pharmaceutical product. The results of this study further demonstrated the utility of the interpolation model for describing the temperature dependency of the equilibrium isotherm and the application of this method of calculating the isotherm to a shelf life simulation model, by combining the moisture sorption characteristics of the product and the permeability of a package system at a required temperature, with the aid of a microcomputer. The agreement between experimental data and calculated results was considered to be well within acceptable limits. ACKNOWLEDGEMENT I wish to express warm thanks to Dr. Jack Giacin, my major professor, for his encouragement and comments. Re contributed much appreciated counsel and assistance in directing this study. Many thanks go also to the remaining members of my graduate committee, Dr. Bruce Harte and Dr. Charles Stein for their advice and assistance. Thanks are also due to Ruben J. Hernandez for his suggestions and assistance and the UpJohn Pharmaceutical Company for supplying packaging materials for this study. To my wife Kyung Ja, especial thanks for her continued patience, support and encouragement. Finally, I wish to express my affection and respect to my parents. Their love, financial support, and encouragement provided the motivation which made this achievement possible. TABLE OF CONTENTS LIST OF TABLES . . . . . LIST OF FIGURES . . . . . INTRODUCTION . . . . . LITERATURE REVIEW . . . . . DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE EFFECT OF page iii iv TEMPERATURE ON MOISTURE SORPTION ISOTHERM AND SHELF LIFE ESTIMATION . . . . MATERIALS AND METHODS . . . . Determination of initial moisture content Moisture sorption isotherm . . Water vapor permeability of package Conditions of actual storage testing at constant environment . . Conditions of actual storage testing at fluctuating environment . Prediction calculation . . . RESULTS AND DISCUSSION . . . . Initial moisture content . . Equilibrium moisture isotherm . Water vapor permeability of package Moisture content change simulation CONCLUSION . . . . . . APPENDIX I . . . . . . APPENDIX II . . . 27 35 35 36 39 41 42 43 45 45 46 56 59 69 70 71 APPENDIX III APPENDIX IV REFERENCES ii 72 76 94 LIST OF TABLES Table 4 page 1. Equilibrium relative humidities for saturated salt solutions . . . . . . . 38 2. Storage conditions and the corresponding time intervals . . . . . . . . 44 3. Initial moisture content of multivitamin tablets. 45 4. Equilibrium moisture content of tablets at 20.6 0C 52 5. Equilibrium moisture content of tablets at 30.0 °C 52 6. Experimental and calculated equilibrium moisture contents at 20.6 °c . . . . . . 53 7. Experimental and calculated equilibrium moisture contents at 30.0 0C . . . . . . 53 8. Net weight gain of packaged desiccant at 15.5 °C 56 9. Net weight gain of packaged desiccant at 22.0 °C 57 10. Net weight gain of packaged desiccant at 35.0 0C 57 11. WVTR and P of the package system at 15.5, 22.0 and 35.0 0C . . . . . . . . 60 12. Experimental and calculated results of storage test at 22.0 °c, 63.3 %RH . . . . . 62 13. Experimental and calculated moisture content values for the package system at fluctuating storage environments . . . . . . 65 iii LIST OF FIGURES Figure . page 1. A diagram outlining the simulation model for predicting shelf life . . . . . . 7 2. Cs versus temperature . . . . . . 49 3. B versus temperature . . . . . . 50 4. J versus temperature . . . . . . 51 5. Experimental isotherm data and calculated isotherm curve at 20.6 0C . . . . . 54 6. Experimental isotherm data and calculated °c. . . . . 55 isotherm curve at 30.0 7. Net weight gain of packaged desiccant at 15.5, 22.0, and 35.0 °C for the package system . . 58 8. Temperature effect on permeability constant (P) for the package system . . . . . 59 9. Experimental and calculated results of storage test for the package system at 22.0 0C, 63.3 %RH . 63 10. Experimental and calculated results of storage test for the package system at fluctuating storage environments . . . . . . . 66 iv INTRODUCTION The shelf life of a moisture-sensitive product can be estimated from knowledge of the products equilibrium sorp- tion isotherm curve, the initial and the permissible final moisture content of the product, the barrier properties of the package,' as well as the relative humidity and tempera- ture of the storage environment. The moisture sensitivity of the product, the relative humidity and temperature of storage and the products turnover period all contribute to determine the selection of the package system. To avoid unnecessary expense, it is wise to determine whether any of the packaging requirements can be met by simpler methods, such as a change in product formulation, air conditioning of the storage facilities, lowering of storage temperature, use of desiccants, quicker turnover or other suitable means (Heiss, 1958). The changes wrought by the influence of moisture may be of different kinds and can be caused either by an increase or decrease in moisture content of the product. The change can be the result of: (1) Physical processes, such as desiccation accompanied by hardening, or moisture adsorp- tion accompanied by caking, loss of texture and other undesirable consequences; (2) Physico—chemical processes, 2 such as crystallization from over-saturated melts, and formation of hydrates; (3) Microbiological processes: and (4) Chemical reactions, which may be divided into non- enzymatic, such as browning reactions or auto-oxidative changes, and enzymatic processes involving constituent enzymes, both phenomena being greatly dependent on moisture content. In general, all the changes listed above are time and temperature dependent. Among jointly occurring changes, that change is most important which leads at first to a noticeable quality deterioration. Although, with some products, loss of nutritive values or vitamin levels is also important (Heiss,1958). The shelf life of a moisture sensitive product in any type of package and storage environment can be estimated either by actual field tests or by calculation from thermo- dynamic equations and from empirical relations simulating the storage conditions. 0f the two methods, the field test is the more direct because only two assumptions need to be made; the first is that the storage location employed for the test is typical of the area which it purports to represent, and the second, that weather conditions during the test were normal for the time of year in that area. Because the storage life in a particular area is greatly influenced by the time of year in which the product is first placed in the region, the accumulation of shelf life data by actual field tests in all market areas for all 3 seasons becomes a very elaborate, expensive, and time consuming procedure. Shelf life data can be obtained much more readily by calculation from laboratory measurements of package performance plus weather data, provided that the assumptions made in developing the predicting model are correct. In estimating shelf life by calculation, the basic assumption made is that over the range of atmospheric conditions normally encountered, the rate of water vapor gain or lost by a packaged moisture sensitive product is proportional to the difference of water vapor pressure existing inside the package and in the atmosphere to which the package is exposed. This assumption has been discussed by Carson (1937) and by Halladay (1942), both of whom concluded that it holds under normal conditions, but not when the relative humidity is abnormally high (Felt, 1945). In describing a moisture sorption isotherm, one must specify the temperature at which the isotherm was obtained. Because of the nature of water binding, at constant water activity, moisture-sensitive products hold less water at higher temperatures than at a lower one. Thus, an impor- tant factor affecting the stability of moisture-sensitive products is water activity. The water activity, Aw, is defined as: % ERH Po Aw = -—-——- = 100 Ps ,(at constant temperature) [1] 4 Where Po is the vapor pressure in equilibrium with the product, Ps is the vapor pressure of pure water at a given temperature and ERH is the equilibrium relative humidity in contact with the product. Both chemical reaction rates and microbial activity are directly controlled by water activity (Scott, 1957: Labuza, 1970; Troller and Christian, 1978). Salwin (1959) and Labuza (1970) showed that most deteriorative reactions in food systems have the lowest rate at the Brunauer-Emmett-Teller (BET) monolayer (Brunauer et al., 1938), which usually corresponds to the 0.2-0.4 Aw range. An increase in Aw beyond this region can result in an increase in reaction rate, generally by a factor of 50-100% for each 0.1 Aw change (Labuza,1985). This change in products Aw can occur under two different conditions. First, if