ASTM D5201-05a(2020)
(Practice)Standard Practice for Calculating Formulation Physical Constants of Paints and Coatings
Standard Practice for Calculating Formulation Physical Constants of Paints and Coatings
SIGNIFICANCE AND USE
4.1 Physical constants of paints and coatings are required in all aspects of their formulation, manufacture and use. This practice demonstrates standard methods agreed upon for calculating formulation values for some of these physical constants. The calculations are the same for either metric or inch/pound units.
4.2 These formula values may not be used to replace measured values required by government regulations unless specifically stated in the governing documents.
4.3 Some regulations allow compliance determination using formulation data instead of analytical data. This formulation data may not yield the same results as the required analytical method, which could be performed on a sample from any production batch of the coating. In these cases, the user may wish to compare formulation data to analytical data and develop a factor that adjusts for variability of raw materials, variability of production batches, cure volatiles, and variability of the analytical methods.
SCOPE
1.1 This practice covers procedures commonly used in the paint industry to formulate paints and coating materials. It describes procedures for calculating formulation values for weight solids, volume solids, solvent content, volatile organic compound (VOC) content, hazardous air pollutant (HAP) content, and density of liquid paints and coatings. These values are calculated from basic formulation data. These calculations may be related to either as-supplied (unreduced) or as-applied (reduced) coating materials, including multicomponent types.
1.2 These calculated, formulation-based values may or may not be acceptable for VOC regulatory purposes, depending on the specific wording of the applicable regulation. Some regulations require analysis of the coating. Some rules allow the use of formulation data, however, some adjustments may be needed to the values calculated in this practice before they are used for regulatory purposes (see 4.3).
1.3 For purposes of this practice, it is assumed that volatile components evaporate and the materials that remain are identified as coating solids. For example, solvents are normally used to adjust viscosity for application and appearance of the coating. Other liquid materials, such as plasticizers, reactive diluents, etc., that are expected to be retained in the dried film to affect the final physical properties should be classified as part of the coating solids. Standards such as Test Methods D2369, D4758, D5403, and Guide D2832 may be used to determine volatile or nonvolatile content of specific components. For purposes of this practice it is assumed that the blended formulation behaves as an ideal solution with no volume change on mixing (see 6.2).
1.4 Volatile by-products of cross-linking reactions (cure volatiles) are not considered in these calculations since the object of this practice is to define paint physical constants based on formulation information. Variations in raw materials, variations in the production processes, test methods, and test method accuracy are not taken into account in these calculations.
1.5 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard. However, they may be readily converted into SI units, if required by the user (for example, see Note 4).
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
Relations
Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D5201 − 05a (Reapproved 2020)
Standard Practice for
Calculating Formulation Physical Constants of Paints and
Coatings
This standard is issued under the fixed designation D5201; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope object of this practice is to define paint physical constants
based on formulation information. Variations in raw materials,
1.1 This practice covers procedures commonly used in the
variations in the production processes, test methods, and test
paint industry to formulate paints and coating materials. It
method accuracy are not taken into account in these calcula-
describes procedures for calculating formulation values for
tions.
weight solids, volume solids, solvent content, volatile organic
compound (VOC) content, hazardous air pollutant (HAP) 1.5 Thevaluesstatedininch-poundunitsaretoberegarded
content,anddensityofliquidpaintsandcoatings.Thesevalues as standard. The values given in parentheses are mathematical
are calculated from basic formulation data. These calculations conversions to SI units that are provided for information only
may be related to either as-supplied (unreduced) or as-applied andarenotconsideredstandard.However,theymaybereadily
(reduced) coating materials, including multicomponent types. converted into SI units, if required by the user (for example,
see Note 4).
1.2 These calculated, formulation-based values may or may
1.6 This international standard was developed in accor-
not be acceptable for VOC regulatory purposes, depending on
dance with internationally recognized principles on standard-
the specific wording of the applicable regulation. Some regu-
ization established in the Decision on Principles for the
lationsrequireanalysisofthecoating.Somerulesallowtheuse
Development of International Standards, Guides and Recom-
of formulation data, however, some adjustments may be
mendations issued by the World Trade Organization Technical
needed to the values calculated in this practice before they are
Barriers to Trade (TBT) Committee.
used for regulatory purposes (see 4.3).
