Dimensional StabilityDimensional Stability

IntroductionIntroductionWood fibers swell under the influence of water.

Thus, the dimensions and shape of paper or board change with change in moisture content.

Poor dimensional stability causes many problems including misregister in multicolor misregister in multicolor printing, curl, cockling, wavy edges and printing, curl, cockling, wavy edges and asymmetric shrinkage in fusers of laser printers asymmetric shrinkage in fusers of laser printers and copiers and during drying of ink on press.and copiers and during drying of ink on press.

We consider the control of moisture content and We consider the control of moisture content and relate moisture change to dimensional changes.relate moisture change to dimensional changes.

Moisture in paperMoisture in paper• In equilibrium, the moisture content of paper In equilibrium, the moisture content of paper

depends on temperature and partial vapor depends on temperature and partial vapor pressure of water (i.e. on relative humidity).pressure of water (i.e. on relative humidity).

• The moisture content is highest in humid cold The moisture content is highest in humid cold conditions.conditions.

• Pulp composition effects the moisture content of Pulp composition effects the moisture content of paper.paper.

• The fiber wall structure changes when water is The fiber wall structure changes when water is removed.removed.

• Depending on pulp type, these changes may be Depending on pulp type, these changes may be partially irreversible.partially irreversible.

Relative humidityRelative humidity• The relative humidity of air is defined in terms of The relative humidity of air is defined in terms of

the vapor pressure of water.the vapor pressure of water.

• We denote the water vapor pressure as PWe denote the water vapor pressure as Pww and and

the saturation vapor pressure as Pthe saturation vapor pressure as Pwsws..

• At a given temperature below the critical At a given temperature below the critical temperature, Ptemperature, Pwsws is the pressure at which water is the pressure at which water

vapor is in equilibrium with liquid water.vapor is in equilibrium with liquid water.

• PPwsws must increase with temperature, since more must increase with temperature, since more

hydrogen bonds break on heating.hydrogen bonds break on heating.

• The relative humidity is defined asThe relative humidity is defined as

RH=PRH=Pww / P / Pwsws

• The relationship between temperature, relative The relationship between temperature, relative humidity and water vapor pressure is given in humidity and water vapor pressure is given in Figure 1.Figure 1.

• Wood fibers are hygroscopic, i.e. Wood fibers are hygroscopic, i.e. they absorb water readily.they absorb water readily.

• The moisture content is absorbed The moisture content is absorbed mass of water/ mass of oven dry mass of water/ mass of oven dry paper.paper.

• The moisture content decreases The moisture content decreases with increasing temperature or with decreasing with increasing temperature or with decreasing relative humidity.relative humidity.

• The effect of moisture The effect of moisture content on temperature content on temperature and relative humidity and relative humidity are shown in Figure 2.are shown in Figure 2.

• Mechanical pulps Mechanical pulps contain more moisture contain more moisture than chemical pulps (Figure 3).than chemical pulps (Figure 3).

• Fines are more important for Fines are more important for moisture in mechanical pulps.moisture in mechanical pulps.

• Amorphous cellulose and Amorphous cellulose and hemicellulose are more hemicellulose are more important for chemical pulp important for chemical pulp moisture.moisture.

Hysteresis and dynamic phenomenaHysteresis and dynamic phenomena• The effects of hysteresis on moisture content The effects of hysteresis on moisture content

are that the moisture content of paper at a given are that the moisture content of paper at a given relative humidity is different in absorption from relative humidity is different in absorption from dry conditions than in desorption from humid dry conditions than in desorption from humid conditions.conditions.

• This is clearly evident in This is clearly evident in Figure 3.Figure 3.

• A pair of boundary curves is A pair of boundary curves is given in Figure 4.given in Figure 4.

• Depending upon the humidity Depending upon the humidity history, the moisture content history, the moisture content can be anywhere between the boundary curves.can be anywhere between the boundary curves.

• The difference in moisture content at fixed RH & The difference in moisture content at fixed RH & T becomes large at high humidity or low T becomes large at high humidity or low temperature.temperature.

• Thermal energy, or heat of desorption, is Thermal energy, or heat of desorption, is necessary to remove water from fibers and the necessary to remove water from fibers and the heat of adsorption releases when water adsorbs heat of adsorption releases when water adsorbs on fibers.on fibers.

• Hysteresis is not a dynamic effect and the loop Hysteresis is not a dynamic effect and the loop does not collapse even if moisture content does not collapse even if moisture content changes very slowly.changes very slowly.

• This is in part due to capillary condensation, This is in part due to capillary condensation, whereby liquid water is trapped in pores.whereby liquid water is trapped in pores.

• Another explanation is based on swelling Another explanation is based on swelling stresses.stresses.