a product formulated at some stable initial Aw is packaged in a moisture permeable packaging material and held at high external humidity, the product will gain moisture from the atmosphere. The products Aw will increase, resulting in a decrease in shelf life. The second condition can occur when the product is packaged in an impermeable packaging material and then subjected to an upward temperature shift. In general, at a constant moisture level in the product, Aw increases with increasing temperature (Labuza, 1985). Although water vapor adsorption at higher temperatures is less than that at lower temperatures for a given 5 relative humidity, and the rate of water vapor permeation generally increases with an increase in temperature, reactions which contribute to a products keeping quality or shelf life at one temperature can become insignificant at a different temperature. For example, an enzymatic reaction becomes more dominant as the temperature is increased (Heiss, 1971). Ragnarsson and Labuza (1977) evaluated several parameters that affected accelerated shelf life studies and concluded that temperature was the most important parameter in those tests. During storage, the product in an impermeable package may be exposed for long periods to a temperature higher than the temperature at which it was packed. Thus, at a constant moisture content, the products Aw will increase with increasing temperature. Therefore, reactions that can lead to quality loss will increase in rate as a result of an increase in both Aw and temperature (Labuza,1984). For example, if Aw increases by 0.1, which doubles the rate of quality loss, and if a 10 oC shift has a Q10 effect of 4, then shelf life would be decreased by 2x4 or a factor of eight times. The Q10 factor is defined as: Rate at (T+10) Shelf life at T Q10 = = [2] Rate at T Shelf life at (T+10) where T is the temperature in oC. Therefore, it is impera- tive to determine moisture sorption isotherms for moisture 6 sensitive products at a minimum of two temperatures to determine the magnitude of the Aw shift (Labuza, 1984). The primary objectives of this study were to develop a mathematical model for describing the equilibrium moisture isotherm of a moisture sensitive pharmaceutical product as a function of temperature and moisture content, to establish the validity of the model developed and to apply this model to simulate the shelf life of a packaged moisture-sensitive pharmaceutical product. A computer program in BASIC language was developed. A diagram outlin- ing the approach developed is shown in Figure 1. A detailed discussion of the model and the assumptions made in developing the model are presented in the Section "Development of Mathematical Models for the Effect of Temp- erature on Moisture Sorption Isotherm and Shelf Life Estimation". Product Environmental Package Hygroscopicity ' Severity ' Effectiveness Experimental Environmental product and Data at Factors Packaging Material Various (Le. 96 RH, Characteristics Temperatures Temp ('C) (Le. Wt, Mo, P) L i J BET Expression at Each Temperature BETFParameters Expressed! ; ' a + * as a unct on of Temperature Shelf Life by Cubic Polynomial Expression [Expression] f ‘ J l l Predict Shelf Lliej F'GURE 1- A diagram outlining the Simulation Model Ior predicting shelf life. LITERATURE REVIEW Shelf life prediction based on mathematical modeling has been applied to packaged food products for nearly 40 years. Oswin (1945a, b, 1946) developed solutions for pre- diction of moisture transfer in a packaged product under steady state conditions of constant external temperature and humidity. Heiss (1958) discussed the relationship between the moisture sorption properties of foods, the package per- meability with respect to water vapor, and the shelf life of the product and developed a mathematical model describing the moisture change of a packaged moisture sensitive product for constant temperature and humidity. Work in this area was further carried out at the Massachusetts Institute of Technology (MIT) (Karel, Proctor & Wiseman, 1959; Karel & Labuza, 1969; Karel, 1967). The use of simple mathematical models and computer solution was introduced by this group to predict the chemical deterioration of food products caused by moisture and oxygen permeation and subsequent reactions with the product. Shelf life prediction with emphasis on physical deterioration due to the gain or loss of moisture to a critical value was most typical until the MIT studies were described. Karel and his co-workers modified Heiss's mathematical 8 9 models, introducing computer solutions to predict the relationship between deteriorative reactions in dehydrated cabbage and the product's moisture content (Mizrahi, Labuza & Karel, 1970) and simplified mathematical expressions to optimize flexible film packaging of food for storage (Labuza, Mizrahi & Karel, 1972). Other investigators have generated similar solutions for the prediction of moisture transfer during storage of both moisture sensitive foods and drug preparations (Veillard et al., 1979; Lockhart, 1980: Peppas & Khanna, 1980). All of these studies have employed concepts similar to those originally introduced by Oswin (1945a, b, 1946), Heiss (1958) and Karel, Proctor & Wiseman (1959), with the simulation model employing storage conditions of constant temperature and relative humidity. Mizrahi and Karel (1978) reported a method of evaluating a kinetic equation formulated from data obtained by monitoring the extent of nonenzymatic browning in dehydrated cabbage and the loss of ascorbic acid in tomato powder undergoing continuously changing moisture content and temperature. Mathematical models have been used in both the food and pharmaceutical sciences to describe how much faster a react- ion will go if the product is held at some other temperature, including high abuse temperatures, such as used in Accelera- ted Shelf Life Testing. If the temperature-accelerating factor is known, then extrapolation to lower temperatures, such as those found in distribution, could be used to pre- dict expected product shelf life (Labuza, 1982). 10 Solutions for moisture change prediction of packaged pharmaceutical products, during storage, have been developed over the past decade. Veillard et al. (1979) conducted moisture transfer tests in blister packages. Reamer et al. (1977, 1978)‘ compared the permeation characteristics of commercially available unit dose repackaging systems and proposed a procedure so that a pharmacist could evaluate the moisture permeation of any unit dose repackaging system. Nakabayashi et al. (1980 a,b,c, 1981 a,b,c) predicted both physical and chemical changes of tablets packaged in semi- permeable blister packages. Included in this work were pre- dictions of tablet hardness, chemical assay, color, dis- integration, and dissolution rates, as they relate to moisture change. Kentala et al. (1982) used a modeling approach to predict the moisture gained by tablets repackaged at the hospital pharmacy level. In their studies, the moisture content change was first estimated by an iteration procedure. By knowing the moisture content change, certain moisture content dependent characteristics were further calculated. As indicated by Labuza (1982), most reactions fit a zero- or first-order mathematical expression: dc n - a; = K(C) [3] Where C is the value of a certain characteristic of the product, n is the order of the reaction and K is the rate ll constant. Other reaction orders in addition to zero and first are possible, such as that found for vitamin C degradation in food package systems where oxygen is limiting (Singh et al., 1976). However, most quality change reactions can be fitted to either zero or first order. If the extent of degradation of the active ingredient in a product is directly related to its moisture content, the reaction rate could be described by: - - = KC M [4] where M is the moisture content and x is a constant (Carstensen, 1966). The effect of temperature on the reac- tion rate can be described by the Arrhenius equation, where the log of the rate constant is proportional to the inverse of the absolute temperature: K = Ko exp ( -Ea/RT ) [5] where: K a the rate constant, Ko = pre-exponential factor, Ea = activation energy, R - gas constant, and T a absolute temperature. From Equation [5], a plot of In K vs the reciprocal of absolute temperature gives a straight line, the slope of 12 which is the activation energy divided by the gas constant R. Thus, by studying a reaction and determining K at elevated temperature, one could then extrapolate to a lower temperature and predict the rate of the reaction at the desired lower temperature (Labuza, 1982). A model intended to predict moisture change of a pack- aged moisture sensitive dry tablet must describe two phenom- ena,transport of water vapor through the packaging