Interactions at the Cellulose-water Interface

Daniel F. Caulfield From Paper Science & Technology

The Cutting Edge I n s t i t u t e of Paper Chemistry (1980)

In order to describe in fundamental terms the The cellulose molecule provides nature and properties of paper one must along which the hydroxyl groups are arrayed, and understand the nature of cellulose’s interaction the with water, for this interaction ultimately con- distributes the polar surfaces through space and trols - either directly or indirectly - paper’s establishes a geometric framework in which in-electrical, thermal, optical, and, most important- teractions can take place. ly, mechanical properties.

The hydrogen bond The approach taken in this review is that the in- The hydrogen bond is an interaction between a

teraction between cellulose and water is essential- hydrogen ly a surface phenomenon: that water interacts atom) and with cellulose because the forces between atoms hydrogen bond has a dissociation energy of the in the solid possess an asymmetry or an im- order of 10 kJ mol-1. This energy is intermediate balance a t i ts surface. Furthermore, the interac- between a typical chemical bond (~500 k J mol-1) tion between cellulose and water, because of their and a typical van der Waals interaction energy hydroxylated natures, is viewed as being through (~1 intermolecular hydrogen bonds. The same short- termolecular hydrogen bond is a true chemical range character of the hydrogen bond that bond formed between the interacting molecules dominates the properties of dry cellulose is also (1). characteristic of its interaction with small quan- studies support more and more conclusively the tities of water. Yet paper is capable of taking up idea that the hydrogen bond is actually an in-large quantities of water from the surrounding at- teraction of the intermolecular or van der Waals mosphere while remaining apparently dry. As type and not some kind of weak chemical bonding more and more water is adsorbed by cellulose, it (2). The special character of the hydrogen bond appears that the short-range nature of the that distinguishes it among van der Waals forces hydrogen-bond interaction develops a long-range is character. equilibrium distance, (2) a charge transfer con­

tribution more important than usual, and (3) a Although, generally speaking, interatomic stronger directionality than usual. Comprehen­

forces are short-range, there are some ways in sive which forces across or between interfaces can be hydrogen bond in general terms (3,4,5). In addi­rather long-range in their action. Interactions in tion, the cellulose-water system stemming from forces understanding to the importance of the hydrogen recognizable a s van der Waals or dispersion bond as i t relates to paper and its properties (6). forces can be of long-range character and have practical importance. These long-range disper- Cellulose morphology sion forces operating over distances much greater In recent decades, studies of pulp fiber struc­than hydrogen-bond distances govern the floc- ture culation and coagulation of pulp fibers and form fibrillar nature of cellulose. Considerable effort the basis for the manufacturability of paper. has been expended in attempts Thus, i t appears that in the cellulose-water characteristics of this fibrillar structure to the systems, interactions of both short-range and strength properties of long-range character play important roles. sheets. Explanations of the strength properties of

single fibers in terms of fibrillar characteristics, Of equal importance to the role that interac- like fibril angle, have met with some measure of

tions play in determining the properties of paper success (7), but explanations of sheet properties is the role that the morphology of cellulose plays. in

the backbone

morphology and structure of cellulose

atom (bonded to an electronegative another electronegative atom. The

kJ mol-1). It is believed by some that the in-

However, recently, quantum mechanical

ascribed to simply (1) i ts rather short

treatises have been written about the

Nissan has contributed considerable

and morphology have emphasized the

to relate the

single fibers and paper

terms of the basic fibrillar structural

Daniel F. Caulfield is a Research Chemist at the Forest Products Laboratory in Madison. He received his Ph.D. in Chemistry at the Polytechnic Institute of Brooklyn. and has been a post­doctoral research fellow at Cornell University. His research interests include materials science, and structure/property relationships for polymers and paper. He is a member of ACS and TAPPI.

70

I N T E R A C T I O N S A T THE C E L L U L O S E - W A T E R I N T E R F A C E 71

characteristics of fibers have been less successful. In particular, the important sheet properties that depend upon moisture content cannot be understood in terms of the basic fibrillar struc­ture of cellulose, because the fibril is an element of structure a t a level below the level of mor­phology at which cellulose interacts with water. The elementary cellulosic fibril is presently viewed as a largely crystalline structure whose amorphous characteristics arise from the limited cross-sectional dimensions of the crystallites, and perhaps to a lesser degree from crystalline im­perfections and lattice defects. This crystalline morphology of cellulose is somewhat complicated in the case of wood pulp fibers by the presence of large quantities of hemicellulose which cannot be incorporated in great proportions into a cellulose crystal, and which have been viewed as being present in an amorphous sheath over the crystalline cellulosic core. In any event, the in­teraction of water with cellulose under ordinary conditions does not result in a change in the crystalline nature of cellulose. Water does not in­teract with glucose moieties buried within the cellulose crystallites but can act only upon the surfaces of cellulose crystallites. One must in­vestigate the level of morphology that includes the surfaces of fibrils and the spaces between fibrils in order to understand the interaction between cellulose and water and to understand the effects of water on the properties of paper.

Lamellar structure The apparent feature of morphology just larger

than the fibril in the complex architecture of the cell wall is the lamellar arrangement of the fibrillar components. The lamellate structure of the cell wall of pulp fibers has been reported over the years in many studies starting with the early microscopical research of Bailey (8).He presented cross sections of swollen lignified cell walls ex­hibiting clear concentric lamellae far greater in number than corresponded to the usually recognized P, S1, S2, and S3 layers. Many subsequent studies firmly established the ex­istence of concentric lamellae in lignified cells. Lamellations were also observed in chemical pulp fibers by many researchers, including Page and DeGrâce (9) who reported increases in delamina­tion that occurred on the beating and refining of pulps. Dunning (10) demonstrated that the tendency for separations between lamellae within the cell wall may stem from differences in fibrillar orientation in adjacent layers.

The microscopic examination technique known as layer expansion makes manifest the full impor­tance of the internal surface structure of fibers (11). This technique involves the rapid

Figure 1. Electron micrograph of a layer-expanded cross-section of a southern pine kraft pulp fiber (Magnification 4200x) (U.S.D.A. Photo by Southern Regional Research Center, courtesy Linda Lee Muller).

polymerization of a monomer (like butyl methacrylate) which has penetrated the cell wall of fibers enlarged by swelling in 50% aqueous methanol. After sectioning and removal of the embedding polymer, the cell wall exhibits an ex­tensively honeycombed appearance. Because of artifacts stemming from sample preparation, this honeycombed appearance is not believed to repre­sent the true undistorted structure of the swollen cell wall, but it does demonstrate vividly the potentially vast internal surface structure in swollen fibers. Researchers a t the Southern Regional Laboratory of the Science and Educa­tion Administration of the USDA have made ex­tensive use of this layer-expansion technique for characterizing the internal structure of treated and untreated cotton fibers. They have shown that in untreated fibers embedded dry in methacrylate, no layering occurs, and for fibers that have been crosslinked, layering is markedly reduced (12).

