Volume And Density For Web Page - Micromeritics
Volume and Density Determinations for Particle TechnologistsPaul A. WebbFebruary 2001
Volume and Density Determinations for Particle TechnologistsIntroductionThere are a number of manual and automatedmethods for determining volume and density.This article, however, focuses on laboratorymethods that are most often used in researchand quality control applications.Another large area of application is on-linemonitoring in production control. An excellentoverview of density determinations in thisapplication is by Capano (1).The Density EnigmaWhen first introduced to density, perhaps ingrade school, we were taught that it simply isthe mass of an object divided by its volume. Wethought that was pretty much the whole story,but sooner or later we discovered that thisdefinition was only the beginning.Thedifficulty in defining density is exemplified bythe American Society for Testing and Materials’book of standard definitions (1) where one findsover forty definitions based on mass per unitvolume. The British Standards Institute (2) hasnarrowed it down to fourteen types of densities.Determining the mass of an object is ratherstraightforward; it is the determination ofvolume that conceals the difficulty. The‘volume’ of a solid object, whether a singlepiece or a mass of finely divided powder, is oneof those concepts that can’t be bundled up into asingle, neat definition.A layman’s dictionary typically defines volumein vague terms such as ‘the space occupied byan object.’McGraw-Hill’s Dictionary ofScientific and Technical Terms (4) expands onlyslightly on that definition, offering “A measureof the size of a body or definite region in threedimensional space .” One must consult aparticle technology’s lexicon to appreciate thevarious conditions under which volume isdefined. Two sources for these definitions arethe British Standards Institute (BSI) and theAmerican Society for Testing and Materials(ASTM). Here one finds that the ‘volume’ of amaterial is the summation of several rigorouslydefined elemental volumes.A common masonry brick will serve as a goodexample of an object that contains all types ofelemental volumes and differs in materialvolume according to the measurementtechnique, measurement method, and conditionsunder which the measurements are performed.A brick obviously is composed of solid materialand it has a volume that can be calculated aftermeasuring its length, width, and thickness.However, it also contains surface irregularities,small fractures, fissures, and pores that bothcommunicate with the surface and that areisolated within the structure. Voids that connectto the surface are referred to as open pores;interior voids inaccessible from the surface arecalled closed or blind pores.Surface irregularities compose another type ofvoid volume. For example, assume the bulkvolume of the brick is determined from linearmeasurements of its length, width, andthickness. It generally is understood that thevalue of volume determined in this way islimited in accuracy because the surfaces are notperfect. If a perfect plane were to be laid on oneof the surfaces, there would be many voidssandwiched between the two surfaces. For lackof a standard definition, this will be referred toas ‘external void volume’ and will refer to thevoid volume between solid surface and that of aclosely fitting envelope surrounding the object.It does not include pores that penetrate theinterior of the particle. The meaning of the termis admittedly vague, but this volume can bedetermined or, at least, estimated under certainanalytical conditions and can provide anindication of surface roughness. Figure 1demonstrates the concept.When a solid material is in granular orpowdered form, the bulk contains another typeof void: interparticle space. The total volume ofinterparticle voids depends on the size andshape of the individual particles and how wellthe particles are packed.