1.3 For purposes of this practice, it is assumed that volatile
2. Referenced Documents
components evaporate and the materials that remain are
2.1 ASTM Standards:
identifiedascoatingsolids.Forexample,solventsarenormally
D153Test Methods for Specific Gravity of Pigments
used to adjust viscosity for application and appearance of the
D1475Test Method for Density of Liquid Coatings, Inks,
coating. Other liquid materials, such as plasticizers, reactive
and Related Products
diluents, etc., that are expected to be retained in the dried film
D2369Test Method for Volatile Content of Coatings
to affect the final physical properties should be classified as
D2832GuideforDeterminingVolatileandNonvolatileCon-
part of the coating solids. Standards such as Test Methods
tent of Paint and Related Coatings
D2369, D4758, D5403, and Guide D2832 may be used to
D3960PracticeforDeterminingVolatileOrganicCompound
determine volatile or nonvolatile content of specific compo-
(VOC) Content of Paints and Related Coatings
nents. For purposes of this practice it is assumed that the
D4758Test Method for Nonvolatile Content of Latexes
blended formulation behaves as an ideal solution with no
(Withdrawn 2007)
volume change on mixing (see 6.2).
D5403Test Methods for Volatile Content of Radiation Cur-
1.4 Volatile by-products of cross-linking reactions (cure
able Materials
volatiles) are not considered in these calculations since the
1 2
This practice is under the jurisdiction of ASTM Committee D01 on Paint and For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Related Coatings, Materials, and Applications and is the direct responsibility of contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Subcommittee D01.24 on Physical Properties of Liquid Paints & Paint Materials. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Dec. 1, 2020. Published December 2020. Originally the ASTM website.
approved in 1991. Last previous edition approved in 2014 as D5201–05a (2014). The last approved version of this historical standard is referenced on
DOI: 10.1520/D5201-05AR20. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5201 − 05a (2020)
E29Practice for Using Significant Digits in Test Data to 3.1.5 formula solvent content, n—the calculated weight of
Determine Conformance with Specifications the solvents in a specific volume of paint (such as pounds of
solventpergallonofpaint),whichisdeterminedbytotalingall
2.2 U. S. Environmental Protection Agency Documents:
solvents present.
Code of Federal Regulations Title 40 Part 51.100 (s)
4,5 3.1.5.1 Discussion—Volatile by-products of cross-linking
Definition of VOC Clean Air Act, Section 112
reactions (cure volatiles) are not included in the formula
Code of Federal Regulations Title 40Part 63, Subpart
solvent content.
NNNN, Table3 (Default Organic HAP Mass Fraction for
3.1.6 formula volatile density, n—the calculated density of
Solvents and Solvent Blends) and Subpart RRRR Table4
the combined volatile composition (includes VOC, exempt
(Default Organic HAP Mass Fraction for Petroleum Sol-
solvents, water, ammonia, etc.).
vent Groups)
EPAFederal Reference Method24– Determination ofVola-
3.1.7 formula VOC content, n—calculated amount based
tile Matter Content, Water Content, Density Volume
upon total formula solvent content, (such as pounds of solvent
Solids, and Weight Solids, of Surface Coatings
per gallon of paint) exclusive of water or solvents that are not
EPAFederalReferenceMethod311–AnalysisofHazardous
VOC.This is a theoretical value that may be an approximation
Air Pollutant Compound in Paints and Coatings by Direct
of the VOC content that would be obtained by an analytical
Injection into a Gas Chromatograph
determination, for example, EPA Reference Method 24.
EPA 450/3-88-018U.S. Environmental Protection Agency
3.1.7.1 Discussion—Solvent and VOC are not equivalent
Protocol for Determining the Daily Volatile Organic
terms. See 40 CFR 51·100 (Par·S) for the current EPA
Compound Emission Rate ofAutomobile and Light Duty
definitionofvolatileorganiccompound(VOC)anddescription
Truck Topcoat Operations
of compounds that are exempt. Ammonia and water are not
VOC, as they are not organic compounds.