The appearance of layer-expanded fibers (Fig. 1) coupled with his own research on the sorption properties of pulp fibers led Scallan (13) to pro­pose a useful model for the lamellar structure of the cell wall. He suggested that the delamination into more-or-less concentric layers could be ex­plained by the entry of water into hydrogen-bonded areas between microfibrils in such a way that the tangentially-bonded surfaces are disrupted preferentially over the bonded surfaces lying in the radial direction. This entry of water into the more accessible tangentially-oriented

72 PAPER SCIENCE A N D TECHNOLOGY.. . The Cutting Edge

Figure 2. A segment of a water-swollen cell wall showingdelamination and formation of parallel-plate pores (Scallan (13)].

Figure 3. Water isotherm.

planes between microfibrils (assumed to be parallel to the 101 planes within the crystals) would delaminate the cell wall into concentric layers. Scallan further postulated, in keeping with the microscopic observations, that cleavage is not exclusively in the tangential planes, but only preferentially there. A much smaller degree of cleavage in the radial direction results in a tor­tuously porous structure in which the pores are largely long slit-like openings or parallel-plate pores (Fig. 2). A smaller number of radial open­ings introduce occasional constrictions in the parallel-plate spacings and provide openings and channels between pores. These openings are looked upon as providing pathways for move ment of reagents into the cell wall and pathways for diffusing the lignin fragments out of the cell wall during pulping.

A model closely related to Scallan’s was pro­posed by Goring and Kerr (14) to explain the

ultrastructural arrangement of cell-wall com­ponents in lignified tissue. Goring and Kerr observed preferred orientation of both lignin and carbohydrates in layers along the tangential direction. These lignin and carbohydrate lamellae do not appear continuously around the cir­cumference of the cell, but appear in ribbonlike structures with their tangential faces parallel to the middle lamella. Goring and Kerr’s ribbonlike model or interrupted lamella model for the lignified cell wall bears striking similarities with Scallan’s model for the delignified cell wall. Pore spaces in Scallan’s model of the swollen cell wall car, be viewed as resulting from the dissolution of the disk-shaped tangentially oriented lignin platelets of Goring’s model.

Scallan’s model is useful for visualizing the behavior of cellulose’s interaction with water. Ob­taining quantitative verification for some of its essential features requires analysis of adsorp­tion/desorption isotherms.

Sorption isotherms A representative plot of the adsorption and

desorption isotherms of water on cellulose (Fig. 3) demonstrates the typical S-shaped curve for sorp­tion of water on cellulose. The hysteresis that per­sists to low relative vapor pressures is typical of water sorption on cellulose. The generally ac­cepted interpretation of the adsorption curve is that the S-shape results from the superposition of phenomena. A high initial sorption reflects monolayer formation due to direct energetic in­teraction between water molecules and available hydroxyl groups in the amorphous regions, on the surfaces of crystallites. Subsequent more gradual increases in moisture-regain in the midrange of relative humidity reflect the formation of multilayers of adsorbed water. The final sharp in­crease in sorption of the upper region of relative humidity reflects the condensation of water in the capillary structure of the cellulose. The hysteresis represented in Fig. 3 - in which, at any relative humidity, the amount of sorbed water on the desorption isotherm exceeds the amount on the absorption isotherm - is an example of low-pressure hysteresis. The phenomenon of sorption hysteresis in cellulose is well established (15). The amount of water sorbed is not determined uniquely by the vapor pressure and temperature, but depends upon the previous history of the sample.

The sorption isotherms can be analyzed by any of several methods that have been devised to model the sorption process. The Brunauer-Emmett-Teller (BET) (16) model is the most widely used for describing adsorption in

INTERACTIONS AT THE

multimolecular layers. For convenience in plot­ting, the BET equation is usually expressed in the form:

where n represents the amount adsorbed in moles at any given relative pressure, P/P0. The amount of water equivalent to monolayer capacity is given by nm. The constant, C, in the BET equa­tion is defined by the relationship:

where E1 is the heat of adsorption of the first layer, and L the heat of condensation of water vapor to liquid water. The plot of

against P/P0 should yield a straight line, the ratio of whose slope to intercept gives the value of C-1. The value obtained for nm the number of moles required for monolayer coverage, is con­verted to a measure of area of the adsorbing cellulose by knowing the area occupied per water molecule at monolayer coverage on a cellulosic surface. This value has been calculated to be 11.8 Å2 (17). Using a somewhat larger value for the area occupied per water molecule (14.7 Å2), Stamm (18) originally reported water-swollen sur­face areas of cellulosic materials to be of the order of 200 to 300 m2/g.

Numerous objections can be raised to a BET method of analysis of the sorption of water on cellulose. The BET theory makes two simplifying assumptions which, for the case of water on cellulose, are certainly questionable. The surface is assumed to be uniform, and the water adsorbed in all layers above the first monolayer is assumed to be identical in properties to liquid water. Barber (19) has shown that there are marked dif­ferences in energy of adsorption sites on cellulose. It has also been shown that the heat of sorption above the first layer is not constant and equal to the latent heat of condensation of water. Cooper and Ashpole (20) demonstrated, on the contrary, a simple relationship between the heat of wetting of cellulose and its moisture content:

CELLULOSE-WATER INTERFACE 73

The any moisture content, w, is directly proportional

logarithm of the heat of wetting, a t

to that moisture content. Anderson and McCarthy (21) used this relationship to derive an equation that describes the adsorption isotherm of water on cellulose and derived an expression between the reduced pressure and moisture c o n tent:

where K and ß can be considered constants.

This equation is identical to the one derived by DeBoer and Zwikker (22) and by Bradley (23) us­ing Polanyi's polarization theory (24).The basis for adsorption according to the polarization theory is markedly different from that in the BET theory. The BET theory is based on the assump­tion that polarization by a solid surface is limited to the first monolayer; additional layers are held together by the intermolecular forces operative in the normal liquid. According to the polarization theory, multilayer adsorption is attributed to propagated electrical polarization initiated by the polar surface. Although Brunauer, Emmett, and Teller (16) severely criticized the DeBoer-Zwikker-Bradley formulation, they conceded that if the adsorbed molecule has a large permanent dipole moment, i t is possible that many layers may be built up by propagated polarization.