Volume and Density Determinations for Particle TechnologistsTable 1 provides ‘standard’ definitions forvolume in consideration of these elementalMicromeritics Instrument Corp. 2/16/01volumes. Figure 2 illustrates the bases for thedifferences between various volume definitions.Figure 1. A straightedge placed along the edge of a brick demonstrates the concept of ‘external volume,’ the volumecontained by virtue of surface irregularities.Volumes Included in DefinitionVolume DefinitionsSolidMaterialVolumeAbsolute powder volume: (also called Absolute volume): The volume ofthe solid matter after exclusion of all the spaces (pores and voids) (BSI).Apparent particle volume: The total volume of the particle, excludingopen pores, but including closed pores (BSI).Apparent powder volume: The total volume of solid matter, open poresand closed pores and interstices (BSI).Bulk volume: The volumes of the solids in each piece, the voids within thepieces, and the voids among the pieces of the particular collection (impliedby ASTM D3766).XEnvelope volume: The external volume of a particle, powder, or monolithsuch as would be obtained by tightly shrinking a film to contain it (BSI).Open PoreVolumeXClosedPoreVolumeInterparticleVoid etric volume: The volumes of a material calculated frommeasurements of its physical dimensions.XXXSkeletal volume: The sum of the volumes of the solid material and closed(or blind) pores within the pieces (Implied by ASTM D3766).True volume: Volume excluding open and closed pores (implied by BSI).XThe sum of the volumes of the solid in each piece and the voids withineach piece, that is, within close-fitting imaginary envelopes completelysurrounding each piece (Implied by ASTM D3766; see Table 2).Void: Space between particles in a bed (BSI).XXXXXXTable 1. Definitions of various types of volumes. BSI British Standards Institute, ASTM American Society forTesting and Materials.3
Volume and Density Determinations for Particle TechnologistsMicromeritics Instrument Corp. 2/16/01Volumes Included in DefinitionDensity DefinitionsSolidMaterialVolumeOpen PoreVolumeClosedPoreVolumeInterparticleVoid Vol.Absolute powder density: The mass of powder per unit of absolutevolume (BSI).Apparent particle density: The mass of a particle divided by its apparent(particle) volume (BSI).Apparent powder density: The mass of a powder divided by its apparentvolume (BSI).Bulk density: (also called Bulk powder density): The apparent powderdensity under defined conditions (BSI).XXXXXThe mass of the particles divided by the volume they occupy that includesthe space between the particles (ASTM D5004).XXXXThe ratio of the mass of a collection of discrete pieces of solid material tothe sum of the volumes of: the solids in each piece, the voids within thepieces, and the voids among the pieces of the particular collection (ASTMD3766).XXXXEffective particle density: The mass of a particle divided by its volumeincluding open pores and closed pores (BSI).Envelope density: The ratio of the mass of a particle to the sum of thevolumes of: the solid in each piece and the voids within each piece, that is,within close-fitting imaginary envelopes completely surrounding each piece(ASTM D3766).XXXXXXThe ratio of the mass of a particle to the envelope volume of the particle(implied by BSI).XXXSkeletal density: The ratio of the mass of discrete pieces of solid materialto the sum of the volumes of: the solid material in the pieces and closed (orblind) pores within the pieces (ASTM D3766).Tap density (also called Tap powder density): The apparent powderdensity obtained under stated conditions of tapping (BSI).XTheoretical density: The ratio of the mass of a collection of discretepieces of solid material to the sum of the volumes of said pieces, the solidmaterial having an ideal regular arrangement at the atomic level (ASTM).True density (also called True particle density); The mass of a particledivided by its volume, excluding open pores and closed pores (BSI).XXX“ExternalVoid”volumeXXXXXXXXXTable 2. Definitions of various types of densities that follow from the volume definitions of Table 1. BSI BritishStandards Institute, ASTM American Society for Testing and Materials.4
Volume and Density Determinations for Particle TechnologistsMicromeritics Instrument Corp. 2/16/01A single particle containingopen and closed pores.An assemblage of porousparticles in a container.Interparticle voidTheenvelope“External” voidincluded withinthe envelopeParticle CharacteristicsABulk VolumeEnvelopeVolumeBApparent or SkeletalVolumeCTrue or AbsoluteVolumeFigure 2. Illustration of various volume types. At the top left is a container of individual particles illustrating thecharacteristics of bulk volume in which interparticle and “external” voids are included. At the top right is a singleporous particle from the bulk. The particle cross-section is shown surrounded by an enveloping band. In theillustrations at the bottom, black areas shown are analogous to volume. The three illustrations at the right representthe particle. Illustration A is the volume within the envelope, B is the same volume minus the “external” volume andvolume of open pores, and C is the volume within the envelope minus both open and closed pores.5