3. Terminology
4. Significance and Use
3.1 Definitions of Terms Specific to This Standard:
4.1 Physicalconstantsofpaintsandcoatingsarerequiredin
3.1.1 formula density, n—(see Test Method D1475), the
all aspects of their formulation, manufacture and use. This
calculated mass of a unit volume of material at the specified
practice demonstrates standard methods agreed upon for cal-
temperature.
culating formulation values for some of these physical con-
3.1.1.1 Discussion—In this practice, density is expressed in
stants. The calculations are the same for either metric or
pounds per U.S. gallon (lb/gal) since this is commonly used in
inch/pound units.
the coatings industry. Where dry materials are concerned,
4.2 These formula values may not be used to replace
actual density (not bulk density) should be determined analyti-
measured values required by government regulations unless
cally or obtained from supplier information. UseTest Methods
specifically stated in the governing documents.
D153 where applicable.
4.3 Someregulationsallowcompliancedeterminationusing
3.1.2 formula HAP content, n—calculated amount based on
formulation data instead of analytical data. This formulation
formula content (such as pounds of HAPper gallon of coating
data may not yield the same results as the required analytical
solids).
method, which could be performed on a sample from any
3.1.2.1 Discussion—This is a theoretical value that may be
production batch of the coating. In these cases, the user may
an approximation of the HAP content that would be obtained
wish to compare formulation data to analytical data and
by an analytical determination, for example, EPA Reference
develop a factor that adjusts for variability of raw materials,
Method 311.
variabilityofproductionbatches,curevolatiles,andvariability
3.1.3 formula percent volume solids content, n—the calcu-
of the analytical methods.
lated volume of nonvolatile material in a formula divided by
the total volume of the paint material, times 100%.
5. Calculations
3.1.4 formula percent weight solids content, n—the calcu-
5.1 Calculated values should be rounded to the appropriate
latedweightofnonvolatilematerialinaformuladividedbythe
number of significant digits in accordance with Practice E29,
total weight of the coating material, times 100%.
GuidelinesforRetainingSignificantFiguresinCalculationand
Reporting of Test Results.
5.2 Formula Density (weight per unit volume):
Available from Superintendent of Documents, U.S. Government Printing 5.2.1 The formula density (D) can be calculated from the
f
Office, Washington, DC 20402. They are also available at the EPA website:
total weight (W) and total volume (V) of the formulation.The
f f
http://www.epa.gov/ttn/atw/coat/coatingscalc.html.
formulation volume can be calculated from the weight and
A list of hazardous air pollutants (HAPs) may be found at the following
density of each ingredient as given by the following equation:
website: http://www.epa.gov/ttn/atw/188polls.html. Modifications to this original
list may be found at the following website: http://www.epa.gov/ttnatw01/
D 5 W /V 5 @W 1W 1…W #/@W /D 1W /D 1…W /D #
f f f 1 2 n 1 1 2 2 n fn
atwsmod.html or at the Code of Federal Regulations, Title 40, Part 63, Subpart C.
AvailablefromU.S.GovernmentPrintingOfficeSuperintendentofDocuments,
5 @sum#W /@sum#W /D (1)
i i i
732 N. Capitol St., NW, Mail Stop: SDE, Washington, DC 20401, http://
www.access.gpo.gov. Refer to EPA 450/3-88-018 dated December 1988. This where:
protocol makes reference to the paint formulation physical constants for VOC and
n = number of items in the formulation,
volume solids content.
D5201 − 05a (2020)
where:
D = formula density, lb/gal (g/L),
f
W = total weight of formula, lb (g),
S = formula weight percent of solids (nonvolatile), %,
f
W
V = total volume of formula, gal (L),
W = total weight of formula, lb. (g),
f
f
W = weight of ingredient, lb (g), and W = weight of ingredient, lb. (g), and
i
i
D = density of ingredient.