It is clear that the main factor determining the adsorption-at a given relative pressure is the heat of adsorption. The greater the heat of adsorption, the greater the amount adsorbed in the monolayer region, and the sharper the knee on the isotherm. The heat of adsorption of water varies from one material to another, as the interaction energies depend upon properties which are characteristic of the particular solid. Thus, although the shape of the water-adsorption isotherm varies from one solid to another solid, the change in shape should be small if the dif­ference in the heat of adsorption is slight. Hagymassy, Brunauer, and Mikhail (25) have pro­vided water isotherms on poreless solids that can be used as standard isotherms for evaluating the sorption of water on cellulose. They point out that the C constant of the BET equation serves as an adequate measure of the heat of adsorption for the purpose of selecting the appropriate stan­dard isotherm. Their isotherms presented as t-curves – curves that give the statistical thickness of the film adsorbed on nonporous ad­sorbents as a function of relative pressure – pro­vide a means for measuring the water-swollen in­ternal surface of cellulose by an adsorption technique independent of the BET hypothesis. In

74 PAPER SCIENCE AND TECHNOLOGY... The Cutting Edge

Weatherwax’s (17) analysis of the transient pore structure of cellulose, values of the BET equation C constant ranged from 6 to 23. This led Weather-wax to select the characteristic water isotherm [from Hagymassy et al. (25)] with C=23 as his standard curve. The thickness of the adsorbed water layer, t, can be computed by multiplying the number of adsorbed monolayers by 0.30 nm, the monolayer thickness for water. If the surface area of the adsorbent remains constant during sorption, a plot of volume adsorbed (as liquid) against t, in nanometers, will be a straight line. The surface area of the adsorbent St is then pro­portional to the slope of the line:

where St is the specific surface area in m2/g and the volume of adsorbed water Ve is given in cm3/g. Weatherwax compared results from t plots with results from BET measurements on several cellulosic materials and found excellent agree ment between both methods (17) (Table I).

Table I. Comparison of specific surface areas calculated from the water isotherms

by the BET method and the “t” isotherm (17)

Specificsurface Isotherm

Sample branch BET “t”

m2/g m2/g Maple wood Ascending 176 192

Descending 258 242 Maple Ascending 172 177 holocellulose Descending 186 205 Aspen Ascending 234 202 holocellulose Descending 275 247 Cellophane Ascending 216 233 Filter paper Ascending 128 128

It is interesting to note that Hagymassy’s standard water isotherm (C=23), the standard used by Weatherwax, is amazingly linear above 0.15 P/P0 when plotted according to the DeBoer-Zwikker-Bradley formulation (Fig. 4). The results obtained by the BET method, whose theory re jects the concept of polarization effects beyond the first adsorbed layer, are in substantial agree­ment. A possible explanation for this agreement may lie in the differences in the region of the ad­sorption isotherm that provides the values for specific surface by each method. BET plots for water on cellulose are linear only over a limited range, generally between 0.12 and 0.32 relative vapor pressure, a region that generally cor-

Figure 4. Hagymassy’s isotherm plotted according to the De Boer Zwikker and Bradley formulation.

responds to less than monolayer coverage. The t plots, on the other hand, are linear over a much larger range of relative vapor pressures, from 0.17 to 0.86 P/P0, a range that corresponds roughly to 1.0 to 3.2 monolayers.

The linearity of the water adsorption isotherms plotted by the t method is evidence that constant cellulose-water interfacial area exists from com­pletion of one monolayer of water until the equivalent of at least three have been adsorbed. Despite a constant surface area, the volume of water adsorbed increases with increasing relative humidity. Only one type of capillary structure possesses this ability: parallel-plate pores, effec­tively infinite in length and width compared to the distance between the plates. This is essen­tially the same type of pore as pictured in Scallan’s model.

Water-swollen surface areas are two orders of magnitude greater than the microscopically observed external surface area of dry cellulose, or the surface area measured on dry cellulose using nitrogen as the adsorbate (Stamm (18), and Stone and Scallan (26)]. In the dry state cellulose is an almost poreless solid. Nitrogen sorption, gaseous nitrogen pycnometry, and mercury pycnometry all indicate that dry cellulose has an almost negligible void volume. Yet upon exposure to moisture a vast internal surface structure ap­pears to exist. This led Stamm (18) to introduce the concept of a transient capillary surface of cellulose. Stone and Scallan (26) using nitrogen adsorption techniques on solvent-dried materials deduced that the transient capillary system in swollen cellulose consists of spacings about 3.5 nm wide between lamellae each less than 10 nm thick. Weatherwax (27), using nitrogen sorption on papers dried by a critical point method at dif­ferent stages of desorption from the water-saturated state, concluded that the pores in

76 PAPER SCIENCE AND TECHNOLOGY... The Cutting Edge

network may require prying apart several polymer chains. Because the shape of the created cavity (pictured as a wedge) does not match the shape of the entering molecule, more bonds between chains are ruptured than can be formed with the entering molecule.

Recently Nissan (30) attempted to use the cluster integral concept of Zimm and Lundberg to provide some rationale for the experimentally observed behavior of tensile modulus in regime II. In this region, where the moisture content, w, is between that corresponding to monolayer coverage, wc, and saturation, wsat, the experimen­tally determined dependence of tensile modulus on moisture content is given by the expression:

where A and K are the intercept and slope, respec­tively. Nissan’s analysis of many data in the literature gives for the slope K a value of 6.704 ±0.894, when lnE is plotted as a function of moisture content.

In Nissan’s theoretical formulation of the behavior in regime II:

This shows the same functional form as the ex­perimentally observable dependence of tensile modulus on moisture content. The slope C. I. represents the cooperative index – that is, the number of bonds that break simultaneously. Nissan assumes that the number of bonds break­ing cooperatively equals the number of water molecules per cluster as obtained from Starkweather’s (35) analysis of the cellulose-water system in terms of Zimm and Lundberg’s cluster integral concept. Using Starkweather’s (35) data and Némethy and Sheraga’s (36) value of 57 water molecules per cluster at saturation, Nissan arrives at an average value for the cooperative index over the entire isotherm of 6.71. This value matches the experimental value for the slope K=6.7. This agreement seems for­tuitous because there is no reason why the behavior over the whole regime should be gov­erned by the simple average of the cluster in­tegral over the regime. If, as Nissan suggests, the cooperative index is taken to be equal to the cluster integral, it should reflect the same dependence on moisture content that the cluster integral does rather than having a constant value.

The truly remarkable feature about the dependence of tensile modulus on moisture con­tent in regime II

is not the magnitude of the slope K but the fact that it is constant over the whole regime. A con­stant value for the slope

means that a molecule of water has the same quantitative effect in reducing the logarithm of tensile modulus anywhere in the regime. A molecule of water adsorbed at 60% relative humidity has the same quantitative effect in causing a fractional decrease in modulus that a molecule at 98% RH has. The constant slope ex­tends all the way to the fiber saturation point of paper. Above saturation the modulus becomes constant as expected, It should be recalled that the original concept of fiber saturation point (37) arose from an explanation of the effect of moisture on the properties of wood. When logarithms of the tensile properties (like modulus) were plotted against moisture content, two in­tersecting straight lines were obtained. The point of intersection of the lines (i.e., the upper limit of regime II) corresponded to a moisture content that was also obtained by extrapolating adsorp­tion isotherms to unit relative vapor pressure. For wood, fiber saturation points correspond to moisture contents about 30% (38). Fiber satura­tion points for papers can range up to about 100%, and for never-dried pulps, up to about 300% (39). The constancy of slope over the whole of regime II has been verified by sonic methods for a paper exhibiting a fiber saturation point of 75% (40). It is clear that at such a high moisture content most of the water cannot be in direct con­tact with a cellulose surface. In a recent article, Caulfield (41) suggested that this constancy of slope up to moisture contents corresponding to several molecular layers of adsorbed water is con­sistent with the polarization theory of Polanyi.