Volume and Density Determinations for Particle TechnologistsMicromeritics Instrument Corp. 2/16/01Three volume definitions, those of apparentpowder volume, bulk volume and envelopevolume, have subtle differences. Apparentpowder volume is most rigidly defined. It is thesum total of the four volumes indicated by thecolumn headings in Table 1. Bulk and tapdensities are obtained from bulk and tapvolumes, which are apparent powder volumesobtained under specified conditions. Usually,this involves placing the powder into a rigidcontainer of specific dimensions while takingspecific steps to control compaction. In the caseof a monolithic sample, bulk volume may becalculated from dimensional measurements orby displacement of some medium in which it isimmersed.density determines the type specific gravity. Forexample, true specific gravity is calculated usingtrue volume measurements. It is the ratio of thetrue density of the material (determined at aspecific temperature) to the true density of water(at a specific temperature).The difference between envelope and bulkvolumes often is unclear. As can be seen inTable 1, ASTM’s definition of envelope volumemust be inferred from their definition ofenvelope density in Table 2. It implies that thedefinition pertains only to a single particle,while BSI’s definition encompasses a particle ora monolith (singular implied), and a powder (bydefinition, a collection of fine particles).Although not a complete list, the followingrepresents the most common methods by whichvolume and density are determined manually.The reason for expressing the temperatures isthat the density of pure, air-free water at 3.98 Cis 1.00000 g/ml. This is the maximum densityvalue; density decreases with both higher andlower temperatures. If one assumes a density of1.000 for water at room temperature the errorintroduced is about 0.3%.Volume and Density Determination MethodsUsing Manual Laboratory DevicesPycnometry (Specific Gravity Bottles):Apycnometer is a vessel with a precisely knownvolume. When one thinks of densitydeterminations, one usually thinks of apycnometer. Although a pycnometer is used todetermine density ρ or specific gravity, itmeasures volume V; a balance is used todetermine mass m.Manual pycnometers(glassware) typically are used to determine thedensity or specific gravity of liquids by fillingthe vessel, then weighing. Density is calculatedby ρ m/V and specific gravity by the sameequation and dividing both sides by the densityof water with reference to temperature.In regard to this document and others byMicromeritics, envelope volume and envelopedensity are defined following ASTM’sdefinition, that is, in terms of a single particle ormonolith. Bulk properties pertain to collectionsof particles. A third definition, that ofgeometrical volume, is adopted and pertains to avolume calculated from the linear dimensions ofthe bulk or monolithic material.Essentially the same process can be used todetermine the volume of an unknown, enclosedspace. First the object containing the void isweighed empty. It is then filled with a liquid ofknown density and reweighed. The weightdifference m is the weight of the liquid andfrom these data, volume can be calculated by V m/ρ. As will be explained, this process isused to ‘calibrate’ sample cells used in mercuryporosimetry.A Few Words About Specific GravitySpecific gravity, in general, is the ratio of theweight in air of a given volume of material at astated temperature to the weight of the samevolume of water (or other reference) at a statedtemperature. It, therefore, is dimensionless andis sometimes expressed in the form, forexample, 6.25 25/25 C. In this format, 6.25 isthe specific gravity value and 25/25 C indicatesthat the sample temperature was 25 C and thereference water temperature was 25 C. Thetype volume measurement used in calculatingAnother pycnometer method is to place aquantity of a dry, pre-weighed solid sample inthe pycnometer and fill the rest of the6
Volume and Density Determinations for Particle Technologistspycnometer with a liquid of known density(typically water), the weight of the pycnometerfilled only with the liquid having previouslybeen established. The density of the sample canbe determined from the known density of thewater, the weight of the pycnometer filled onlywith the liquid, the weight of the pycnometercontaining both sample and liquid, and theweight of the sample. This is a common methodused in characterizing soil samples (5).Hydrostatic Weighing (Displacement Method):By this method, the volume of a solid sample isdetermined by comparing the weight of thesample in air to the weight of the sampleimmersed in a liquid of known density. Thevolume of the sample is equal to the differencein the two weights divided by the density of theliquid.Conversely, if the volume of a solid object isaccurately known, the density of the liquid canbe determined by the loss of weight of theimmersed object. This is the basis for thehydrometer method (see next section).If the sample is porous, one must determine ifthe pores are to be included or excluded fromthe volume. If they are to be included or thesample will react with the displacementmedium, a sealing coating can be applied (seeBulk / Envelope Volume by Coating). If porevolume is to be excluded, the liquid mustdisplace the air and completely fill the pores.Various pretreatment methods are usedincluding evacuation and boiling (6,7,8).When determining volume by directlymeasuring the displaced volume, liquids, fineparticles or gases can be used as thedisplacement medium. If the sample material isporous, fine particles will not penetrate into thesmaller pores that water can enter. Mercury,being a non-wetting liquid, also will notpenetrate pores under ambient pressure as willwetting liquids (9). Gases, Helium in particular,will penetrate readily into very fine pores.Hydrometers: A hydrometer is a vertical floatthat measures the density or specific gravity of aliquid or liquid/solid suspension (slurry). Thehydrometer, inscribed with a graduated scale7Micromeritics Instrument Corp. 2/16/01along its length, sinks into the liquid until it hasdisplaced a volume of liquid equal in weight tothat of the float. Specific gravity or density isread directly from the inscribed scale at theliquid surface after buoyancy and gravitationalforces equalize (10).Float-Sink or Suspension (Buoyancy) Method:This method requires a liquid of known andadjustable density in which the sample is placed.The density of the liquid is adjusted until thesample either begins to sink or float (11), or issuspended at neutral density in the liquid (12).The density of the object is then equated to thatof the liquid. This method also is used toseparate materials by their density.Density Gradient Column (13): A densitygradient column is a column of liquid that variesin density with height. A sample is placed in theliquid and observed to determine at whatvertical level in the column the sample issuspended. The density of the liquid at thatlevel is the density of the sample, and that valueis determined by standards of known density.Tap Density and Vibratory Packing Density:These are very similar methods for determiningthe bulk density of a collection of particlesunder specific conditions of packing. In theformer case, packing is achieved by tapping thecontainer (14) and in the latter by vibrating thecontainer. The particles under test should notbreak up under test conditions.Bulk / Envelope Volume by Coating: Coatingthe sample allows determination of bulk volumeor apparent volume of solids while preventingabsorption or reaction with suspension liquids.Penetration of the coating into the open pores ofthe sample must be considered.Following the referenced method (15), the massof the sample is obtained. The sample is dippedinto molten wax of known density. Afterwithdrawal, any air bubbles in the wax coatingare pressed out, and the coated sample isweighed. The difference in weight before andafter coating is the weight of the wax, anddividing this number by the density of the waxprovides the volume of wax composing thecoating. The volume of the coated sample is
Volume and Density Determinations for Particle Technologistsdetermined by hydrostatic weighing. From thisvolume, the volume of wax (or other coating) issubtracted, yielding the bulk (or envelope)volume of the sample.Volume and Density Determinations byLaboratory Analytical InstrumentsThe displacement method is the underlyingprinciple used in all automated volumedetermining methods discussed below.Skeletal VolumePycnometryandDensitybyGasA gas pycnometer operates by detecting thepressure change resulting from displacement ofgas by a solid object. Figure 3 helps explain thetechnique. An object of unknown volume Vx isplaced into a sealed sample changer of knownvolume Vs. After sealing, the pressure withinthe sample chamber is measured Ps. Then, anisolated reference chamber of known volume Vris charged to a pressure Pr, which is greater thanthat of the sample chamber. A value isolatingthe two chambers is opened and the pressure Psysof the system is allowed to equilibrate. The gaslaw, PV nRT is applied to determine thevolume of the unknown as follows:Assume the system is maintained at a constanttemperature T and there is no net loss or gain ofgas, that is, the number of gas molecules n isconstant throughout the experiment.Figure 3. Essentials of the operation of a precalibrated gas pycnometer.Logically, one deduces that when the valve isopened the pressure in the reference volume will8Micromeritics Instrument Corp. 2/16/01fall and the pressure in the sample chamber willrise. The larger the volume of the unknown, thehigher will be the final system pressure, theinitial pressure of the reference chamber beingthe upper limit when 100 percent of the volumeof the sample chamber is displaced by theunknown volume.Mathematically, the initial condition isPs(Vs – Vx) PrVr nRT,(1)where R is the gas constant.After the valve is opened, the condition changestoPsys(Vs Vr – Vx) nRT(2)This leads to the expressionPs(Vs – Vx) PrVr Psys(Vs Vr – Vx) (3)which can be solved in terms of the unknownquantity Vx yielding,(PsysVs PsysVr – PsVs – PrVr)Vx (Psys-Ps)(4)The accuracy and precision of the gaspycnometer in the determination of skeletalvolume and density can be quite high, but reliesgreatly on the sample material and analysis gasbeing free of moisture. The sample also must befree of any volatile substances that cancontribute their partial pressures and cause errorand instability. For these reasons, the gas is apure gas or dry air, and the sample is pretreatedin a vacuum oven to remove volatiles. Thecontribution of the instrument
(ASTM). Here one finds that the ‘volume’ of a material is the summation of several rigorously defined elemental volumes. A common masonry brick will serve as a good example of an object that contains all types of elemental volumes and differs in mate
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Density of soil is defined as the mass the soil per unit volume. 3. Bulk Density: Define (U) Bulk density is the total mass M of the soil per unit of its total volume. 4. Dry Density: Define (U d) The dry density is mass of soils per unit of total volume of the soil mass. 5. Define: Saturated Density (U sat) When the soil mass is saturated, is .
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