Id.Eng. Chem. Prod. Res. Dev. 1981, 20, 147-150
It is thought that if IMP has a solubility in the range of the threshold treatment, then IMP could be an ideal threshold agent because the low solubility could serve as an automatic dosing device, and the increase of solubility with calcium concentration through an ion-exchange mechanism will provide automatic control of the IMP addition rate. Since IMP usually contains a small amount of soluble phosphate byproducts, solubility of IMP was determined by repeatedly slurrying an IMP sample with deionized water, filtering, and determining the amount of dissolved material. The slurry was suspended in a shaker in a water bath controlled at 25 f 0.5 “C. When the amount of dissolved solid in the filtrate has reached a constant low value, this value is considered to be the solubilityof IMP. For NaP03-II,the solubility is 0.0085 g/100 g of water, or about 85 ppm, which is more than adequate for most threshold treatments. For NaP03-III,the solubility is close to 0.1 g/100 g of water. The solution rate of NaP03-II in an agitated or recirculated system at 25 “C is quite fast. The amount of NaP03-11 dissolved reaches 38 ppm in about 1min and then follows a linear relationship to reach 60 ppm in about 60 min. The solubility of NaP03-II increases with the increase of water hardness and reaches about 100 ppm with a water hardness of 150 ppm as CaC03. The effectiveness of IMP as a threshold agent was evaluated against known sodium phosphate glass, sodium tripoly- and sodium pyrophosphate. Results indicate that IMP is as effective as sodium phosphate glass and slightly superior to sodium tripoly- and sodium pyrophosphate.
147
rates with heat and mass transfer rates so that conversion of intermediate amorphous phases to other sodium phosphates such as NaP03-I will not occur. Water vapor and cation impurities catalyze the conversion of NaPOJI to NaP03-I. NaP03-II has a desirable low solubility in the range usually applied in threshold water treatment. Since NaP03-11is nonhygroscopic and requires lower energy to produce than the traditional sodium phosphate glass used in the threshold treatment, NaP03-II seems to be an ideal threshold agent. Acknowledgment I am in debt to S. H. h s e y for his help in many tests and determinations. Literature Cited Crawford, J. E.; Smith, B. R. J. Colbid Inrerface Sol. 1965, 27, 623. Dombrovskii, N. M. Russ. J. Inorg. W m . 1902, 7, 700. KarCKroupa, E. Anal. Chem. 1959, 28, 1091. Kern, W.; Heymer, G. U.S. Patent 3432260, Mer 11, 1969. Kern, W.; kymer, G. US. Patent 3656896, A p 18, 1972. Kolloff, R. H. A .S. T.M. Bull. 1959, 237, 74. Lyons, J. W.; Van Wazer, J. R. “Phosphorus and Its Compounds”, Inters& ence: New York, 1961; Chapter 26. Morey, G. W. J. Am. Chem. Soc. 1959, 75, 5794. Moore, E. L.; Metcalf, J. S. “Advances In X-ray Analysis”, Vd. 5, Plenum: New York, 1961. Partridge, E. P.; Hicks, V.: Smlth, G. W. J . Am. Chem. Soc. 1941, 63, 454. Vd. Shen, C. Y.; Canis, C. F.; Jolly, W. L. “Preparatlve Inorganic R e ” , 2, Intersclence: New York, 1965. Shen, C. Y.; Dyroff, D. R.; Jolly, W. L. “Preparatlve Inorganlc Reactions", Vol. 5, Interscience: New York, 1968. Shen, C. Y.; Metcalf, J. S. US. Patent 3230040, Jan 18, 1966. Strauss, U.; Day, J. J . Am. Chem. Soc. 1959, 81, 79. Taylor, G. E.; Erdman, A. G. U.S. Patent 2356799, May 27, 1943. Topiey. B. ouert. Rev. 1948, 3 , 345. Van Wazer, J. R. “Phosphorus and Its Compounds”, Voi. I, Intersclence: New York, 1958, Chapters 9, 10, 12. Van Wazer, J. R.; Griffith, E. J.; McCullough, J. F. A m / . Chem. 1954, 26, 1755.