Lamellar structure and wet stiffness Important relationships between water’s effect

on tensile modulus and the lamellar structure of cellulose were discerned in making a detailed analysis (42,43) of the pore structure of papers wet-stiffened by crosslinking. Acetal crosslinks introduce swelling restraints to the cellulose structure that act as additional bottlenecks in lamella-like pores. Most crosslinks do not greatly reduce the available surface area accessible to water as determined by t isotherms, because the small water molecule can apparently diffuse past an acetal-bond constriction. This bond does, however, impose a swelling restraint so that the

INTERACTIONS AT THE CELLULOSE-WATER INTERFACE 77

Table II. Cell wall structure of crosslinked kraft linerboards calculated from water

desorption isotherm and fiber saturation point (42)

Total Mean specific Fiber radius Volumetric Elastic

SampleNo. Treatment

Acetal content

surface area

saturation point

of pores rw

dimensional stabilization

modulus of wet paper

% m2/g g/g nm % GPa 1 Control 0 247 0.707 2.86 0 0.146 2 Swollen 30% NaOH 0 26 1 1.00 3.83 -42 0.056 3 Crosslinked 0.4 259 0.438 1.69 38 0.277 4 Crosslinked 0.98 279 0.380 1.36 46 0.351 5 Crosslinked 1.42 294 0.356 1.21 50 0.362 6 Crosslinked 1.56 289 0.411 1.38 42 0.352 7 Crosslinked 0.36 259 0.606 2.35 14 0.225 8 Crosslinked 0.55 264 0.385 1.46 46 0.654 9 Crosslinked and

swollen 30%NaOH 0.56 279 0.690 2.47 2.4 0.147

10 Crosslinked and swollen in liquid NH3 0.41 278 0.540 1.94 24 0.221

formation of multilayers is impeded. The striking effect of the introduction of crosslinks is the reduction of the fiber saturation point of the crosslinked paper (Table II). The fiber saturation point obtained from polymer exclusion measurements provides a measure of the volume of water inside the cell wall at saturation. As a result of coupling this measurement with the measure of the available surface inside the swol­len cell wall obtained from the t isotherm and knowing that the pores are of the parallel-plate type, it is possible to calculate a mean pore width,-rw, available to water within the swollen cell walls. There is a strong negative correlation be­tween this mean radius of water-swollen pores and both the volumetric dimensional stabilization and the wet modulus of the crosslinked papers (Fig. 5).

The pore structure of crosslinked paper was also analyzed by means of N2 adsorption on aerogels prepared from swollen crosslinked papers (43). Surface areas were determined by the BET method, and pore size distributions in the mesopore range were calculated from the ascend­ing isotherm by Bodor’s (44) modification of Brunauer’s “modelless” method (45) but assum­ing parallel-plate pores. The surfaces of aerogels available to nitrogen are always smaller than the surfaces available to water and indicate that a general shrinkage of pore radius and volume by about 39% is unavoidable during the preparation of aerogels by the WAC (46) critical point drying method. In addition, the introduction of acetal crosslinks causes new bottlenecks in the pore structure of the aerogels. A nitrogen molecule 0.355 nm in diameter apparently cannot

Figure5. Correlationbetweenrw.dimensionalstability,and wettensilemodulus.

penetrate a pore segment restricted by an acetal bridge only 0.29 nm in length. The detailed pore size analysis reveals that crosslinking, which is effective in wet-stiffening of paper, affects prin­cipally the smallest pores in the cell wall (Table III). This is understandable because only when cell wall segments on opposite walls of a parallel-plate pore can be bridged by the short acetal linkage can the crosslink protect the nearby hydrogen bonds that provide the paper’s tensile modulus. It has been shown that the direct load-bearing contribution of crosslink bonds is not im­portant to wet-stiffening (40). Rather, crosslinks function as swelling restraints to the network so that a larger fraction of the preexisting hydrogen bonds function to retain a larger fraction of the paper’s dry tensile modulus. In this respect even crosslinked paper should be considered a hydrogen-bond-dominated solid.

1 2 3 4

6 7

5

8 9

10

78 PAPER SCIENCE AND TECHNOLOGY... The Cutting Edge

Table III. Cell wall structure of kraft linerboard aerogels

calculated from nitrogen isotherm (43)

Specific surface areaaccessible to nitrogen

Specific volume of nitrogen adsorbed

(as liquid) Mean Sample

No.a Total In mesopores Total In mesopores

poreradius, -rn

m2/g m2/g cm3/g cm3/g nm 179 109 0.254 0.221 1.42 226 143 0.356 0.313 1.58 63.1 26.7 0.0835 0.0645 1.32 65.2 26.3 0.0692 0.0501 1.06

63.4 24.7 0.0713 0.0526 1.12 82.0 33.6 0.0944 0.0704 1.15

197 111 0.250 0.209 1.27

21.5 9.0 0.0289 0.0225 1.34 87.6 0.0947 0.0764 1.0845.2

12.530.2 0.0414 0.0325 1.37

aSame samples as in Table II.

Creep When a sheet of paper is strained and held a t

constant length, the initial stress relaxes with time. Similarly, when a sheet of paper is sub­jected to a constant stress, i t will deform and the strain will increase with time. This creep (or, equivalently, stress relaxation) has been de­scribed by Nissan in terms of kinetics of hydrogen-bond breaking (29). He views stressed hydrogen bonds as being less stable than unstressed bonds, so that stressed bonds flicker open and closed in different unstressed configura­tions. Because this stress relaxation process is viewed in terms of chemical bond rear­rangements, the classical concepts of chemical kinetics can be applied. If the relaxation is assum­ed to result from a cooperative process in which a bonds break simultaneously, Nissan suggests the basic kinetic equation:

Where -stressed bonds of initially No

represents the rate a t which N -stressed bonds relax into the unstressed state, k is the rate con­stant, and a (the order of the reaction) is the cooperative index of bonds breaking simultaneously. Analysis of experimental data led Sternstein (47) to suggest that perhaps more likely a spectrum of cooperative indices is in­volved, and Nissan’s extensive analysis (6) of available experimental data on creep and stress relax-ation in terms of hydrogen-bond breaking in­dicates a measure of validity to this interpreta­tion. However, enigmas remain regarding the role of water in creep or stress relaxation process.

Nissan (6) has shown in his analysis of Haughten and Sellen’s (48) data on stress relaxa­tion that the principal cooperative index of cellulose a t 7 5 % R H exhibits maxima in the cooperative index about -70°C and -150°C. Nissan (6) questions if these maxima indicate second-order transition temperatures and the meanings of such transitions.