material, and adsorption of water by the drug product. The permeation of water vapor through a polymeric film can be described by Fick's First and Second Laws of diffusion and Henry's Law of solubility, and depends on the permeant concentration gradient that exists across the film. Most of the early prediction models used relatively simple expressions for describing the transport of moisture through the package and onto the product. The absorption of water vapor by the drug product can be described by the equilibrium moisture isotherm. The concept of equilibrium moisture content (EMC) is important in the study of moisture change of packaged moisture sensitive pro- ducts and is an integral component of the simulation models developed for estimation of shelf life. The EMC is defined as the moisture content of a product after it has been expo- sed to a particular environment. The water activity of the product at various moisture contents and temperatures will determine whether this product will gain or loss moisture when exposed to a surrounding environment. The EMC of a 13 hygroscopic product is reached after the moisture content of the product has come to equilibrium with the moisture of the surrounding atmosphere. Plotting EMC versus equilibrium water activity (or % ERH) results in a sigmoidal type curve. This is the moisture sorption isotherm which is usually used to describe the water sorption or desorption character- istics of a product. A mathematical expression of the mois- ture sorption isotherm is necessary and is incorporated into the model for shelf life simulation of packaged moisture- sensitive products. Several commonly used isotherm models are listed below: (1) The B.E.T. equation (Brunauer et al., 1938) Aw 1 Aw (c-1) -———-—-— = ---—--- + w [6] (l-Aw)M Mm c Mm c A modification of the B.E.T. equation (Brunauer, 1945) n n+1 Mm C Aw 1-(n+l)Aw + nAw M = -—-——' T [7] n+1 (l - Aw) 1+(C-1)Aw - CAw Caurie et a1. (1976) rearranged the B.E.T. equation and proposed the following equation: 1 A 1 1 (l-Aw) (1-Aw)M Mm CMm Aw 14 The Caurie equation derived from the B.E.T. equation (Caurie, 1979) 2C/Mm 1 l l-Aw M CMm Aw (2) The Freundlich equation (Freundlich, 1926) l/n M = c Aw , n>1 [10] (3) The Halsey equation (Halsey, 1948) r -a Mm Aw = exp[ :1 [——-J [11] RT) M (4) Linear equation (Chirife, 1978) M a + b Aw [12] (5) The Langmuir equation (Langmuir, 1918) K1 K2 Aw M a [13] 1 + K2 Aw (6) The Mizrahi equation (Mizrahi et al., 1970a) a + M Aw = -————-- [14] b + M (7) The Oswin equation (Oswin, 1946) n Aw M = a[. J [15] l-Aw 15 (8) The Caurie equation (Caurie, 1970) ln W = ln a - b Aw [16] 100 - % water where w = water concentration = % water Where a, b, c, K1, K2, n and r are constants, R is the gas constant, T is the absolute temperature and Mm is the mono- layer moisture content. Further, a number of theoretical, semi-theoretical and empirical models have been proposed to describe the effect of temperature on water sorption isotherm behavior. Several mathematical equations have been formulated for describing the effect of temperature on sorption isotherms. They can be classified into the following two general appro- aches. One is based on assumed physical mechanisms such as molecular adsorption or capillary absorption or the combina- tion of the two to devise the models. Such kinetic or statistical models, borrowed from physical chemistry or physics, contribute substantially to the understanding of factors affecting a products hygroscopicity. However, the development of an adequate kinetic description of the pheno- mena often requires more detailed information than is avail- able or readily obtainable. For heterogeneous biological products, no single kinetic model has been found satisfac- tory. The other approach is based on either thermodynamic equations or empirical equations. The latter method offers 16 additional insight into the problem in question and usually provides a simple working equation .for engineering use (Chen, 1971). Several equations for describing the temperature depen- dency of the sorption isotherm are listed below: (1) The Henderson equation (1952): The empirical equation may be written as, n 1 - Aw = exp[-( kM )] [17] This equation may be rearranged to give; 1n [-ln(l-Aw)] = n In M + In R [18] From Equation [18], a plot of 1n[-ln(1-Aw)] versus the amount of water sorbed should give a straight line. However, Rockland (1969) observed that two or three 'localized isotherms' may be distinguished when the experimental sorption data are plotted according to Equation [18]. Thus, for curve fitting purposes, the utility of Henderson's equation would be severely restricted if two or more pairs of constants were needed to define the sorption isotherm. Singh & tha (1974) applied the Henderson equation to desorption equilibrium moisture curves of groundnut and chillies at various temperatures. They used Henderson's original expression which included a temperature term, n 1n(1-Aw) = kTM [19] 17 and determined the constants K and n from the experimental data at different temperatures. Singh & tha (1974) concluded that Henderson's equation correctly describes the temperature dependency of the exper- imental isotherms. (2) The Day and Nelson equation (Day and Nelson, 1965) Day & Nelson (1965) observed that the T term in Henderson's equation does not eliminate the temperature dependence of constants k and n. They omitted the term T and related the constants k and n to an empirical power function of temperature. The proposed four-parameter equation is: ln(l-Aw) = -k1 T 1M 2 [20] Chen & Clayton (1971) tested the applicability of this equation to describe the temperature dependency of corn desorption isotherms over a wide temperature range. (3) The Chung & Pfost equation (Chung & Pfost, 1967) Chung & Pfost (1967) proposed a model of the form, a 1n Aw = - -— exp(-bM) [21] RT This model is based directly upon an assumption regard- ing the manner in which the free energy change for sorption is related to moisture content. This equation cannot be 18 used to predict the effect of temperature, since the use of the temperature term (T) does not eliminate the temperature dependence of parameters a and b (Agrawal et al., 1969: Nellist & Hughes, 1973). (4) The Chen & Clayton equation (Chen & Clayton ,1971) Chen & Clayton (1971) modified Chen's equation (Chen, 1971) and proposed a four-parameter equation for relating temperature, water activity and moisture content. The proposed equation is: n n In Aw = - k1 T $xp(-k2 T 2M) [22] The authors found that the proposed equation described adequately the temperature dependency of corn isotherms between 4.4 and 60 oC. (5) The Halsey modified equation (Iglesias & Chirife, 1976a) Iglesias & Chirife (1976a) empirically modified Halsey's equation. They proposed a three-parameter equation, n In Aw = - exp[(k1 T + k2)M ] [23] and found that it may be used to predict reasonably well the effect of temperature on water sorption isotherms of some food materials. Among the foods tested were, chicken, corn, fish protein concentrate, laurel, nutmeg, thyme and wheat flour. They stated that the merits of this equation should 19 be judged, Considering that it is simpler than the usual four-parameter equations reported in the literature to characterize the effect of temperature on the isotherms (see Day & Nelson (1965), and Chen & Clayton(197l)). Where a, b, k k h, k, and n are constants, M = moisture 1' 2' content dry basis, R a gas constant and T = absolute temp- erature. Usually most sorption behavior can be adequately described by one or more of the isotherm models. Reviews of these models have been reported by Labuza (1968, 1975), Boquet et al. (1978), Chirife et a1. (1978) and Vanden Berg and Bruin (1981). Labuza (1968), Loncin (1980) and Iglesias and Chirife (1976b) have shown that the Clausius-Clapeyron equation can be applied to predict the isotherm Aw value at any tempera- ture, if the corresponding heat of sorption is known at constant moisture content. The equation is: Al Os 1 l (6) ln—=—[—-—] [24] A2 R T1 T2 Where A1, A2 are water activities at absolute temperature T1 and T2: R = gas constant (1.987 cal/mole K): Qs = excess heat of sorption (cal/mole). To determine Qs, the sorption isotherm must be measured at a minimum of two temperatures. However, additional temperatures in the range of study will give a better estimate. This is because several assumptions are made in applying the Clausius-Clapeyron equation. 