• Swelling stresses arise in the fiber wall because Swelling stresses arise in the fiber wall because crystalline cellulose doesn't swell.crystalline cellulose doesn't swell.

• At small amounts of water, the deformations are At small amounts of water, the deformations are reversible and elastic.reversible and elastic.

• At larger amounts of water, the swelling stress At larger amounts of water, the swelling stress may exceed a yield limit and cause plastic may exceed a yield limit and cause plastic deformations.deformations.

• Weakly bonded micelles may free more OH Weakly bonded micelles may free more OH groups to absorb water.groups to absorb water.

Dynamic phenomenaDynamic phenomena• The diffusion time of moisture into paper is The diffusion time of moisture into paper is

proportional to basis weight squared for proportional to basis weight squared for relatively high basis weight paper.relatively high basis weight paper.

• The diffusion time is proportional to basis weight The diffusion time is proportional to basis weight for low basis weight paper.for low basis weight paper.

• This is characteristic of boundary layer This is characteristic of boundary layer formation at the sheet surface.formation at the sheet surface.

• In the boundary layer, the local humidity and In the boundary layer, the local humidity and temperature differ from the ambient conditions.temperature differ from the ambient conditions.

• The heat of sorption governs the conditions in The heat of sorption governs the conditions in the boundary layer.the boundary layer.

• With moisture adsorption, temperature With moisture adsorption, temperature increases and RH decreases in the boundary increases and RH decreases in the boundary layer.layer.

• This retards the diffusion process because the This retards the diffusion process because the relative humidity seen by the sheet surface is relative humidity seen by the sheet surface is lower than the ambient RH.lower than the ambient RH.

• The sorption rate increases if heat exchanges The sorption rate increases if heat exchanges effectively between paper and its surroundings effectively between paper and its surroundings (air blows).(air blows).

• Sometimes dimensional stability problems occur Sometimes dimensional stability problems occur when opening a moisture sealed package when opening a moisture sealed package where the vapor pressure differs from that of the where the vapor pressure differs from that of the surrounding air.surrounding air.

Interaction of water with fibersInteraction of water with fibers

• The amount of absorbed water is a small The amount of absorbed water is a small fraction of the dry mass that the paper has when fraction of the dry mass that the paper has when dried in an oven.dried in an oven.

• On the other extreme, the water content of a wet On the other extreme, the water content of a wet pulp can be higher than the dry mass.pulp can be higher than the dry mass.

• Solids content, the ratio of dry mass to the total Solids content, the ratio of dry mass to the total mass, gives the water content in cases such as mass, gives the water content in cases such as a wet paper web.a wet paper web.

• The water retention value (WRV) of a pulp is a The water retention value (WRV) of a pulp is a common measure of total amount of water common measure of total amount of water retained by a wet pulp.retained by a wet pulp.

• Fibers absorb water either as free waterFibers absorb water either as free water

– Inter-fiber free water in the pores, orInter-fiber free water in the pores, or

– Intra-fiber free water in the lumen of fibers,Intra-fiber free water in the lumen of fibers,

or as bound wateror as bound water

– Freezing bound water in the pores of the fiber Freezing bound water in the pores of the fiber wall orwall or

– Nonfreezing bound water, chemically bonded Nonfreezing bound water, chemically bonded to the hydroxylic and carboxylic acid groups to the hydroxylic and carboxylic acid groups in fibers.in fibers.

• Figure 5 shows shows the proportions of water Figure 5 shows shows the proportions of water in the drying of TMP.in the drying of TMP.

• Only water molecules bound to Only water molecules bound to hydroxyl groups remain in hydroxyl groups remain in fibers at moisture contents fibers at moisture contents below 20%.below 20%.

• The pores of a fiber wall are active when The pores of a fiber wall are active when moisture content is 20-40% or RH > 90% at moisture content is 20-40% or RH > 90% at T=23°C.T=23°C.

• Free water is significant only at higher moisture Free water is significant only at higher moisture content.content.

• Differential scanning calorimetry can resolve the Differential scanning calorimetry can resolve the fractions of free and bound water.fractions of free and bound water.

• The solute exclusion technique gives The solute exclusion technique gives information about the distribution of water in the information about the distribution of water in the pores of the fiber wall.pores of the fiber wall.

• With this technique, pores are filled with With this technique, pores are filled with macromolecules of different sizes.macromolecules of different sizes.

• As the molecular size increases, the volume As the molecular size increases, the volume accessible to them decreases.accessible to them decreases.

• Water fills the remaining pores and eventually Water fills the remaining pores and eventually reaches saturation.reaches saturation.

• This is called the fiber saturation point.This is called the fiber saturation point.