In recent years researchers in fields unrelated to paper have observed similar apparent transi­tion phenomena. Using dynamic mechanical methods for measuring tensile modulus and inter­nal friction, Radjy and Sellevold (49) found two low-temperature transitions in many porous substances including porous Vicor glass, hard­ened portland cement paste, bentonite clay, silica gel, aluminum oxide, and wood! These transitions (i.e., internal friction peaks and modulus transi­tions) appear to be general phenomena that exist in any substance that adsorbs water. Radjy and Sellevold found that one transition generally oc­curred between 0° and -40°C and another near -90°C. The first peak they called a “capillary” transition, and associated i t with the freezing of capillary water within the porous solid. The lower transition (for wood -93°C) they called the “adsor­bate” transition, and associated it with the water adsorbed on the internal surface of the microporous substance. The detailed features of both transitions appear sensitive to the extent and nature of the internal surface, pore structure, and moisture content. Although the transitions appear to be general phenomena related to the presence of water in porous materials, the mechanism responsible for the transition is still

INTERACTIONS AT T H E CELLULOSE-WATER INTERFACE 79

Table IV . The size distribution of the mesopores in the aerogels

of untreated and crosslinked kraft linerboards (43)

Mean radius Fraction of total number of mesopores found in each pore group (%)

pore group 1a 2 3 4 5 6 7 8 9 10

nm 65.8 0.00985 0.00105 27.2 .0280 .00701 17.9 .0490 .0257 12.9 .0860 .0678 9.29 .107 .174 7.04 .236 .339 5.39 .642 .605 3.95 1.07 1.35 3.01 2.08 2.59 2.44 4.83 4.20 2.05 5.28 6.04 1.77 7.10 8.10 1.56 8.70 10.09 1.39 9.87 11.49 1.24 10.81 13.55 1.12 12.28 14.54 1.02 12.86 14.25 .927 13.06 12.95 –.854 10.94

0.0140 0.0134 0.0139 0.0249 0.0069 0.0262 0.0074 0.0357 .0148 .0491 .0393 .0359 .0285 .0251 .0044 .0792 .0602 .119 .0587 .0500 .0865 .119 .0074 .0689 .109 .140 .0823 .0776 .172 .152 .0143 .109 .115 .157 .132 .127 .341 .177 .0312 .0530 .169 .163 .202 .200 .444 .276 .0613 .0905 .476 .206 .275 .352 .610 .502 .112 .318 .807 .306 .421 .771 1.36 .489 .156 .577

1.70 1.00 1.13 1.52 2.58 .774 .543 1.08 2.91 2.52 2.22 2.26 4.04 1.51 1.54 1.90 5.15 4.65 3.83 4.44 5.92 3.50 2.87 2.90 6.24 6.44 5.78 6.41 7.51 6.02 4.75 4.36 9.28 9.17 8.51 8.67 10.02 7.74 8.07 6.68

11.71 11.23 12.15 10.92 11.27 10.55 12.06 9.98 14.73 13.38 13.46 13.21 12.07 13.08 14.08 15.42 16.69 15.35 15.49 15.16 12.75 16.17 14.33 18.16 19.17 17.45 17.25 16.92 13.09 18.24 15.71 18.81 10.65 17.60 18.96 18.85 13.26 20.66 16.34 19.38

– – – – 4.44 – 9.31 –

aSame samples as in Table II.

not understood. Radjy and Sellevold suggest that they result from proton movements in lattice defects, presumably of the Bjerrum type. This mechanism implies that the adsorbed water should a t least have a pseudo-crystalline-type structure so that Bjerrum-type defects can be realized. In nuclear magnetic resonance studies of adsorbed water on cellulose, Kimura e t al. (50) found changes in proton movement at low temperatures that support the hypothesis of Bjerrum-type defects.

Another unresolved problem concerning the role of water in the creep of paper involves the ef­fect of varying relative humidity. It is well known that a strip of paper loaded a t 35% RH creeps less than when loaded at 90% RH. But Byrd (52,52) has shown that if paper loaded either in tension or compression is placed in an atmosphere whose relative humidity is cycled between 35% and 90% RH, the creep is even greater than if the paper is loaded a t a constant 90% RH. This phenomenon was also recently reported in the edgewise com­pressive loading of corrugated fiberboard (53). Creep rates of samples cycled between 35% and 90% RH are 3 to 14 times higher than creep rates on test specimens loaded a t constant 90% RH. This increased rate of creep deformation results in a related decrease in rupture life during cyclic humidity changes. Thus, paper products under either tensile or compressive loading, and cycled between 90% and 35% RH, will fail sooner than i f loaded in a constant 90% RH environment. This phenomenon must be related in a fundamental

way to the hysteresis of water sorption on cellulose.

Figure 6. Nitrogen sorption on cellulose aerogel showing high-pressure hysteresis loop indicative of "bottleneck" pores.

80 P A P E R SCIENCE A N D T E C H N O L O G Y . . . The Cutting Edge

Sorption hysteresis and lamellar structure of Paper

Both water sorption on cellulose and nitrogen sorption on cellulose aerogels prepared from swollen cellulose exhibit sorption hysteresis. Whereas the hysteresis in water sorption (Fig. 3) extends over the entire isotherm (so-called low-pressure hysteresis), the nitrogen sorption hysteresis on water-swollen cellulose aerogels ex­hibits a pronounced loop (Fig, 6) at high relative vapor pressures (43). The hysteresis that occurs at high pressure is most readily explained as resulting from capillary condensation in the mesoporous structure of cellulose.

Kelvin’s equation relates the radius of a cylin­drical capillary, rm, to the relative vapor pressure, P/P0, that will cause condensation within the capillary:

is the surface tension, Vis the molar volume of the liquid, Tis the temperature, and R is the gas constant. This equation states that the vapor pressure over a concave meniscus is lower than that over a plane surface of the liquid at the same temperature. Capillary condensation of vapor within a pore should then occur at some pressure below saturation vapor pressure. Kelvin’s equa­tion is useful in obtaining from the isotherm a measure of the distribution of pore sizes. Dif­ferences between the adsorption and desorption branch of the isotherm arise from capillary con­densation: i.e., from the filling and emptying of pares at different relative pressures.

The menisci in pores that are true parallel-plate pores are hemicylindrical (Fig. 7). One radius of curvature is infinite and the other radius of cur­vature is equal to one-half the distance between the walls. The effective Kelvin radius is equal to the separation between the walls, rm = d (54). Pores that are true parallel-plate pores present an extreme case of hysteresis. Because the mean cur­vature of a planar wall is infinite, no condensation can occur until saturation. Once condensation has occurred, however, a hemicylindrical meniscus forms that will not empty on the desorption branch of the isotherm until the relative vapor pressure falls to a value of

and then it will discharge completely. The pores in cellulose cannot be truly parallel-plate-shape pores but must be more topologically complex. For example, the ends of pores must taper, giving

Figure 7. Hemicylindrical menisci of liquid layers in true parallel-plate pores.

them cone-shaped tips. Cone-shaped pores, on the other hand, fill and empty without hysteresis (54). Constrictions in parallel-plate spacings and open­ings between parallel-plate pores (asenvisioned in Scallan’s model) yield an overall pore structure that can be described as consisting of bott le necked pores. Tho explanation of hysteresis in terms of bottlenecked pores in which narrow con­strictions between larger cavities ease the forma­tion of menisci is well established (55).