20 First, the heat of vaporization of pure water (AHv) and the excess heat of sorption (Qs) do not change with temperature. Secondly, the equation applies only when the total moisture content of the system remains constant. These assumptions could be met for a pure system at low temperature. However, for complex systems like foods and pharmaceutical prepara- tions , some irreversible changes can occur in the water binding properties of the system, especially with extrapola- tion to very high temperatures such as during extrusion processing (Labuza, 1985) In the field of shelf life simulation, a relatively simple equation describing the moisture sorption isotherm with a limited number of parameters is most desirable. A perfect moisture sorption isotherm model considers all factors and can describe any shape of sorption isotherm. However, such an equation would be useless because of the difficulty of determining its constants accurately (Young and Crowell, 1962). Assuming a linear isotherm for the enclosed product, Mizrahi, Labuza & Karel (1970) have shown that the gain or loss of moisture under constant environmen- tal conditions is given by: e-M A5130 ln-—-——-—-=--—-—-———-t [25] Me - Mi k W L where: Me = equilibrium moisture content of the atmosphere (g water/100g dry solids), 21 Mi = initial moisture content (9 water/100g dry solids), M = moisture content (g water/100g dry solids) found at time t, k = isotherm constant, film permeability in g.mi1/day.m2 .mmHg, >‘Ul ii = package area (m2 ), Po = vapor pressure of pure water at temperature T, in mmHg, - thickness of packaging material (mil), W - weight of dry solids (g), and = time. Iglesias (1979) described a shelf life simulation tech- nique based on the B.E.T. equation. The shelf life simula- tionmodel used was: 1 dPi 1 (c - 1) dPi Mm APdt [-—-—-a+— 2][—--]= Po (1-Aw) Po [1+(C-1)Aw] Pe-Pi WL where: Pi = water vapor pressure inside the package, Pe = water vapor pressure outside the package, Mm = monolayer moisture content, t" ll thickness of packaging material. As applied in the above models, the linear and B.E.T. isotherm equations can only be used to approximate a narrow range of water activities (i.e. equilibrium moisture 22 content). When a broader range is considered, the Mizrahi isotherm equation becomes more suitable. In this case, the shelf life simulation model is: (Mizrahi et al., 1970a) B AeB-A AeB-A+(Ae-1)M M-Mi WL — -—————— 1n + = [27] Ae-l (Ae-l) AeB-A+(Ae-1)Mi Ae-l AtPPo where: A,B - the constants of Mizrahi isotherm equation: Ae = water activity external to the packaging. Wang (1985) developed a shelf life simulation model for a packaged solid drug product as follows: Mt W dM t - -—:—-— . [28] PPs [Ae - f(M)] Mo where: t = time W a dry weight of product P = permeability constant of the package Ps = saturated vapor pressure of water dM = instant moisture content change Mo = initial moisture content Mt = moisture content at time t Ae = water activity external to the package f(M) = a function of moisture content 23 It should be remembered that in the actual distribution environment, the product can experience fluctuations in temperature and surrounding relative humidity and shelf life estimation based on constant conditions may not be a good representation. Thus some management decision is needed to relate real world to constant "laboratory" storage. If the actual distribution conditions were available (at very high cost), the data could be used to integrate the true shelf life. The storage stability of moisture-sensitive products can be predicted either by establishing the kinetic model of deterioration reaction or by the "no model" method. In the first approach (Mizrahi & Karel, 1977), the kinetic constants are determined for the appropriate. model. The model is then used to simulate storage behavior. If the rate of deterioration is only a function of moisture content and temperature, then storage behavior can be simulated for any constant or variable history of moisture content and temperature. Traditionally, the evaluation of the kinetic parameters for the kinetic model has been limited to storage tests under several constant conditions. A dynamic, non- isothermal test was first developed for pharmaceutical products (Rogers, 1963). However, it was applicable only in the specific case where the rate of reaction was a function of temperature solely. The "no model" method (Mizrahi and Karel, 1977), on the 24 other hand, is based on data obtained from samples undergo- ing continuously changing moisture content and temperature. To calculate storage stability, no kinetic model needs to be established, and no kinetic parameters need to be deter- mined. However, this method is not applicable to cases in which periods of constant moisture content can be expected. In such cases, a method for evaluating the kinetic equation from the "no model" data is needed. This approach may also present a procedure for determining kinetic parameters through tests conducted under conditions in which moisture content is changing. The "no model" method for moisture-sensitive products under fluctuating storage environments is: D - Do - (P1M+P2M2)exp[(P3+P4M+P5M2)x(l/Tr - l/T)] [29] where D and Do are the deterioration indexes at Mt and Mo, respectively, and M = Mt - Mo {where Mt and Mo are moisture content (g water/100g solids) at times t and t=0 (days), respectively), Tr is reference temperature, and P1, P2, P3, P4 and P5 are the equation parameters. The first term in Equation [29] (i.e., (P1M+P2M2)) is the deterioration index expressed as a function of M at the reference temperature for the reference moisture gain curve. The energy of acti- vation for that system is given as: Ea = R(P3+P4M+P5M2) [30] 25 The kinetic model for moisture-sensitive products under fluctuating storage environments is: E(M) 1 1 f(M,T) = f(M)T1 exp -- -— - - [31] R T1 T where E(M) = energy of activation as a function of M, and R - the gas constant. Once the kinetic model f(M)Tl is evalu- ated at any given temperature, T1, the energy of activation can be evaluated from this equation as follows: RTlT f(M,T) 1n -——-—- [32] T-Tl f(M)T1 E(M) = .Rogers (1963) described an accelerated Istorage test with programmed temperature rise for experiments dealing with the first order decomposition of riboflavine and of sucrose in aqueous solutions. The rate constant of a reac-. tion at room temperature and the activation energy can be calculated from values of the concentration of the reactant as a function of time. log f = log ko - log (1+Eb/R) + (1+Eb/R)log(1+t) 1+R/Eb + log [ 1-(ko/kt) ] [33] where f is (So-St) for zero order, [2.303 log (So/St)] for first order, (1/St - 1/So) for second order, etc. 26 where: t time S the concentration of the reactant kc and kt - the corresponding rate constants at the start and at time t E = the activation energy for the reaction R = the molar gas constant b = the programme constant Theoretically, permeability is dependent both on the diffusivity (which increases with increasing temperature and increased pore size) as well as the solubility or concentra- tion of the permeant in the film (Paine, 1962). Solubility of the vapor decreases with increasing temperature (Cardo, 1983). It is clearly evident from the water sorption isotherms of moisture-sensitive products that for a given moisture content an increase in temperature results in an increase in the water activity. This suggests that the product becomes less hygroscopic with increase of temperatures. Consequently, in an atmosphere of constant relative humidity the product can absorb higher moisture levels at lower temp- eratures than at higher temperatures (Bandyopadhyay,1980). By measuring the moisture sorption isotherm of a product at a particular temperature and determining the moisture permeability constant of a package at that tempera- ture, the shelf-life of the packaged product can be predict- ed based on moisture uptake. DEVELOPMENT OF MATHEMATICAL MODELS‘ FOR THE EFFECT OF TEMPERATURE ON MOISTURE SORPTION ISOTHERM AND SHELF LIFE ESTIMATION As previously stated, Wang (1985) has described a model for predicting the moisture uptake of a packaged moisture sensitive product, stored at constant temperature and relative humidity conditions (see Equation 28). The model as described by Wang did not consider the effect of temperature on the package permeability and on the sorption characteristics of the product. Therefore, for application of this model, experimental data is.necessary at the specific temperature or temperatures .of interest. Such data includes the product equilibrium sorption isot- herm and the permeability of the package at the temperature or temperatures of concern. As indicated above, the moisture content of packaged moisture sensitive pharmaceutical products will depend upon the water vapor permeability of the package and the sorption characteristics of the product under the condit- ions of storage. To account for temperature fluctuation during storage, it was of interest to develop a more general model which would consider the effect of tempera- ture on the water vapor transmission rate of the package, and on the adsorption of moisture by the product. The 27 28 model must also be able to account for changes