S = weight percent solids of ingredient, %.
i
i
5.2.1.1 An example would be as follows where the weight 5.5 Formula Volume Percent Solids (Nonvolatile)—
(W) and density (D) of each ingredient are known: Generally the volume solids content is calculated by subtract-
ing the volume of all solvent from the total volume, since the
Ingredient Weight Density Volume
W, (lb) D, (lb/gal) V, (gal)
volume of the solvent portion is usually more readily available
1 81.50 7.74 10.530
than the volume of solid materials. The volume of the solvent
2 6.10 7.90 0.772
portion may be obtained directly from the formula data or
3 0.40 8.72 0.046
4 12.00 7.65 1.569
determined by dividing the weight (W) by the density (D) of
Formula 100.00 D 12.917
f
each solvent. Calculate percent of solids by volume using one
D 5100/12.91757.74lb/gal.
f
of the following equations, depending on available informa-
tion.
5.2.2 Ifthedensityofanyoneoftheingredientsinaproduct
5.5.1 Calculate volume percent solids by subtracting the
is unknown, it can be calculated as long as the density of the
volume of solvents from the total volume of paint, as follows:
paint and the other ingredients in that formulation are known.
This situation may occur with a resin solution where the
S 5 total vol of paint 2 vol of solvents / total vol of paint 3100
~~ ! ~ !!
v
density and volume of the polymer solids are unknown, as in
(5)
the following example:
where:
Weight Density Volume
Ingredient
W, (lb) D, (lb/gal) V, (gal)
S = volume percent of solids (nonvolatile)
v
Polymer solids 50.00 D V
ps ps
or
Solvent A 25.00 6.95 3.60
Solvent B 25.00 7.18 3.48
5.5.2 Calculatevolumepercentsolidsdirectlyifthevolume
Formula 100.00 7.50 V
f
of solids and volume of paint are known:
where:
S 5 ~volumeofsolids!/~totalvolumeofpaint! 3100 (6)
V
V = volume of total formula, gal = 100.00/7.50 = 13.3 gal,
f
where:
V = volume of polymer solids, gal = 13.33 − (3.60 + 3.48)
ps
S = volume percent of solids (nonvolatile)
= 6.25 gal, and
v
D = density of polymer solids, lb/gal = 50.00/6.25 = 8.00
ps
or,
lb/gal.
5.5.3 When the volume solids of each ingredient in a
formulationisknown,thevolumesolidsoftheformulationcan
5.3 Formula Solvent (Volatile) Density:
be calculated by totaling the volumes and volume solids of
5.3.1 The density of the solvent (volatile) portion can be
each ingredient as follows:
calculated using the following equation:
5.5.3.1 Calculate the volume (V) of each ingredient from
i
D 5 @V D 1V D 1V D 1…V D #/@V 1V 1V 1…V #
s 1 1 2 2 3 3 n n 1 2 3 n
the formula weight (W) of each ingredient, divided by its
i
5 sum V D / sum V (2)
@ # @ #
i i i
density (D):
i
where:
V 5 W /D (7)
i i i
D = density of solvent portion, lb/gal (g/L),
s
5.5.3.2 Determinethetotalvolume(V)oftheformulafrom
f
V = volume of individual solvent, gal (L),
i
the sum of the volumes of the individual ingredients:
D = density of individual solvent, lb/gal (g/L), and
i
n = number of items in the formulation.
V 5 ΣV (8)
f i
NOTE1—Theaboveformulapertainstoallsolventsincorporatedinthe
5.5.3.3 Formula volume solids content (S ) is calculated in
vf
formulation.
the following manner. The volume of each ingredient (V)is
NOTE 2—If the weight (W) of the solvents in the formulation is known
i
rather than the volume, the overall solvent density can be determined multiplied by the volume percent solids of that ingredient (S )
vi
using the alternative equation, as follows:
and the sum of these volume solids is divided by the total
volume of the formula to give formula volume solids. This is
D 5 Sum W /Sum W /D (3)
~ !
S i i i
shown symbolically as follows:
5.4 Formula Weight Percent Solids (Nonvolatile)—If the
S 5 ~Σ ~S V !!/V (9)
vf vi i f
weight percent solids content of each ingredient is known, the
total formulation weight percent solids can be determined by
5.5.3.4 An example would be as follows:
summing up the weight of solids in each ingredient divide
...
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