For cellulose, the description of pore structure as consisting of bottlenecked pores is visually helpful in understanding the phenomenon of high-pressure hysteresis of nitrogen sorption on water-swollen cellulose aerogels. In reality, a descrip­tion in terms of interconnected pore spaces with

INTERACTIONS AT T H E CELLULOSE -WATER INTERFACE 81

constrictions between pores rather than discrete bottles is probably more appropriate. Everett (56) has discussed the general phenomenon of capillary condensation and evaporation in pores of this type.

I t should be emphasized that, whereas Kelvin's equation and the concept of capillary condensa­tion in bottlenecked pores provide an explanation of hysteresis in sorption of N2 on swollen cellulose aerogels, they can in no way explain even the high-pressure hysteresis of water on cellulose. Dry cellulose is an almost poreless solid and the big pores in wet cellulose do not preexist – that is, they are not present until the water makes them. So an explanation of water sorption hysteresis in terms of the filling and emptying of preexisting bottles or openings is inappropriate. In addition, the hysteresis of water sorption on cellulose extends to very low relative vapor pressures, where no condensation exists and Kelvin's equation cannot apply. For example, 50% RH corresponds approximately to monolayer coverage according to the BET analysis and corresponds to approximately 1.79 equivalent layers of water according to the t isotherm. Below 50% RH, according to BET for­mulation, a complete monolayer has not formed, and below 18% relative humidity according to the t isotherm an adsorbed thickness equivalent to a monolayer has not formed. Yet water exhibits sorption hysteresis even below 10% RH. Clearly the concepts of condensation and of a liquid meniscus have lost their meanings in regions where even one monolayer is not complete.

For cellulose, the pore sizes available to water extend well into the micropore range below 1.0 nm. The mechanism of adsorption within a micropore is undoubtedly different than on a plane surface. Adsorption on an open surface is the result of the interaction of a water molecule with one surface only. For adsorption within micropores, because of the overlap of fields of force from neighboring walls, a cooperative pro­cess probably occurs such that pores fill com­pletely a t low relative vapor pressures (54). The process thus resembles the capillary condensa­tion in mesopores but because no true meniscus is realizable, this process in micropores is best designated as pore filling.

A different explanation of the general phenomenon of low-pressure hysteresis has been described by Everett et al. (57). Their explanation, originally proposed for adsorption of hydrocar­bons on charcoal, seems especially appropriate for the case of water on cellulose in that it pro­vides not only an explanation of hysteresis but

Figure 8. Sorption hysteresis as explained by irreversible changes in structure. Chemical potential in a system can ex­ist in several states of which only two are shown: I and II. Suffix 1 refers to solid (cellulose) and Suffix 2 refers to adsor­bate (water) [Everett (56)].

also a possible explanation of the increased creep under cyclic humidity. Their suggestion is that low-pressure hysteresis is associated with some distortion of the structure with consequent change in pore structure and adsorptive behavior. A thermodynamic description of the phenomenon is aided by a schematic representation (Fig. 8)of the chemical potential, µ, of solid adsorbent dur­ing adsorption and desorption in a system show­ing low-pressure hysteresis. The unperturbed solid is represented by I , the perturbed or ex­panded structure by II . When no adsorbate is present, so that I is the stable form of the empty solid structure. Conversion of I to I I during adsorption can occur reversibly at 0, or more likely by a jump a t some point P beyond 0 on the adsorption isotherm. On desorption, the system follows curve II and, a t low pressures, recovery by the solid of its original properties is very slow, retarded by a high-energy barrier. In the particular instance of the water-cellulose sys­tem where intercalation occurs by interlamellar penetration, one can describe the process in terms of a spreading pressure which enables an ad­sorbed film to pry open lamellae. The significance of spreading pressure was demonstrated by Christensen and Kelsey (58) who showed that on the adsorption isotherm larger amounts of moisture can be adsorbed by cellulose a t a given relative vapor pressure if that vapor pressure is obtained by one large step from a lower pressure rather than of many smaller incremental in­creases up to the same vapor pressure.

82 PAPER SCIENCE A N D TECHNOLOGY.. . The Cutting Edge

In the cyclic exposure of a stressed paper specimen, if a pore which has been pried open by an adsorption step does not close reversibly on desorption, then the next pulse of higher humid­ity will pry further into the separating lamellae. This sequential prying can progressively lower the number of stress-carrying hydrogen bonds and increase the rate of creep over what would oc­cur a t the constant higher humidity.

According to Everett et al. (57) low-pressure hysteresis is not expected in a loosely structured solid that can expand and contract elastically over a wide range, nor in a sufficiently strong and rigid solid where local deformations brought about by adsorption forces do not strain the material beyond its elastic limits. Low-pressure hysteresis is likely only in solids which are of in­termediate rigidity. Everett’s explanation of low-pressure hysteresis in many ways bears similarities to the earlier excellent work by Barkas (59) on swelling pressure and sorption hysteresis in gels. He proved by thermodynamic arguments that if a material is plastic – that is, one which shows permanent distortion under stress of sufficient magnitude – then hysteresis in the sorption isotherm must result. And accord­ing to Barkas, the principal cause of hysteresis in wood is its plasticity. Everett’s more recent sug­gestion that the inelastic distortion of the solid results from the intercalation of adsorbate molecules in the pore structure of the solid seems most appropriate for the case of water sorption on cellulose.

I t is also pointed out by Everett (57) that stress-strain hysteresis in charcoal is closely related to its sorption hysteresis. He suggests that a promising approach to understanding the behavior of charcoals is to treat low-pressure hysteresis as a consequence of stress-strain hysteresis in the solid brought about by stress in­duced by adsorption. Such a renewed approach should be equally fruitful in the analysis of the cellulose-water system.

Glass transitions The approach taken in this review has been that

the mechanical properties of paper stem from in­teractions in the cellulose-water system that are essentially surface interactions. This view seems eminently valid for crystalline cellulose especially a t low moisture regains, but when the solid substrate incorporates significant quantities of amorphous materials, the picture in the highly swollen state becomes describable in other terms. If the surface layers exhibit a large degree of water solubility, i t is tempting to describe the in­teraction on a molecular level in terms of a gel

system involving discrete polymeric chains rather than lamellar surfaces. In this view one describes water as a plasticizer and interprets its effect on the mechanical properties of cellulose as due to lowering of the effective glass-transition temperature of the polymer. Some success has been demonstrated for this approach. Salmén and Back (60) recently have shown agreement between theory and experiment if one considers only the amorphous fraction of the cellulose as the component interacting with water. The ap­parent difference between these views, however, is more semantic than substantive. A decrease in glass-transition temperature caused by an in­crease in moisture content can be explained by a mechanism that entails the replacement of inter-catenary hydrogen bonds by interaction with water. Goring (61) suggested a description recon­ciling both views. His suggestion is “that water does not plasticize cellulose a t a molecular level . . . but a t the microfibrillar level. Instead of bonds between molecules being loosened by water, bonds between microfibrils are loosened.”