in both moisture transport and absorption over time. The water vapor transmission of a package is described based on Fick's Law and Henry's Law (Karel, 1975): dQ -——- a PPs(Ae - Ai) [34] dt where: Q = quantity of water permeated through the package (9): As - water activity external to the package, Ai = water activity internal to the package, Ml ll permeability constant of the package, (g HZO/day.mmHg.package), t = time (day), P5 = saturated vapor pressure of water at temperature of test (mmHg). In describing the water vapor transmission rate (WVTR), the parameters P and Ps are temperature dependent. Therefore, temperature will influence the WVTR of a package, since diffusion and absorption are activation-energy-controlled processes, with the permeability coefficient increasing exponentially, as described by the Arrhenius relationship. The permeability can be related to the diffusion coeffi- cient (D) and solubility coefficient (5) by P = 0x3 [35] 29 where D - Do exp(-Ed/RT) [36] S = So exp(-Es/RT) . [37] Substituting D and S into Equation [35] _ Ed+Es P = DoSo exp(- ) [38] RT Therefore P = Po exp{-Ea/RT} [39] where P is the water vapor permeability constant, and Do, So and Po are preexponential terms. Ed, Es and Ea are the activation energies, R is the gas constant and T is absolute temperature (Labuza, 1981). The effect of temperature on the moisture sorption isotherm of a moisture-sensitive product may be taken into account by considering only the effect of temperature on the monolayer moisture content. Thus, knowing the varia- tion with temperature of the monolayer, it is possible to predict the temperature dependence of the equilibrium sorp- tion isotherm (Iglesias, 1986). The BET model represents isotherms reflecting apparent multilayer adsorption and assumes that a number of layers of adsorbate molecules form at the surface. A further assumption is that a given layer need not complete forma- tion, prior to initiation of subsequent layers. The equili- brium condition will therefore involve several types of surfaces, in the sense of the number of layers of molecules on each surface site (Webber, 1972). 30 For adsorption from solution, with the additional assumption that layers beyond the first have equal energies of adsorption, the BET equation takes the simplified form: BCJ [40] qe (Cs - C)[1 + (B - l)(C/CS)] in which Cs is the saturation concentration of the solute, C is the measured concentration of the solute remaining in solution at equilibrium which is equivalent to relative humidity (RH), J is the number of moles of solute adsorbed per unit weight of adsorbent in forming a complete mono— layer on the surface, qe is the number of moles of solute adsorbed per unit weight at concentration .C. B is a constant, expressive of the energy of interaction with the surface and is approximately equal to exp((El-EL)/RT), where E1 is the heat of adsorption of the first layer, EL is the heat of liquefaction, R is universal gas constant and T is absolute temperature (Brunauer, 1936). A plot of qe vs. C/Cs gives a sigmoid-shaped isotherm curve. The constant B, as a rule, will be large compared to unity, and therefore the isotherm will consist of two regions. The low concentration (C < Cs) region will be concave to the concentration axis and at higher concentra- tion, as C approaches Cs, qe becomes large, and the curve becomes convex to the concentration axis. Equation [40] can be rearranged in a linear form to 31 give: C 1 8-1 C —————=-—-+ —— [41] (Cs-C)qe BJ BJ Cs By plotting C/(Cs-C)qe against C/Cs in Equation [41], a straight line of slope (B-1)/BJ and intercept 1/BJ can be obtained for data that follows this model. Thus, from the slope and intercept the two constants J and B can be derived. The B.E.T. equation has been applied in this work to correlate several experimentally described isotherms as a function of temperature. For each temperature, values of C/(Cs-C)qe were plotted versus C/Cs. Since Cs is an un- known value, for the purpose of this study, a value of Cs was selected which gave a correlation coefficient closest to unity, when C/(Cs-C)qe was plotted versus C/Cs. Values of Cs were always selected less than 100 because C/Cs must be equal to unity when C becomes equal to Cs. Therefore, for each isotherm, values of Cs, B and J were obtained. Values of Cs, B and J were found to be "smooth" func- tions of temperature, allowing correlation of each of these values with temperature (T). The relationship between these respective constants and temperatures is shown graphically in the Results and Discussion section (see page 49-51). A cubic algebraic expression was applied to fit these coefficients. The set of equations describing the 32 moisture content as a function of temperature and relative humidity can then be expressed as: B(RH)J M = 1 [42] (Cs - RH)[l + (B - l)(RH/Cs)] where: M = moisture content (9 water/100g solids), Cs = A + B T + c T2 + D T3 [43] 1 l 1 1 ' B = A + B T + c T2 + D T3 [44] 2 2 2 2 ' J = A + B T + c T2 + o T3 [45] 3 3 3 3 ' where T is temperature expressed in degree Celsius and A1, A2, A3, B1, 82' B3, C1, C2, C3, D1, D2, and D3 are constants of the polynomials. The range of application of this set of equations cannot be larger than the range of temperature and relative humidity values from which the constants were calculated. By combining the permeability of the package and the moisture sorption characteristics of a moisture-sensitive product derived as shown above, a moisture change simula- tion model can be developed, as follows: dQ _ -—- = PPs(Ae - Ai) [46] dt dQ Since dM = -——- [47] W 33 Therefore, WdM _ ’ = PPs(Ae - Ai) [43] dt W.dM dt -= [49] PPs(Ae - Ai) t Mt W dM dt - _ . [5°] PPs (Ae - Ai) 0 Mo where dM is the instant moisture content change, W is the dry weight of product, Mo is the initial moisture content and Mt is the moisture content at time t. _As mentioned previously, water activity can be expressed as the function of moisture content, thus A1 = f(M) [51] From equations [50] and [51], the moisture change simula- tion model can be described as: Mt W dM t = _ . [52] FPS [Ae - f(M)] MO By using this model and equations [42 - 45] , the relation- ship between t and Mt can be calculated at any required 34 temperature within the range of temperature and relative humidity values from which the constants (see Equations 42- 45) were calculated. The time required to reach the critical moisture content is the shelf life of the packaged product. In Equation [52], the terms dM and f(M) are expressed by the following equations, derived from the equilibrium sorption isotherm data of the product at the temperature of test: 2 3 M = A + B(RHi) + C(RHi) + D(RHi) = f(RHi) where i = 1, 2, ----- , n For numerical integration purpose, dM 3AM 1+1) Define: f(M) = M-1 = A + BM + CM2 + DM3 To take into account the temperature variation of the equilibrium sorption isotherm, the BET equations were applied (Equations 42-45) to obtain the equilibrium moisture content and the associated relative humidity values of the product at the desired temperature. The resultant isotherm data was then fitted by the above described polynomial equations and substituted into Equation [52] for shelf life estimation. Moisture content change estimation of a packaged solid drug product under fluctuating temperature and relative humidity environments, by using this simulation model with the aid of microcomputer, is demonstrated in this study. MATERIALS AND METHODS An orange flavored chewable multivitamin tablet (UpJohn Company) was selected to be used for this study, as a moisture-sensitive product. In addition to the vitamin components, the other major ingredients of the tablet formulation included sucrose, mannitol, lactose, corn starch, dextrins, silica, calcium stearate and artificial orange flavor. The blister package system used to package the tablets was evaluated. The package system was fabri- cated from 7.9 mil polyvinyl chloride (PVC). The backing materials for the package system were a lamination of 1 mil polyethylene (PE)/1.6 mil polyvinylidene chloride (PVDC). (see Appendix I for the product and packaging material specifications) Determination of Initial Moisture Content The initial moisture content was determined by a gravimetric procedure, which is a standard and accurate method of moisture determination (AOAC, 1980), Approximate- ly 10 g of tablets were ground into a powder. A sample (ca. 1.5 g) of the ground powdered tablets was accurately weighed into each of three 25 ml weighing bottles equipped with a ground glass cover. The uncovered weighing bottles 35 36 were placed in a National vacuum oven and the samples dried to constant weight (ca. 16 hours) at 50 oC and pressure equilibrium of 50 mmHg. A current of dry air, dried by passing through concentrated sulfuric acid, was drawn through the vacuum oven during the drying period