Summary Molecular dehydration of NaH2P04to NaP03-11 requires careful balance of nucleation and crystallization
Received for review June 30, 1980 Accepted September 19,1980
Curl Properties of Paper Structures Charles Green Xerox Corporation, Webster, New York 14580
Paper curl can be predicted by applying principles of viscoelastic and dimensional properties of paper considered as a layered structure. Paper is studied as a simple two-layered structure consisting of wire and felt side layers. The layers were analyzed by measuring moisture expanshdty from 0 to 95% relative humidity on each layer. Differences in expansivity were explainable in terms of a difference in fiber orientation between layers. Irreversible curl is formed when paper is heated or exposed to high relative humidity. This is shown to be related to the moisture expansion of contraction properties of the two layers. Increased contraction is assoclated with higher irreversible contraction when paper is stress-relieved. Methods of measuring differences in irreversiblecvltendencies of papers obtained from different manufacturers are also discussed. These methods use high humidity and heat treatments to produce curl.
Introduction When paper is manufactured, structural (fiber orientation) and compositional differences are built into the layered structure. These differencescan be related to the internal stresses developed in the sheet because of a variation in shrinkage within a sheet thickness. A model of the formation of differentialinternal stresses will be presented with experimental data on the synthesis 0196-432 7 I81 I1220-0147$0 1.OOlO
of curl. This will be followed by an analysis of the layered structure of two papers with divergent curl characteristics. Finally, the stress relief methods developed for measuring curl properties of paper will be reviewed. Dimensional Reactions Basic Relationships. If a sheet has a curvature of radius, R, the difference in the length of the inner and outer surfaces is given by 27r times thickness (Figure 1). 0 1981 American Chemical Society
148
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 1, 1981 I
r\
'\ AFS AMD '\
U ACDW
ACDB
AMDw
< AMDB
Figure 3. Effect of differential fiber orientation. I-AX+
0)
;I---------- L - - - _-J l+Ayd
Figure 1. Basic relationship.
C)
Figure 4. Formation of differential internal stresses.
I
b .0.004"
Figure 2. Typical curl relationship. Table I. Some Properties of Cellulose Fibers property longitudinal transverse dimensions, mm
0.5-5
moisture expansivity, 0.05-0.1 %/%
0.01-0.02 (flattened thickness) 1.0
H,O
thermal expansivity dry,"c-' x 106 modulus of elasticity, psi
0.1-1.4 1-3 x
lo6
12-14 -8 x
lo4
The fractional difference in length is the ratio of the paper thickness to the curl radius. The difference in length of the two surfaces for a curl radius of 8 in. is 0.05% for a 4 mil thickness (Figure 2). Effect of Composition and Structure. Paper made on a Fourdrinier machine consists of a wire (WS)and a felt side (FS or top side). One characteristic of this process is that differences in composition and structure are formed between the wire and felt sides of a sheet. These differences include variations in filler, fines, starch and fiber orientation. These variations between wire and felt side cause differences in moisture expansivity, which produce curl properties. The most easily understandable is the reversible curl property (Spitz and Blickenderfer, 1963). One surface expands or contracts more for a given moisture change. If the moisture change is reversed, the curl formed will revert toward its original form. Irreversible curl is curl formed by the release of internal stresses, which are produced in the drying process. Internal stresses are partially released by remoisturization at high relative humidity or by the application of heat. (Internal stresses are more nearly completely released by wetting.) When they are released paper usually shrinks. Therefore, paper will curl toward the surface which has
Table 11. Expansion of Handsheet Dried without Constraint sample
Pulp
expansion from 50 to 8 5 RH,%
a b c d e
unbeated Spruce Kraft 20-min beaten Spruce Kraft 30-min beaten Spruce Kraft unbeaten hardwood Kraft 15-min beaten hardwood Kraft
0.56 0.64 0.68 0.52 0.78
Table 111. Curl of Laminated Handsheets differential expansion, combination % curl." 0.04 3.9 b, c a, d 0.04 4.0 0.08 4.4 a, b c, e 0.10 4.9 c, d 0.16 7.1 a, e 0.22 10.1
concave side C
a b e C
e
the higher relief (higher shrinkage) of internal stresses (Green, 1979). Effect of She& Structure on Curl Properties of Cellulose Fibers. Cellulose fibers themselves are anisotropic. Their properties depend on the axis of measurement. Typical differences in longitudinal and transverse Properties in paper are given in Tab1 I. These properties are related to curl when the fiber orientation varies through the sheet thickness. For example, if the average wire and felt side fibers are oriented as shown in Figure 3, the expansivity is larger in both the machine direction felt side and cross direction wire side. Formation of internal stresses. Using Figure 4a as a model of sheet shrinkage properties, a sheet will assume a curvature (shown in Figure 4b) when dried without constraints. If the sheet is dried with a flattening constraint, it will be flat or only slightly curvd concave toward surface x (Figure 412). In this case the paper has internal stresses with magnitudes represented by x i and y+ If the paper were rewetted and dried without constraint, it would
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 1, 1981 149 I
I
I
I
Table IV. Zero-Span Tensile Strength, Pulmac, psi
2t -
0
0
paper B
paper A
lot
1
WS MD
27
CD
15
FS MD CD MDlCD wire MD/CD felt
20.5 17 1.8 1.21
23 25 25 21 0.92 1.19
7 t
0.10 0.20 DIFFERENCE IN EXPANSIVITY Yo
Figure 5. Effect of expansivity on permanent curl of 2-ply sheets.