• Fibers swell upon water absorption because Fibers swell upon water absorption because water molecules penetrate between hydrogen water molecules penetrate between hydrogen bonded fibrils in the fiber wall as shown in bonded fibrils in the fiber wall as shown in Figure 6.Figure 6.

• The phenomenon, called The phenomenon, called Hornification refers to the Hornification refers to the irreversible loss of water irreversible loss of water absorption capacity in absorption capacity in drying.drying.

• On rewetting, the once dried pulp absorbs less On rewetting, the once dried pulp absorbs less water than before drying.water than before drying.

• Hornification only occurs in chemical pulps.Hornification only occurs in chemical pulps.

• It probably arises from the irreversible collapse It probably arises from the irreversible collapse of pores between fibrils indicated from D to B in of pores between fibrils indicated from D to B in Figure 6.Figure 6.

• Beating can partially reverse hornification.Beating can partially reverse hornification.

• Cellulose and hemicellulose contain three OH Cellulose and hemicellulose contain three OH groups per six carbon atoms.groups per six carbon atoms.

• Lignin contains one or two OH per 10 carbon Lignin contains one or two OH per 10 carbon atoms.atoms.

• In amorphous hemicellulose, internal bond is In amorphous hemicellulose, internal bond is weak, OH available for water.weak, OH available for water.

• In crystalline cellulose, bonding is strong, OH In crystalline cellulose, bonding is strong, OH are not available for hydrogen bonding with are not available for hydrogen bonding with water.water.

• Figure 7 summarizes Figure 7 summarizes the removal of water the removal of water from fibers during the from fibers during the different phases of different phases of papermaking, along papermaking, along with the changes in fiber cross section.with the changes in fiber cross section.

• The cross section is important because most The cross section is important because most shrinkage of paper comes from the transverse shrinkage of paper comes from the transverse shrinkage of fibers.shrinkage of fibers.

• Paper starts to shrink at 50-60% solids.Paper starts to shrink at 50-60% solids.

HygroexpansionHygroexpansion• We will outline the hygroexpansion We will outline the hygroexpansion

phenomena that are relevant for different phenomena that are relevant for different papers.papers.

• We will relate the hygroexpansivity of paper We will relate the hygroexpansivity of paper to the microscopic structure of the fiber to the microscopic structure of the fiber network.network.

• We also consider the effects of We also consider the effects of hygroexpansivity on furnish composition and hygroexpansivity on furnish composition and control variables in the papermaking control variables in the papermaking process.process.

General phenomenaGeneral phenomena• The hygroexpansive strain, The hygroexpansive strain, hh, of paper is the , of paper is the

incremental change in dimensions when the incremental change in dimensions when the moisture content changes in the either the MD or moisture content changes in the either the MD or CD.CD.

hh is a linear reversible function of the moisture is a linear reversible function of the moisture

content as seen in Figure 8. content as seen in Figure 8.

• The hygroexpansivity The hygroexpansivity is defined asis defined as

==hh//mcmc

where where is the hygroexpansivity is the hygroexpansivity and and mc is the change in moisture content.mc is the change in moisture content.

• In the reversible region, In the reversible region, is independent of the is independent of the actual moisture content change.actual moisture content change.

• When plotted against relative humidity, the When plotted against relative humidity, the hygroexpansive strains are generally nonlinear.hygroexpansive strains are generally nonlinear.

• Figure 9 shows the same data as Figure 8, Figure 9 shows the same data as Figure 8, except that RH is the x axis.except that RH is the x axis.

• Hysteresis results from Hysteresis results from the moisture content-the moisture content-relative humidity relative humidity relationship.relationship.

• The strain values at given RH are different in The strain values at given RH are different in adsorption and desorption.adsorption and desorption.

• The slope, dThe slope, dhh/dRH is different in the two /dRH is different in the two

directions.directions.

• The internal stresses of paper release when The internal stresses of paper release when moisture content increases sufficiently.moisture content increases sufficiently.

• As a result, paper shrinks irreversibly if it was As a result, paper shrinks irreversibly if it was initially dried under restraint as shown in Figure initially dried under restraint as shown in Figure 8.8.

• Freely dried paper shows no irreversible Freely dried paper shows no irreversible shrinkage.shrinkage.

• In machine made papers, hygroexpansion is In machine made papers, hygroexpansion is different in MD and CD.different in MD and CD.

CDCD=0.1-0.15 is typically 3-5 times larger than in =0.1-0.15 is typically 3-5 times larger than in

MD.MD.

zz is one or two orders of magnitude larger than is one or two orders of magnitude larger than

in MD and CD.in MD and CD.

• The wet expansion of paper is important in The wet expansion of paper is important in offset printing, where approximately 1g/moffset printing, where approximately 1g/m22 is is applied to the paper surface.applied to the paper surface.