to remove water vapor. After the drying period, the samples were immediately covered, the weighing bottles transferred to a desiccator and weighed soon after reaching ambient tempera- ture (i.e. 23 oC). The average initial moisture content, determined on a dry weigh basis, was calculated from the loss of weight of the sample. The expression used to cal- culate the initial moisture content (IMC) is shown in Equation [53]. Wi - Wf IMC = x 100 [53] Wf where: IMC = initial moisture content (g water/100 g dry weight of tablet), Wi weight before drying (g), Wf weight after drying or dry weight (9). Moisture Sorption Isotherm Moisture sorption isotherms can be obtained by either gravimetric or manometric methods. Gravimetric methods have been preferred for obtaining complete moisture sorp- tion isotherms (Pomeranz and Meloan, 1977). In this study, 37 a gravimetric method was used. In developing moisture sorption isotherm data, care was taken to insure the relative humidity containers employed were maintained at constant temperature and relative humidity. The equili- brium moisture content is usually expressed as percent moisture, on a dry weight basis. The dry weight of the product must therefore be determined and used as the refer- ence basis for the isotherm. Thus, the initial moisture content must be measured with a high degree of accuracy. The moisture sorption isotherms constructed in this study were determined by placing tablets of known initial moisture content in a series of humidity containers, main- tained at two constant temperatures, and registering the weight change. Relative humidity chambers, ranging from 12 to 65%, were prepared by placing saturated solutions of appropriate salts into tightly closed 5 gallon plastic containers. The sorption isotherms of the tablet were determined at 20.6 and 30 0C respectively. The salt solu- tions employed and their corresponding relative humidities are summarized in Table 1. Salt solutions were prepared by slowly adding deioniz— ed water to the salt in a crystallization dish, with con- stant stirring, until about half of the salt crystals were dissolved. The relative humidity within each bucket was monitored by humidity sensors (American Instrument Company) which were mounted in the lid of each container. This 38 procedure was used to assure constant relative humidity values were maintained. Chemically pure salts and deioniz- ed water were used in the salt solutions preparation. Table 1. Equilibrium relative humidities for saturated salt solutions RH (33) Saturated Salt Solution Formula 20.6 °c 30.0 °c Lithium Chloride LiCl.H20 10.7 11.0 Potassium Acetate KC2H302 23.4 22.3 Magnesium Chloride MgC12.6H20 31.2 30.5 Potassium Carbonate K2C03.2H20 42.2 41.7 Magnesium Nitrate Mg(N03)2.6H20 53.2 50.7 Sodium Nitrite NaNO2 60.9 58.9 Approximately 8 g of tablets (10 tablets) were weighed into petri-dishes and the tared dishes placed in the respective humidity buckets with their lids off. Three replicates and one control were used at each condition of temperature and relative humidity. At predetermined time intervals, the humidity buckets were opened and lids re- placed on each petri-dish. The lidded petri-dishes were allowed to equilibrate at ambient temperature (i.e. 23 0C) for 30 minutes and then weighed on a analytical balance. This procedure was repeated until a constant weight was obtained. The equilibrium moisture content was calculated 39 by the following equations: (Af - Ai) - x = [541 N x M = IMC + -—— x 100 [55] Wf where: Wf = dry weight of tablets (g), X - net weight gain of each tablet (g), _Af = final weight of test (g), A1 = initial weight of test (g), number of tablets in each test, M = equilibrium moisture content (g water/100 g dry weight of tablet). Moisture sorption isotherms were obtained by plotting the average equilibrium moisture content of the three re- plicates versus relative humidity at each temperature. water vapor Permeability of Package Desiccant tablets were packaged in the blister package and heat sealed at 132 0C, with a dwell time of 1.5 seconds and pressure of 114 psi, by a commercial sealing unit at the UpJohn Pharmaceutical Company. Twenty individual 4o desiccant filled blisters and ten empty blisters were weighed and stored in containers placed in temperature and humidity controlled walk-in chambers.) Empty blisters were used as controls in the same containers. At predetermined time intervals, the blisters were removed from the humidity buckets and allowed to equilibrate at ambient temperature (i.e. 23 °C) for a fixed period of time (about 30 minutes). Average net weight gain of the desiccant filled blisters was obtained by subtracting the average control weight change from the observed gain of each blister: Y = (Tf — Ti) - (Cf - c1) [56] where: Y x net weight water permeated (g), Tf - final weight of test package (g), Ti = initial weight of test package (9), Cf - final weight of control package (9), Ci = initial weight of control package (9). The water vapor transmission rate for the blister package system was obtained from the slope of a plot, where the net weigh gain was plotted as a function of time elapsed. The permeability constant of the package was then determined by the following equation: [57] 41 where: P = water vapor permeability constant of package (g water/day.mmHg.package), WVTR = water vapor transmission rate (g water/day.package), R = relative humidity of surrounding environment (‘3). Ps = saturated water vapor pressure at test temperature (mmHg). Condition of Actual Storage Testing at Constant Environment Test conditions of 22 oC and 63.3% RH were used for this study. Twenty individual blisters were filled with tablets, weighed on an analytical balance, and placed in a constant temperature/humidity container for a fixed period of time. Ten empty blister packages were placed in the environmental bucket as controls. At predetermined inter- vals, the blisters were removed from the humidity bucket and allowed to equilibrate for about 30 minutes at ambient temperature (i.e. 23 OC). The blister packages were then weighed and the moisture content of the tablets determined gravimetrically. After the blisters were weighed they were put back to the humidity bucket and stored. This procedure was repeated until the color of the tablets was changed (approximate 2 months). 42 Conditions of Actual Storage Testing at Fluctuating Environment Nine temperature/humidity combinations were selected for this study. The humidity containers at each tempera- ture of test were prepared as detailed in the previous section (see Moisture Sorption Isotherm). Twenty individual blisters were filled with tablets, weighed on an analytical balance, and placed in a constant temperature/humidity container for a fixed period of time. Ten empty individual blister packages were placed in the environmental container as controls. At the end of a pre- determined time period (i.e. 2-4 days), the blisters were removed from the humidity container and allowed to equilibrate for about 30 minutes at ambient temperature (i.e. 23 oC). The blister packages were then weighed and the moisture content of the tablets determined gravimetri- cally. After the blisters were weighed they were trans- ferred to another temperature/humidity regime and stored. Again, the packages were removed after a predetermined time interval, weighed and the moisture content of the tablets determined. This sequence was repeated until the packaged tablets had been exposed to all temperature/humidity conditions. The conditions under which the samples were stored and the corresponding time intervals are listed in Table 2. The moisture gain or loss by the packaged tablets was 43 determined from equation [56] and the following equation: x 100 [58] M = IMC + Wf Prediction Calculation Moisture content change of the packaged tablet as a function of elapsed time was calculated on a microcomputer. A BASIC program was developed, based on the simulation model described in the previous section (see Development of Mathematical Model) for the effect of temperature on mois- ture sorption isotherm and shelf life estimation. 