-CD smn PAPER A
I
I 0
20
40
€0
I 80
L 101
20
0
40
RH
60
80
I00
RH
Figure 7. Curl of paper strips.
Figure 6. Differential dimensional changes of ground paper strips.
take on a curvature similar to that in Figure 4b since the internal stresses have been released. Synthesis of Paper Curl. We can demonstrate the formation of differential internal-stress expansivity characteristics by making wet handsheets with varying expansivity in two separate layers (Green, 1979). Pulps with expansion characteristics given in Table I1 were made into handsheets laminated wet in combinations given in Table 111. The sheets were then dried without constraint, except for weight sufficient to obtain flat samples. The handsheets were cut in 4 X 4-in. samples and heated at 105 "C for 5 min and reconditioned at 50% RH. The average curl is given in Table III and in Figure 5. The resulting permanent curl obtained was always toward the surface of the higher expansivity material. Apparently, more internal stress is formed in the higher expansivity portion of the laminate because of the restraint by the layer with lower expansivity. Curl can also be synthesized by laminating strips of paper with differing internal stresses produced by tensile straining. For example, by use of common rubber cement a strip of paper tensile strained sufficiently to produce a residual strain was glued to an unstrained strip of the same paper. Upon exposure to radiant heat, the laminated strip curled toward the tensile strained layer. Effect of Fiber orientation on Differential Dimensional Changes. Differential fiber orientation has been shown to cause curl (Glynn, 1961). Two papers with opposite curl patterns were selected for study. Strips were precision ground to half sheet thickneas and cycled through high humidity and low humidity. The relative changes in sample lengths between wire and felt side strips of papers A and B are given in Figure 6. For paper A the relative contraction of the felt side MD strip and the wire side CD strip are greater. The reverse is true for paper B, indicating that the properties affecting differential shrinkage are the reverse of paper A.
a2O
r
e
D
05' SURFACE TEMP O F
1
SURFACE TEMP O F
EFFECT Of DRYING TEMPERATURE ON PAPER CURL
Figure 8. Effect of drying temperature on paper curl.
By the use of zero-span tensile strength testa one variation between the two papers was shown to be differential fiber orientation (Table IV). The wire side of paper A has a higher MD/CD zero-span strength ratio than the felt side. Because fibers are stronger along the longitudinal axis, it can be concluded that paper A has more MD-oriented fibers on the wire side than on the felt side. Similarly, paper B is more oriented on the felt side. These facta are in agreement with the concept that the higher the restriction of shrinkage, the higher the internal streas with ita accompanying higher stress-relief potential. For example, the higher potential shrinkage of the CD wire side of paper A, because of high MD orientation, also has higher stress relief (i.e., contractions) under humidification. The higher differential shrinkage by drying, which is additive to the irreversible shrinkage, can also be observed from Figure 6. Strips of papers A and B were also exposed to high humidity cycling to compare the results with differential dimensional changes. The curl results agree with ground strip dimensional changes (Figure 7). Effect of Drying Temperature on Paper Curl. Papers A and B were also used to study the effect of drying temperature on paper curl produced in drying. Sheets were thoroughly wetted and then passed over a felted dryer 2 f t in diameter. The WS or FS surface was held against the dryer surface in different experiments (Figure 8).