Properties of water in cellulose pores So far we have considered the effect of water on

the properties of cellulose and how the intercala­tion of layers of water molecules between the lamellae of cellulose modify important properties of paper. In just the same way that interaction between water and cellulose modifies the proper­ties of cellulose, the interaction also clearly modifies the properties of water.

Water in thin layers between solid surfaces has often been reported to exhibit properties different from its bulk properties (62). So it is not surpris­ing that water in the microporous and mesoporous capillaries of cellulose will exhibit modified properties.

I t was mentioned earlier that in very narrow capillaries the force fields from neighboring walls overlap in such a way as to enhance the energy or interaction with an absorbed molecule. This enhanced interaction probably helps account for several phenomena. If the initial intercalation of water into the structure results in the disruption of network hydrogen bonds, then the new bonds formed with water must be of higher energy to ac­count for high initial heats of wetting (63). This enhanced interaction within microcapillaries also helps explain the apparent high densities reported for adsorbed water (64).

As increasing amounts of water are adsorbed, the transient capillaries expand, and the adsorp­tion potential decreases. Thus the first monolayer of water in the smallest pores can be considered

INTERACTIONS AT THE CELLULOSE-WATER INTERFACE 83

the most tightly bound water. Water in larger capillaries, further from the cellulose surface than the first layer, should not sense the presence of the surface, according to the BET concept. Yet, according to the Polanyi theory, the adsorption potential arising from the surface may extend several layers from the surface.

Froix and Nelson (65) using a pulsed n.m.r. technique studied the nature of water adsorbed on cotton cellulose. They distinguished several types of water of different apparent mobilities. They verified the existence of bound water reported by others (66). But they suggest two types of bound water: primary bound water (up to 0.09 g/g) and secondary bound water (from 0.09 g/g to 0.20 g/g). This secondary bound water is in­cluded in what they call “free” water (and equate to nonfreezing water). They point out, however, that “free” water in cellulose does not have the n.m.r. properties of bulk water but exhibits a line broadening, indicative of restricted motion. Thus it seems that the n.m.r. properties of water in layers both at the surface of cellulose and to a lesser degree in layers removed from the surface of cellulose are modified by cellulose.

Water in the porous structure of cellulose has reduced solvent capacities. I t is clearly unable to act as solvent for molecules too large to enter the pore. This apparently trivial case has been used by Stone and Scallan (67) and Feist and Tarkow (68) to develop accurate methods for determining the fiber saturation points of cellulosic materials. These polymer-exclusion methods also afford a means of determining in principle the pore size distribution in the swollen state. But even some molecules small enough to be able to enter the porous structure of cellulose find that not all the water within the pores can act as solvent. Rowland (69) recently reported that small water-soluble molecules characterized by limited hydrogen-bonding capabilities find only a frac­tion of the water in accessible pores available as solvent water. On the other hand, water-soluble solutes that hydrogen-bond as well as saccharides find all the water in an accessible pore available as solvent water.

Thus a number of phenomena seem to indicate that the effect of cellulose on the properties of water is not limited only to the first layer of ad­sorbed water. Similarly we have also seen that water in layers removed from the first monolayer has a clear effect on the tensile modulus of cellulose. This apparent action a t a distance im­plies molecular interactions of a long-range character. But the interaction between water and cellulose is clearly through hydrogen bonds which

are bonds of a short-range character. If one ac­cepts the polarization principles built upon Polanyi’s theory, one can explain the apparent long-range interaction as an interaction “transmitted” over large distances but based on the short-range interaction provided by the hydrogen bond. One possible conclusion that has been drawn from this interpretation is that long-range correlation based on short-range interac­tion implies structuring of some sort in the water within cellulosic capillaries (41).

Long-range interactions in the cellulose-water system

Perhaps a n al ternate approach to understanding the apparent long-range character of interactions in the cellulose-water system is by first considering conditions in which interactions stem clearly from dispersion forces. The discus­sion so far has dealt with the interactions of cellulose and water in which the system can be considered as water in cellulose. There are cir­cumstances in which the system is more ap­propriately considered cellulose in water. In pulp suspensions, the interactions between cellulosic fibers is not by means of hydrogen bonds. There are electrostatic repulsions between the usually negatively charged cellulosic particles and the always-present attraction between particles due to van der Waals or dispersion forces. To the ex­tent that pulp suspensions represent true col­loidal systems, there is a balance between the electrostatic forces of repulsion and the disper­sion forces of attraction. The Deryaguin-Landau-Verwey-Overbeek theory (DLVO theory) (70), which explains the balance of attractive van der Waals forces and repulsive electrostatic forces, provides the basis of understanding necessary for controlling the flocculation of papermaking fur­nishes. Let us for a moment consider flocculation of a fiber suspension that occurs a t a high moisture level, as for example on the paper machine wire. On flocculation, the forces of at­traction between fibers do not immediately become interfiber hydrogen bonds because a t these high moisture levels there are too many layers of water molecules between fibers. The main attractive forces between fibers must re­main the van der Waals or dispersion forces that were present in the suspension. I t seems therefore that the wet-web strength of paper must originate from van der Waals forces. Arguments that it originates from frictional forces caused by fiber entanglement, etc., obscure the fact that all such forces must have a basis a t the molecular level in terms of intermolecular forces.

The classical approach to understanding the

84 PAPER SCIENCE AND TECHNOLOGY.. . The Cutting Edge

nature of attraction between particles or between macroscopic bodies is the Hamaker (69) approach, which was incorporated into the DLVO theory of colloid stability. The essence of the Hamaker ap­proach is that the attraction between two bodies stems from the van der Waals forces exerted by the atoms in one particle upon the atoms in the other. These van der Waals or London dispersion forces are assumed to be additive pairwise, and the frequency and strength of each atomic oscillator are assumed to be unaffected by the neighboring oscillator. Another assumption that is made in the Hamaker approach is that only electromagnetic oscillations at UV frequencies produce attraction. Whereas the dispersion force between atoms is short-range, having an inverse seventh power distance dependence, the disper­sion force between large bodies is of much longer range and decays much more slowly with distance. Although poor justification for the assumptions partly invalidates the Hamaker ap­proach, the approach provided the first qualitatively-sound explanation of attraction between particles, and the explanation that van der Waals forces between macroscopic bodies cause long-range interactions.

In 1961, Dzyaloshinskii, Lifshitz, and Pitaeveskii (DLP) published an article entitled "The General Theory of van der Waals Forces" (72). In the authors’ theory, the interacting bodies are considered as continuous media. This ap­proach is valid when the distance between two surfaces, although small, is large compared to in­teratomic distances. From a large distance, two interacting particles see each other as bodies without atomic structure. The interaction between two bodies according to the DLP theory is considered to take place through a fluctuating electromagnetic field. Just as for an individual atom pair where the force of attraction stems from electric fields generated by moving elec­trons, within any material the component positive and negative charges are also always in motion. These transient generate electric fields in duce an electromagnetic parts of the material tromagnetic fields extend boundaries. Each point

charge displacements their vicinity. These in-interaction between all body, and the elec­

outside the material's within a body acts

simultaneously as a generator and receiver of electromagnetic fields.