44 Table 2. Storage conditions and the corresponding time intervals Temperature °C/ %RH Storage time (days) 15.5/54.5 2.0 15.5/64.3 2.0 15.5/79.5 2.0 22.0/47.5 2.7 22.0/61.7 2.0 22.0/75.9 2.2 35.0/49.1 1.8 35.0/55.0 2.2 35.0/71.9 2.1 15.5/54.5 4.0 15.5/64.3 3.8 15.5/79.5 3.3 22.0/47.5 3.8 22.0/61.7 3.3 22.0/75.9 3.9 35.0/49.1 4.0 35.0/55.0 4.1 35.0/71.9 3.9 RESULTS AND DISCUSSION Initial Moisture Content The vacuum oven drying method (AOAC, 1980) was utilized for determination of the initial moisture content of the product. Preliminary experiments of drying tempera- ture and time optimization were carried out to establish the proper drying conditions. A drying temperature of 50 oC and a drying time of 16 hours was found to provide conditions which attended reproducible results. Table 3 presents the results of initial moisture content determination. Table 3. Initial Moisture Content of Multivitamin Tablets Sample Initial Final, Weight Moisture Content Number Weight (g) Weight (9) Loss (g) (g water/100 g dry product) 1 1.5736 1.5544 0.0192 1.220 2 1.3206 1.3042 0.0164 1.242 3 1.6448 1.6243 0.0205 1.246 Average: 1.236 1 0.016 The initial moisture content provides a reference basis for 45 46 the entire study. Therefore, its accuracy is very important. The average initial moisture content obtained was 1.236 t 0.016 g water/100 g dry product (Table 3). Equilibrium Moisture Isotherm The numerical data for the equilibrium moisture content and corresponding relative humidity values for the orange flavored chewable multivitamin tablets, determined at 20.6 and 30 0C are presented in Tables 4 and 5 respec- tively. As discussed in the preceding section, values for the parameters Cs, B and J, from the BET equation, were derived for a series of product isotherms determined at varying temperatures (Wang, 1985) (see Appendix II for these data). A plot of the respective parameters, as a function of temperature, gave a smooth curve relationship. This relationship between Cs, B and J and temperature is shown graphically in Figures 2, 3 and 4 respectively. A cubic polynomial was used to fit these values. Expressions that describe Cs, B and J as a function of the temperature (T) are: Cs = A + B T + C T2 + D T3 [59] 1 1 1 1 B = A + B T + C T2 + D T3 [60] 2 2 2 2 J = A + B T + C T2 + D T3 [61] 3 3 3 3 0 o where T 15 temperature( C) and A1, A2, A3, B1, 82, B3, C1, 47 C2' C3, D1, D2, and D3 are constants: A1 = 76.58275 B1 = .0018434 C1 = .0064685 D1 = .00031281 A2 =-12.28398 B2 = .37558 C2 = -.026349 D2 = .00059872 A3 = .453597 B3 = .015317 C3 = -.000709 D3 = .00000554 By calculating Cs, B and J for a given temperature and sub- stitution of the appropriate constants into Equation [42], the moisture sorption isotherm at this temperature (T) is obtained. For example, the water sorption data at 20.6 and 30 0C were derived by determination of Cs, B and J values from Equations [59 - 61] and their substitution into Equation [42]. The resultant isotherms are expressed by the following third order polynomial equations: At 20.6 °C 2 ' 3 M = 0.0021944+0.094010xRH-0.0030921xRH+0.000036756xRH [62] At 30 °C ' 2 3 M - 0.0012655+0.089817xRH-0.0031432XRH+0.000038135XRH [63] where RH is % relative humidity and M is moisture content of the product expressed as g water/100 g dry product. Moisture sorption isotherms of the multivitamin tablets were obtained by plotting the equilibrium moisture content values obtained from Equation [62] and [63] versus the corresponding relative humidity at the respective temperatures of test. The accuracy of the derived polynomial expressions (Equations 59-61) and the BET equation (Equation42), in ‘Y'1,- 48 describing the equilibrium sorption isotherms of the tablets, was shown by solving the respective equations and comparing the calculated and experimentally determined sorption data. Numerical values for sorption data at 20.6 and 30 0C are summarized in Tables 6 and 7 respectively, where calculated and experimental equilibrium moisture content values are tabulated. As shown the experimental and calculated moisture content values gave good agreement (All of the cases are less than 10%). Figures 5 and 6 present graphically the moisture sorption data for the multivitamin tablets, where the experimental isotherm data points are superimposed on the isotherm curves determined by calculation. As shown, the third order expressions, determined by the Gaussian elimination technique(Conte and Deboor,1980), accurately describe the isotherms over the range of 22% to 61% RH. Since the diffusion of water molecules into the tablets is assumed to be very rapid when compared with the water vapor diffusion of the packaging material, the rela- tive humidity inside the package will dictate the moisture gain or loss of the tablets. Equations [62] and [63] can therefore be used to describe the moisture sorption by the product within the package. The incorporation of these polynomial equations into the shelf life simulation model (Equation 52) can then be used to predict the moisture content change of the packaged product. 49 opspmsonsoa .m> mo Aoov ensemuonaoa .N opsmfim 2.3, as , one , 5.2 L 8.: 3:: p, . r 1 4 l . 4 q .23... 9892.1 " all .. 2.-" N use 5.2 /s. u I so: /./ 3,, .521. .a/I I x/ a; 1...... .. ..,.../.... es ...........6 .. fill}! Lee (aintos aqi go uorieaiuaouoo uorisanies ‘Jeiaurema '1’8'8) so 50 osspwquEma .m> m .m ousmwm Aoov opspmhmnsoa ”as. as v E“ L. spa [ «EL ” sf. ......)liql ms- gs. T - E .. 2.- - N Wis». F .3- on 5.5.x. .. \. E e- I N Q‘ I (zuezsuoo 'Jaiammd 1.11) 8 51 muspmsonsma .m> h .5 ossmflm Auov opspmuonsoa al.1m . se.~m L, In.pw TI ee.- - Nessa . s~.df 3.x. r r . . 4 r. r . if .NA.° ’0. . ,1/; sees.“ ” i_1 mes .-n w aloe” .ee.a was . n I slog“ ,, .. f... ..qvé .,... .on.s ‘Jaiamsaea '1'3'8) P (Jafietouom aoegans Jo; quaqzospe Jo iqsram/paqzospe aintos go setow 52 Table 4. Experimental equilibrium moisture content of tablets at 20.6 °C Relative Humidity Equilibrium Moisture Content (a) (%) (g water/100 g dry product) 10.7 0.710 i 0.011 23.4 0.911 1 0.103 31.2 1.050 1 0.095 42.2 1.309 1 0.037 53.2 1.704 i 0.022 60.9 2.591 t 0.034 Table 5. Experimental tablets at 30 (a) Average of 3 replicate samples. equilibrium moisture O C content of (%) Relative Humidity Equilibrium Moisture Content (a) (g water/100 g dry product) 11.0 22.3 30.5 41.7 50.7 58.9 0.680 0.837 0.910 1.190 1.428 2.212 H- H- H- H- H- H- 0.014 0.089 0.117 0.097 0.063 0.028 (a) Average of 3 replicate samples 53 Table 6. Experimental and calculated equilibrium moisture content at 20.6 0C Moisture Content Relative ----------------------------- Humidity Experimental Calculated % Difference (%) (g water/100g dry product) 10.7 0.710 - - 23.4 0.911 0.950 4.4 31.2 1.050 1.012 3.6 42.2 1.309 1.247 4.7 53.2 1.704 1.764 3.4 60.9 2.591 2.581 0.4 Table 7. Experimental and calculated equilibrium moisture content at 30 oC Moisture Content Relative ----------------------------- Humidity Experimental Calculated % Difference (%) (g water/100g dry product) 11.0 0.680 - - 22.3 0.837 0.834 0.4 30.5 0.910 0.867 4.7 41.7 1.190 1.071 9.9 50.7 1.428 1.426 0.1 58.9 2.212 2.146 3.0 54 oo 0.0N pm o>sso Eponpomw covmasCHmo can wasp shocpomfi Hapsoefinomxm .m ossmflm Ame seHaHssm m>HassC snonpomfl copMHSoHMo can memo Shonpomw HMPCmEflnomxm .0 mssmflm $3 MBHQHEE EHBso onsovm msavnsaosam an Seaman ownxomm one pom poop omonowa mo spasmoa copmasoano use H69208auomxm .oH seawam Issue. uz_p “sauces 666.8 _ 8.5.2. 1h gems; 7:93—22... 688.2 co cm o 1 .1 I u... . _m _ _ 4T: A 28.2. 1. 1.8.. . . . _ . . . . ... . .n .u . . _ . . . . . _ _ . _ _.. . .— .. . . . . . . . _ . . . . . . _ _ . . . _ . _ . .... ... - _ g _ n -_ o. .- _ . . . _ . _ ... . n u u _ . . _ . . . ..H — — . .1101 ... .. L . .uii. 2°.i .0. . .H. . .0 ..u ....\\Q . . _ ... . .. Q . . . u u . . . ... .. .... . . . . . _ . . . . . . . _ _ . . . . _ _ _ . . . _ . . . . u u n . . . . . u _ . . . . _ . . . _ . _ _ . u . _ ... . .. . .. _ _ . _ . u . ... . ._ —.— . u _ u . _ u _ _ ... ..u ... _ . . . H u . . sms<3=831 THEN 3290 ELSE 3310 D=l/ABS(X1(J,K)) GOTO 3320 D=AES(X1(J,K)) IF D>M1 THEN 3330 ELSE 3360 M1=D P1=X1(J,K) MC=J NEXT IF ABS(P1)>0 THEN 3380 ELSE 3750 IF MC<>K THEN 3390 ELSE 3440 FOR J-K TO N+1 A=X1(K,J) X1(K,J)=X1(MC,J) X1(MC,J)=A NEXT FOR J=K TO N+1 Xl(K,J)=Xl(K,J)/Pl NEXT FOR L=K+1 FOR J-N+1 To K STEP -1 Xl(L,J)=Xl(L,J)-Xl(L,K)xXl(K,J) NEXT NEXT NEXT GOTO 3780 PRINT "DEPENDENT OR INCONSISTANT" PRINT "INPUT DATA ERROR" RETURN FOR J=N To 2 STEP -1 FOR I=(J-1) To 1 STEP -1 x1(I,N+1)=X1(I,N+1)-X1(J,N+1)xX1(I,J) X1(I,J)=0 NEXT NEXT RETURN REM PRINT "ENTER TWO PAIRS OF TEMP. CONSTANT:T1,P1,T2,P2 ?" INPUT T1,P1,T2,P2 T1=1/(T1+273) T2-1/(T2+273) P1=LOG(P1)/2.3026 P2=LOG(P2)/2.3026 SL=(P2-Pl)/(T2-T1) II=P2-SLxT2 X8=l/(ZN+273) P3=SLxX8+II PY=1OAP3 PRINT "THE PERMEABILITY CONSTANT AT in FY u mmHg u RETURN AND PERMEABILITY "ZN" DEGREE C IS APPENDIX IV PRACTICAL APPLICATION OF STORAGE TEST Product: An Orange flavored vitamin Packaging Materials: PVC/Aclar, PVC/Saran & PVC Storage Conditions: 18, 22, 26, 30 5 35 °C with 40, 60 & 80 %RH at each temperature Permeability Constants PVC/Aclar: P = 2.0 x 10'6 at 12 °C P = 3.0 10’6 at 22 °C P = 5.4 10"6 at 38 °C. PVC/Saran: P = 4.8 10.6 at 15.5 0C P = 5.5 10"6 at 22 °C P = 7.7 10'6 at 35 °C PVC: P = 5.6 10'5 at 12 °C P = 5.5 10"5 at 22 °C P = 5.5 10'5 at 38 °C (g/day.mmHg.pkg): 76 I . Determine the equilibrium moisture content 77 Temperature (0C) Equilibrium Moisture Content (g water/100 g dry product) 40 %RH 60 %RH 80 %RH 18 1.325 2.488 6.632 22 1.265 2.421 6.504 26 1.199 2.352 6.442 30 1.127 2.307 6.565 35 1.049 2.267 6.715 II. Estimate the product shelf life for all storage conditiOns for the respective package systems. the g water/100 g dry product) (Assume critical moisture content for the product was 1.8 1. Predicted shelf life for the package system (PVC/Aclar) Shelf Life (days) RH (%) ------------------------------------------------- 18°C 22°C 26° 30° 35 * 40 --- --- --- --- --- 60 1553 983 784 509 417 80 495 348 253 188 128 2. Predicted shelf life for the package system (PVC/Saran) Shelf Life (days) RH (%) ------------------------------------------------- 18°C 22°C 28°C 30°C 35°C * 40 --- --- --- --- --- 60 789 590 451 334 264 80 251 191 145 113 81 3. Predicted shelf life for the package system (PVC) Shelf Life (days) RH (%) ------------------------------------------------- 18° 22° 26° 30°C 35°C * 40 --- —-- --- --- --- 60 72 53 49 41 37 80 23 19 16 14 11 * The moisture content of the products will not reach 1.8 g water/100 g dry product under the storage environments 40 %RH. 79 STORAGE TEST AT 18 C/40 %RH l..i..i. 1.3.--. l: i. .. o I; lllai. l- lilil -.ili ll 311.119.11.311 - o l .112. i- is! .l. lilini l 11.10.... C. u .... w. ...u I. w. W ...... 0.. E «J n . ’4 V. ,, /. .. x I / ... 4.61 I.» .3. ..... / f r... .1. x6 aux ya. so ...... x a.» "nod.” . 0; X”./ I ’ifir. 9 .u. . . I w alrLfl‘u l .... 4. iii... a l .. 1 filibuim llwlv. 1141.136. TL .3 3 2 l. l. 9 .1 1 1 1 1 Amadeanaowa 38am. .2 33d.\c~304sa av .52“! H.200 ”I“ a.“ a N o: 1609 1400 1200 469 1880 860 1000 560 200 510396! TIME (4395) 80 STORAGE TEST AT 18 C/ 60 %RH .l. .1 iii. ...lllii i .. al.. A 5. 4. 3 2 a... 2 z 2 2 ’- Ana-0n acne outfits rill-21.1.1.3—l- :11.11...- .J......i l.dlll..l4irl. J V 1600 1000 A PVC/flour a rue/man a we .4. 600 :00 1000 1200 400 J/ 233 /. ..I Ivar. .. h... [Uri 0‘ i. via-Illa. '07! oil "MW” 00.00 g a d J gafi i .0 2 Q. on 7 re 5 4a 3 2 1 I. 9 an in on 1“ 4h 1“ 1“ .h an N. aafl\ah~vflavel av .fizahzoo uznnhaflAv: STORAGE TIME (3195) 81 STORAGE TEST AT 18 C/80 %RH 3U x 0.1 .l.. 004...?! IAN». .II. 50 a: a 2 a 2 he. I: II... .a'. 000- .|,.0lt"."filll' I-l'u‘i"'l-I'i' .' I / u. .4... a . . v.0. 00.0. .01.“! Ii... 00- .i. 0... ‘0“? fill! 70.00 I...“ ‘00 sill"-.. 0| 4 o’.....llc'.lJ.a ' J 0!.‘01".'00‘!I‘I-4J.08 5 L 03 2 9 a 7 5 5 O . . . . . 2 1 9.. . 1 1 1 .. . L PVC/90181- a _‘g a 1 I. A adv a ~02 294'. a sad.\0kheuv‘3 \qv 3.733.920” anus-FaflAV: [,7 PVC/Saran 1 OWC 400 450 SW 100 150 50 STORM! Hill (has) 82 STORAGE TEST AT 22 C/ 40 %RH fi‘.lilil, 0.1.30.3. .l..l.l0.uillui..t.lutll|.l.. d..01llllo.I-:Ill,li. l. I: .m 8 1 n m ..M a... r 6 c a a... uh S t 0 w “a mu ... N as .«o 140 mu 9 I9 3. n.“ v— 1 .-.... o f ,m Rafi . A“ |m I/ a v .5/ / I 0 V 404. {Ia/'0 .. fl...“ 3.51.. m ... /; 2 ....v .1. A .44.! Vault. ¥..m ”I! {01.63 .0 ”cu... ll- .-l- :1... - 1.....- --...- llzuiliHHmwwnhHHWmfiufid m». in-..!.“.iiwaiil° 5 an an 21 1 L] 9 1 1 l. t. l. A 3.40 a n ...I .fulnv ha as...\.ahelb.‘3 3V 8.7-"33.7.00 Hanna-halo: STORAGE UH! (days) 83 clo'.a’..l.'l'l. ’1. ..-. u“-.. 'l STORAGE TEST AT 22 C/60 %RH A PVC/Bela:- ; rue/man 0 PVC I 1060 0.... . l (.0314: 1690 um I 1400 .31-? l.........m..l...l 1m). fl.“ lion 31! I . In- .... dz! IdlulAcf 'Qilvlldll .0 dot! II. to". .4! -‘ lIlHHdWI‘wIUJ ‘0 if ! 5 2 I... 2 9 00 WM 6 s 3 z 2 2 3 3 2 l. 1. a... 0.. L 1. L 1 Amavvn fiend Quid: Rn 83d.\il.dd¢3 3V hzahzoo H‘Q-haflox 550 850 1290 STORAGE 21242 (class) ~4éo 260 84 STORAGE TEST AT 22 C/80 %RH -- | .‘IJ- v... 1". i-.. ... '1 ll o’..-fv.¢ll'l ... II .I:!O'l ‘0‘ TI'I" ..IC'. ‘ ..--All. .. .. .33...- . ..- Any-43....- .. . II. in“ b 1| 0.. d...| '0. zfiigll 4.!l .‘l' ... C1: 2 2 O. 9.. a 1 .1 1“ 1. n37¢~3§ 35¢ a 934\$36‘3 3v I, 3.3V.- . . a! .I «..l Illlv¢ It“ u.’ ‘..!u.-“ 3.. - .4 ill .I,-.-.-.... 1. .11. 1vlllqlw5 Iii-t ..Irvv; .. d! 5. 3 2 0.. A... 9 3 7 6 s 0 0 I I o O 1 i PUC/char 3 PUG/Saran a PVC 4éo 439 586 250 ads :50 239 5103862 IRE (days) lbs 1%9 5'0 3 1h J... 1 9 1.. IL 1 I; .quiiuzoc 33...!” no: 85 STORAGE TEST AT 26 C/4O %RH PUC A PVC/Bohr 5 PVC/Saran 5. d. O O 1 1 Awfiaufifi 3&2 Tile-I...- o.- ...: .. Ii..-- 1 «ma 1..." .-.‘ioJ--U-\OI‘I . .10. 3""; ....- I II 1650 1000 1400 12'00 1 f :00 sronncx 110: (days) do 460 1 kn. TN «9 /; 2 I/ am . vac-(0.!MMWI’ 7.... .. I... mum. .Jm-w. ill-flunzp 1 y'all-L .00 .. .m .d .. a” 1 0|. 1 .3« 33.-.\0l38‘3 flaw 5:39:00 nix-3.!“N0t 86 STORAGE TEST AT 26 C/60 %RH 1.6....0. Il‘i“ -... ‘D. "-l '0')I"..'.!‘ n.- P— .- 4.6.x. non-mu Inn-1|- .A-v. ... ..-.-- -. ...!..-.....I- :4 I. .-..-J- 9. ... 2 Q” .3 z 2 aim 2 2 1 CA A§1un33 3‘1 3 3°u.\§36‘3 iv :23 1.6.19 .qu;. ...-me J.” 5 1 -.. ....mT. 3 I.“ 20 . I‘i _ 0.. PVC/Bela fl PVC/Saran . -5 ll 0'...‘ ' em ...-..m..H..n..~..-:- .... ...! i3 9. 1 I. 9 O . 1 o ”oh-uh.” no: 1000 1200 1400 000 3103363 I!!! (has) 1699 1380 2 500 400 200 87 STORAGE TEST AT 26 C/BO %RH ’l "l'll'o .I‘. A PVC/Och:- Q PVC/Saran 0 rue I 50% 469 439 350 /.. T I // / I /, /, H./ / / . v... .nall I .II A 7 'ICIOI'ID".-. -..... T 0”. II '.01A”.’.."0i.l¥§! ITHV'1I‘IOT.'J‘ ”af‘JUIIJ i-C'ol’l‘mlyt‘ ,cl--.l. .l al.”. ....0 lqlu'.‘d ‘1... 41"]..-‘l‘n. 4"...‘1'J! [.4i'. th .3413 S. 3 2 1 2 9 3 7 6 s 3 CI. 1 9 . . . . . . . . ' . . . . . 2 2 z 2 9‘ 1 1 1 1 1 I... 1 1 1 hanvdnava uncha- a mead.\ol’0‘3 3V .9233:ch Huh-.Pano: 360 150 200 2§o 30ch II!!! (has) 160 53 88 STORAGE TEST AT 30 C/40 %RH 10‘. 9"...- Q- ..I ..--.‘I. {0... -‘l'Cl 'l‘ 9....uu ---Qli I .-.-‘ 1'-0 '1-.- .{ I '0 {.0 ...! .M on 1 u m .4.“ :m an L .1 an No 0 F. C W m. N f m an ...... «U ...... I“ .a u 2 T. : m L N on .M 6 ’1 2 NJ (mix... .Wv /. 3:11.. . nil... ....... I ....-....ll.n.!llli- 0.1.3.1...- l. ... Iotpwmvwflnumvuu “mfg. 2° 5 m. A 3 .m a 1 1 I. 1. 1.. Aauvano.‘ :51- !u 03d.\ah'd(v3 3V .99an200 "Jun-chanoz $10396! II!!! ((1195) 89 STORAGE TEST AT 30 C/60 %RH i..."!‘l'.l ‘I ' . o'll- I'll ...~ ~- 0. 0' III‘ 8 a u n a 1 c u a n. a c c W W W. A; nu AU a .... A. — ... a If /. .vn/ I I max xxx m ; .. 11-. //.. W E! .. V w v . -..... ./ . s I. .1 V ...: ..... U I! a I “3"! “.1 .u {I 9: .CI 0.3 fi r:my :c..:a¢!iu:. IMPWHH: To. 0 . {OI-'2 1x'.i?¢‘ . ‘31-..- ...! 1T. ...}- .04.... ...I- iii-"J 0.19.... .4 ioo.IaH" 1:41AQL3 l4. 3 9. 1 2 9 8 7 S s . 3 9b 1 1 9 I I I . i I O O C 0 l O O l O 2 2 2 2 2 1 CL 1 1 1 ... 1 1 1 nirvana} .9th \u 33d.\afl3¥33 :V h.zan.H’-avnv "Ivan-Foals 12W ' I name: Tm (days) 299 mi) 1600 m 1600 660 460 90 STORAGE TEST AT 30 C/80 %RH ‘l‘l I.‘ ‘i A women: I: PVC/Saran NC bungalow. ant-v a as.~\a¥39; h-V 9:33.050"? ”inn-uhanoz ./.. /.l I -Vu I]. {u/ Val} ./ f / l / / I dun X [If I / /.il If an. ..r: If A 1V.|.i3 :1.va l/..\.i#l/ n Slam-v I 0 r9}!!! ..JIIAV I. l Han/UL”? 1 d d d4 1 d -1!‘ I .‘ . I‘ll I ' JfiJKVIla S L 3 9n 1 2 9 8 7 6 5 3 1b (A 1 9 . u . . . . . . . a 2 2 2 2 2 1 1 I. O. 1 IL I. 1 1.. 160 150 m 250 3' 3&0 469 4&0 599 Stone}: rm: (days) s‘a 91 STORAGE TEST AT 35 C/40 %RH b..— u m I. n. M a w. m c m. w. W an n. O .... a u ..-. q _... H... u .flL-w- Ham. on ill-.9323-.. --9-9-9l.9-9.-!4.o.9..9. ..9 .- 9.-.9......9- 9199.II9¢I.W¢NHTI$§I? . s. . 3. a” I. 1 9.. .... 1 A ‘1" ‘ fl 3* 303‘! ha 33d.\§3853 3v .32“! H200 "I: an .8 2 fl 0: 1800 1699 14’“ 1290 l 3 2 810896! UN! (has) 600 92 STORAGE TEST AT 35 C/60 %RH 2.. / ’ I‘liil .0'. - II-- ‘.'!"u‘. .1 ‘l o'-ll'l..l.- Q i - - 'a-.. I--. a/ 2. ’- [flan «J ., p i 2:1“. - . tin-I, '1p| /. . ...-.- C. in m3 ’9' ‘11 q d--. 1 ‘ 1‘ 1‘ J .J‘D" 5. 4d 3 3 9.. 2 Q. 3 7 5 .3 . . . C . . . . . . . 2 2 2 2 2 1 I. 9.. 1 I. I. Amanda-av. ...-N1 Mu 3’...\a~30" qu FZHFZOO sauna-Faho: A PVC/Relu- C PUG/Saran OH“: 860 Stone: 1199: (am) 1690 1m 1499 who 1050 6699 93 STORAGE TEST AT 35 C/80 %RH H mm 0 M/ n J / / ..A /J / ll ././ l2 1.; /. .Wr Yr.- II 14.. I-(y- III In It ...! I. {I .- .B-. M..- I /’{u. ’0’], «Mu-9. .aur -. ...: n.4,...- A 92-90AHVIII .999... , -l«9'- I 9.x. VAVo o'lollo-|-.Ilo 'i'. I. I .. . 60 A“ 'II .0. i- 30. 3“»? 9 AI".- ‘OH’I-IV g I'd. Alli-1'. J... llIlJ-o‘ilo 1.-.... cl .0 J.-'OI'."-.Iu. I “I I 46-" f-hlchfl "Hr“;b1I-Jg I S. . 3 n!- 1 2 9 a 7 6 5 3 1 1 .4 C . . . . . . . C . . . . . . 2 2 2 2 2 I... 0L 1 1 1 1 Q. 1 IL ‘0' '0!!! .‘a'l.-ot... li"!!.- ' .l- vl'l.l.‘ . '0‘: .. .0 J A RIC/Relax- D FOG/Saran 596 460 459 Aa1m ‘3‘ Qatndi \a 33¢.\.(s¢i" 3V “23.3200 “Ivan-.9o‘no: 260 250 399 3&9 sroanc: I!!! (days) 160 1§o sh REFERENCES REFERENCES AOAC. 1980. "Official Methods of Analysis." 13th ed., Association of Official Analytical Chemists, Washington, DC. pp. 537-538. ADAMSON, A.W. 1979. "A Textbook of Physical Chemistry." 2nd ed. Academic Press, Inc., New York, N.Y. BAKKER-ARKEKMA, F.W., BROOK, R.C., and LEREW, L.E. 1977. "Cereal grain drying." Adv. Cereal Sci. Technol. 2,1. BANDYOPADHYAY, S., WEISSER, H. and LONCIN, M. 1980. Water adsorption isotherms of foods at high temperatures. Lebensm. Wiss. Technol. 13:182-185. BARKER, N. and SCHMIDL, M.K. 1983. Accelerated shelf life testing for the Delmark Company. BIZOT, H. 1983. 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