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 1, 1981
Table VI. Radiant Curl of CD Paper Strips curl height, mm paper WS to heater FS to heater B C
MACHINE DIRECTION (AXIS) CURL
a C -AVE
E L N 0
SIDE 2 TO
CROSS DIRECTION (AXIS) CURL
Figure 9. Dependence of curl on a paper’s fiber orientation characteristics.
paper A B C D E a
Figure 10. Sample mounting position. Table V. Radius of Curvature of 99%RH Humidified Paper Strips long axis radius of paper concave side of strip curvature, in. FS FS FS
FS
ws ws FS FS
ws
CD CD MD MD and CD CD CD CD MD CD MD
1.0 2.5 4.0 8.0
2.0 2.2 2.8 2.8 3.4 3.4
The most dramatic result is that the temperature affects whether curl is toward or away from the dryer surface. Increasing temperatures moved the curl curvature away from the dryer surface. The axis of curvature depended on the paper’s differential fiber-orientation characteristics. Curl toward the wire side of paper A had an MD axis and a CD axis toward the felt side. Paper B exhibits opposite tendencies. These curls correspond to the more oriented wire side of paper A and the felt side of paper B (Figure 9). Use of Stress Relief to Study Curl Techniques such as humidification which cause the release of internal stresses can be used to study differences in curl properties. Strips of paper are mounted as shown in Figure 10, using rubber bands stretched around a circular rod. The samples are then subjected to high relative humidity and returned to ambient relative humidity. The radius of curvature of the sample in the mounting position is measured using a template. Typical results are given in Table V. Heating paper strips can also be used. Samples are exposed to a radiant source. The samples are then placed on a flat surface and height of curl measured. Some results are given in Table VI. By wetting one surface of paper, a differential stress relief can be obtained on that side. That side of the paper will be relatively shorter than the unwetted surface, after drying the paper. The experiment was repeated on a
0
2 FS 34 FS 18 WS 6 WS 6 WS
Table VII. Effect of Differential Wetting on Paper Strips MD strip CD strip side moistened wire felt wire felt
[7
B C D E,F,G,H,I J K L L M N
0
11 ws 23 FS 40 WS 9ws 13 WS
I J
IR”
45 FS 30 FS
45 FS 18 FS
curl in mm (toward moistened sidea) 12 32 19 0 0
2 0
2 30 60
34 3 5 11 10
27 38 21 22 6
After drying.
number of commercially made papers. Strips of paper 4 in. in length are moistened on one surface with a wet blotter for 5 s and allowed to dry. Each paper usually has significantlymore curl for certain wetting conditions. Some papers were found to respond to wetting more than others. For example, paper C has curl which is somewhat less than the other papers (Table VII). There is usually a preferential stress relief toward the wire side in one direction (MD or CD) and toward the felt side in the other direction. This is an expected result if internal stresses are developed from a difference in fiber orientation, as explained previously. Summary Methods for evaluating paper curl properties have been presented. We find that differential expansivity is translated into differential internal stresses when paper is dried. To minimize this effect, paper should be made with expansivity propertiea as equal as possible throughout the thickness. Paper with equal fiber orientation in opposing layers such as twin wire paper may exhibit significant curl in a system which heats one paper surface. Therefore, consistent with good papermaking practice and the requirements of the end use, a paper should be made with a minimum of internal stresses. There are several methods for evaluating curl tendencies of paper. Humidification or thermal methods will reveal, in practical terms, the inherent curl characteristics of a paper. The use of sheet splitting or grinding are expansivity measurements can be used to study dimensional characteristics, both permanent and reversible. Zero-span tensile strength measurements are useful for determining the differences in fiber orientation. Literature Cited Glynn, P. Pub Pep. Mag. Can. 1061, 82(1), T30. Oreen, C. “Characteristics of Paper Which ConMbute to Curl”, 1070 Internetionat Paper Physfcs Conference, Sepl 17-10, 1070 (Tappi-CPPA). S p k , D. A,; Blckensderfer,P. S. Tappl 1009, 48(1 l), 676-660.
Received for review September 4, 1980 Accepted September 22, 1980 This paper is based on a presentation made by the author at a seminar,“Understanding and Assessing Fibrous Structured’,held on June 25-27,1979, at the Institute in Science and Technology, State University of New York, College at New Paltz, New Paltz, N.Y. 12562.