• Typical wet expansion of 1-2% is clearly larger Typical wet expansion of 1-2% is clearly larger than hygroexpansion.than hygroexpansion.

• In printing, the time dependence of dimensional In printing, the time dependence of dimensional changes is often more important than the changes is often more important than the magnitude of the change.magnitude of the change.

Hygroexpansion of the Fiber NetworkHygroexpansion of the Fiber Network

• Over the 0-100% range of RH at room Over the 0-100% range of RH at room temperature, cellulosic fibrils expand temperature, cellulosic fibrils expand approximately 1% in the longitudinal direction approximately 1% in the longitudinal direction and approximately 20% in the transverse and approximately 20% in the transverse direction.direction.

• The corresponding hygroexpansion coefficients The corresponding hygroexpansion coefficients of fibers are of fibers are LL

ff=.03 and =.03 and TTff=.6.=.6.

• Uesaka showed that the machine direction Uesaka showed that the machine direction hygroexpansion coefficient is given byhygroexpansion coefficient is given by

MDMD==LLff+f+f2121TT

ff

The corresponding expression for the cross The corresponding expression for the cross direction isdirection is

CDCD==LLff+f+f2222TT

ff

LLff and and TT

ff are the longitudinal and transverse are the longitudinal and transverse

hygroexpansion coefficients of fiber,hygroexpansion coefficients of fiber,

ff2j2j describes the transfer of stress from direction j describes the transfer of stress from direction j

(j=1 for MD and 2 for CD) in the network to the (j=1 for MD and 2 for CD) in the network to the transverse direction of a single fiber.transverse direction of a single fiber.

• The relative importance of the The relative importance of the jjff depends on the depends on the

stress transfer parameters fstress transfer parameters f2j2j, that are in turn , that are in turn

determined by the inter-fiber bonds.determined by the inter-fiber bonds.

• Numerical calculations by Uesaka and Qi (our Numerical calculations by Uesaka and Qi (our own Dewei Qi) suggested that in a lap joint bond, own Dewei Qi) suggested that in a lap joint bond, such as shown in Figure 10a, the transfer is very such as shown in Figure 10a, the transfer is very ineffective and fineffective and f2j2j<<1.<<1.

• The “wrapped-around” in Figure 10b The “wrapped-around” in Figure 10b was shown to give a much larger was shown to give a much larger transfer factor ftransfer factor f2j.2j.

• The MD hygroexpansivity of paper, The MD hygroexpansivity of paper, MDMD, is at most slightly larger than , is at most slightly larger than

the average axial hygroexpansivity the average axial hygroexpansivity of fibers, of fibers, TT

ff..

• The RBA has only a small effect.The RBA has only a small effect.

• Figure 11 corroborates this, since the higher Figure 11 corroborates this, since the higher paper density has little effect on paper density has little effect on MDMD..

• Wrapped-around bonds Wrapped-around bonds probably form primarily by fibers probably form primarily by fibers in the CD.in the CD.

• In a MD fiber, wet strain and In a MD fiber, wet strain and drying stress straighten drying stress straighten undulations.undulations.

• Stress transfer is effective in compressed fiber Stress transfer is effective in compressed fiber segment and “wrapped-around” bonds.segment and “wrapped-around” bonds.

• Figure 11 shows that higher fiber orientations Figure 11 shows that higher fiber orientations increase hygroexpansion in CD, but not in CD.increase hygroexpansion in CD, but not in CD.

Drying stressesDrying stresses• Drying shrinkage of paper presumably leads to Drying shrinkage of paper presumably leads to

the wrap-around geometry of Figure 10b.the wrap-around geometry of Figure 10b.

• This bonding geometry explains why drying This bonding geometry explains why drying shrinkage has a strong effect on the shrinkage has a strong effect on the hygroexpansion of paper.hygroexpansion of paper.

• If the drying shrinkage If the drying shrinkage of a pulp varies, the of a pulp varies, the hygroexpansivity is hygroexpansivity is approximately linear in approximately linear in the drying shrinkage the drying shrinkage as shown in Figure 12.as shown in Figure 12.

• Nonzero hygroexpansion occurs in fully Nonzero hygroexpansion occurs in fully restrained drying.restrained drying.

• The effect of wet straining depends on the The effect of wet straining depends on the solids content at which the strain is applied as solids content at which the strain is applied as shown in Figure 12.shown in Figure 12.

• If paper is strained at a high solids content, If paper is strained at a high solids content, hygroexpansion decreases hygroexpansion decreases linearly with increasing wet strain.linearly with increasing wet strain.

• The CD shrinkage is smallest at The CD shrinkage is smallest at the center of the web.the center of the web.

• The CD hygroexpansivity is larger at the edges The CD hygroexpansivity is larger at the edges of the web as shown in Figure 13.of the web as shown in Figure 13.