The frequencies at which the charges in a material fluctuate are the same frequencies at which the material can absorb light and other forms of energy from applied electric fields. The absorption spectrum detects the extent to which charges in a material respond to an incident wave.

The continuum approach of the DLP theory is to interpret the attraction between two bodies as arising solely from the spectrum of charge fluc­tuations that are identical with the absorption spectrum of the material. All the spectral com­ponents (not just the UV) that have wavelengths that are large compared to atomic dimensions must be considered, and according to the DLP theory these are completely specified through the complex dielectric permeability of the material.

The great power of the DLP theory is that it provides a rigorous explanation for the attractive forces between two bodies. And this theory is ap­plicable to any bodies at any temperature in­dependent of their molecular nature, embedded in any medium. The only required information is knowledge of the complex dielectric permeabilities of both the bodies and of the medium between them and knowledge of the geometry of the system.

The DLP theory enables one to calculate the force of attraction between two plane solid sur­faces of any material separated by a gap. The gap may be filled with any fluid. The interactions in lamellar systems can also be treated, as can thin liquid films on the surface of a solid body. The theory has been used to provide a better understanding of several systems, i.e., hydrocarbon-water systems (73), mica-vacuum systems (74), plastic water systems (75), and liq­uid helium films (76). Except for the work of Evans and Luner (77) who studied the coagula­tion of microcrystalline cellulose in the light of DLP theory, the theory has been almost totally ignored by researchers concerned with cellulose-water interactions.

There are understandable reasons for the neglect of this theory. First, it is very difficult to understand, couched as it is in the modern ter­minology of quantum field theory. It is also ex­tremely difficult to apply. The limits of distances and range of interaction to which the theory validly applies depend in part upon the properties of the materials involved. Also, in order to apply the theory, one should, in principle, have com­plete information for the materials involved on the strength and location of all absorptions in the energy spectrum for all frequencies from zero through x-ray frequencies. Such complete infor­mation is, of course, never available.

All of these obstacles to the potential applica­tion of the DLP theory to the cellulose-water system are beginning to disappear. Parsegian (78) has provided an excellent review of the theory in a form that can be understood by chemists un-

INTERACTIONS AT T H E CELLULOSE-WATER INTERFACE 85

familiar with the nomenclature and mathematics of quantum field theory. Other excellent reviews have also appeared (79,80,82). Parsegian and Ninham (82) have shown how only partial knowledge of the required absorption data may provide sufficient information to determine the forces between bodies. The partial data for water has been provided by Parsegian (78), and Evans and Luner (77) have shown how approximate data can be obtained for cellulose. Although the theory is rigorous only when the distances are long-range (i.e., large when compared to interatomic distances), work has proceeded on extending the limits of the theory into the short-range distance regime. Mahanty and Ninham (83), for example, have shown that the theories of DLP and BET are reconcilable when one considers the role of in­teratomic forces in adsorption in thick layers.

The DLP theory provides a description of the sorption isotherm in the limit of adsorption of vapor upon a thick layer of previously adsorbed material:

where k is Boltzmann’s constant T is temperature A is the Hamaker constant v is the volume occupied per molecule

in the adsorbed state, and l is the thickness of the adsorbed layer.

This relationship, in which the logarithm of the relative vapor pressure is inversely proportional to the cube root of the thickness of the adsorbed layer, has the same form as isotherms derived earlier by Hill (84) and Halsey (85), using ther­modynamic arguments rather than a molecular-force approach.

This inverse cubic relationship does not fit ex­perimental isotherms for water on cellulose. A possible explanation may be that because of the lamellar structure of cellulose, thick enough layers (or slabs) cannot be formed on a cellulosic surface without influence from the surface on the opposite wall of the slit-like pore. At the high relative pressures where the DLP theory should apply, the sorption mechanism in cellulose is dominated by capillary condensation. (It should, however, be pointed out that even Hagymassy’s (25) t isotherm for water sorption on a poreless substrate also does not fit the DLP description of behavior at high relative vapor pressures.)

In their thermodynamic derivations of isotherms equivalent to the DLP isotherm, Hill and Halsey envision that the effect of the solid on

a molecule of adsorbate distant from the surface is enhanced by the presence of the underlying ad­sorbed layer. Halsey’s (85) description of this phenomenon is that transmission of the van der Waals forces across the adsorbed layer takes place. Now the DLP theory provides a rigorous explanation for this transmission of van der Waals forces.

Whereas the DLP isotherm seems not to describe the sorption of water on cellulose, other aspects of the theory may prove to be helpful in understanding interactions in the cellulose-water system. Luner and Evans have demonstrated that the behavior of suspensions of microcrystal­line cellulose can be explained in terms of the DLP theory and interactions between rod-shaped particles. Continued research along these lines will certainly improve our understanding (and eventual control) of coagulation and flocculation of pulp suspensions and of cellulosic waste water systems.

But over and above colloidal behavior, the DLP theory provides a formalism for treating the at­tractive forces between solid surfaces separated by a liquid medium that might be appropriately extended to explain the effect of water on tensile modulus. If the structure of cellulose indeed con­sists of large parallel plate-like pores, the attrac­tion between the opposite walls might be viewed in terms of the DLP theory. The theory goes con­siderably beyond earlier theories in that it is not limited to considerations of dispersion forces only, but also considers the effects of polar molecules in the system. Although the continuum approach is valid only for large distances (i.e., perhaps fully swollen pores), the lower limits of pore spacings to which the theory might be ap­plied remains a topic that needs considerable theoretical research. In essence there must be an attraction between opposite cellulosic walls of a water-filled parallel-plate pore. This attraction, according to the DLP theory, arises from the ab­sorption spectrum of cellulose and is affected by the complex dielectric permeability of the in­tervening water. The whole of the elec­tromagnetic spectrum causes this attraction, but the effect of some regions of the spectrum may dominate at different separations. (This results because of the finite velocity of electromagnetic radiation.) It seems probable then that as the separation between walls decreases, the attrac­tions become dominated more and more by por­tions of the electromagnetic spectrum that are characteristic of hydrogen-bond frequencies. In this way it might be possible to link the long-range interactions caused by van der Waals or dispersion forces with the hydrogen bonds (a

86 P A P E R SCIENCE AND TECHNOLOGY ... The Cutting Edge

special form of these dispersion forces) which we know are dominant in the short-range interac­tions.

It is noted that although the macroscopic or continuum theory as it now stands is appropriate for colloids and long-range interactions, it is not valid where one is concerned with the short-range cohesive forces responsible for the mechanical properties of condensed phases. At atomic distances, a different form of theory is necessary (i.e., the hydrogen-bond theory). