Coating Formulation Calculations (1) Calculation of Polymer Quantities Since a certain layer thickness has to be achieved in film coating, the amount of coating material must be related to the surface area of the substrate. For this reason it is expressed in mg of dry polymer substance per cm2 of surface area. If we divide the surface area of a substrate A (mm2) by its weight w (mg), we immediately obtain the requisite coating quantity in %, i.e. the polymer consumption in kg of dry polymer substance per 100 kg of substrate for a coating of 1 mg of dry polymer substance per cm2. If lower or higher coating weights are specified for certain dosage forms, we must multiply by this factor l = mg polymer per cm2. Coating weight (%) = A(mm2) • l(mg/cm2)
w(mg) Note that A in this formula refers to the surface area and mg per cm2 to the amount of film former. Both quantities are linked by the factor 100, which leads to the result in percent. Depending on the desired function of a coating, the following values can be used for the calculation of the required amount of polymer: Enteric coatings:
4 – 6 mg for round tablets 5 – 10 mg for oblong-shaped tablets 5 – 20 mg for gelatin or HPMC capsules
Taste-masking coatings:
1 – 2 mg for round tablets 1 – 4 mg for oblong-shaped tablets
Moisture protection:
1 – 6 mg for round tablets 2 – 10 mg for oblong-shaped tablets 5 – 10 mg for gelatin or HPMC capsules
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(2) Calculation of Surface Area (2.1) Simplified Calculations The surface areas of some pharmaceutical dosage forms can be calculated according to the following simplified formulas, assuming that the tablet has the shape of a circumscribed cylinder: A = surface (mm2), D = diameter (mm), H = overall height (mm), L = length (mm), Bw = band width (mm) Tablets: A= π • (D • H + 0.5 • D2)=mm2 Capsules, oblongs: A=π • L • Bw=mm2 Spherical shapes (microtablets, pellets, granules): A= π • D2=mm2 Following the simplified calculations, the following values for the surface area of tablets and capsules can be used: Tablets
Height [mm]
Diameter [mm] 2 3 4 5 6 7 8
5 70 85 100
6 95 115 130
7 120 145 165 185
8 150 175 200 225
9
10
12
210 240 270 300
250 280 315 345
340 380 415 450 505
14 485 530 570 615 660
Surface area [mm2]
Capsules Capsule size Surface area [mm2]
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5 175
4 235
3 290
2 350
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1 410
0 500
00 610
000 800
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(2.2) Exact Calculations The following formulas can serve for the exact calculation of the tablet surface (Bauer et. al. “Coated Pharmaceutical Dosage Forms”, medpharm GmbH Scientific Publishers, Stuttgart, 1988) a)
Round Biconvex Tablet (A=2 π • (rB+r2+Ch2) “CH” can be calculated by means of the following formula: Ch = H – B 2 Side view A = Surface area D = Diameter Ch r = Radius H B Ch = Curvature height B = Band height H = Overall height Top view WR = Curvature radius BW = Band width r D
b) Oblong-Shaped Tablets X= 2 π • (rB +r2 + Ch2)
Z=2B • (L-2r) A=X+Y+Z
The individual calculation steps are based on the hatched areas in the schematic drawing: X = round ends Y = 2x top-hat segment Z = band (2x faces)
Y X
Z
X Y Side view
Side view Ch B
L Top view
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}H
BW
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(3) Estimating the Surface Area of Small Particles Where irregularly formed crystals or granules have to be evenly coated, their surface area has to be estimated with sufficient accuracy to permit calculation of the polymer requirement and the requisite layer thickness of the diffusion shell. It is then also easier to obtain a consistent release rate when the particle size distribution and surface texture have changed. A fast and simple approach is the permeability method according to Blaine (ASTM Des. C 205-55), whereas both nitrogen adsorption and mercury intrusion are much more complicated and time-consuming. Blaine's method serves for quick routine assessment of the specific surface area (in cm2 or cm2 of core volume) of small particles. It is based on the mathematical model of laminar flow through capillaries arranged in parallel, as established by Kozeny-Carman. This model states that the time taken by a constant air volume to flow through a defined product bed is proportional to the square of the specific surface area of this powder, i.e. inversely proportional to the diameter of the equivalent sphere. The apparatus, originally developed by Blaine for measuring micronized ceramic powders, had to be modified for pharmaceutical purposes to serve for larger particles as well.
Air volume (Friedrich manometer) and powder bed (granulate attachment according to Gupte) were increased to extend the measuring range to specific surface areas up to about 100 [cm2/cm3].
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Of critical importance for accurate measurement is a defined porosity of the core bed, which should be kept constant if a particular product is measured several times. This is most easily achieved by tapping the sample in a granulate attachment fastened to a tapping volumeter by means of an adapter. The vacuum required for the airflow is produced by keeping a fluid of known density (e.g. water) out of equilibrium in a U-shaped tube, using a rubber bulb or automatic pipette. For calculation, the measured airflow time has to be corrected by subtracting the no-load value of the apparatus. For better reproducibility, time should be measured electronically with the aid of light barriers activated by the liquid meniscus. The following values can be used to estimate the surface for spherical particles: Spherical Particles Diameter [mm] Surface area mm_] / piece
0.5 0.8
0.8 2
1 3
2 12.5
3 30
4 50
5 80
6 120
For spherical particles with diameters in a range of 0.5 – 1.2 mm the following % polymer weight gains can be used as a guideline: Enteric coatings:
10 – 30%
Sustained-release coatings:
5 – 20%
Taste-masking coatings:
5 – 10%
Moisture protection:
10 – 30%
Depending on the solubility of the active, surface structure, size of the particles and mechanical stability, quite different amounts may be needed. Therefore it is recommended to start with a coating trial in which samples at different polymer weight gains should be taken and tested in order to determine the required amount of polymer.
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This information and all further technical advice is based on our present knowledge and experience. However, it implies no liability or other legal responsibility on our part, including with regard to existing third party intellectual property rights, especially patent rights. In particular, no warranty, whether express or implied, or guarantee of product properties in the legal sense is intended or implied. We reserve the right to make any changes according to technological progress or further developments. The customer is not released from the obligation to conduct careful inspection and testing of incoming goods. Performance of the product described herein should be verified by testing, which should be carried out only by qualified experts in the sole responsibility of a customer. Reference to trade names used by other companies is neither a recommendation, nor does it imply that similar products could not be used. Röhm GmbH & Co. KG is the owner of patent rights covering the use of EUDRAGIT® polymers in compositions, procedures and/or applications which may be subject to license agreements. Compositions, procedures and/or applications falling within the claims of patents related to EUDRACOL™ and EUDRAPULSE™ will always require separate license agreements. ® = registered trademark EUDRAGIT = reg. Trademark of Röhm GmbH & Co. KG, Pharma Polymers, Darmstadt, Germany
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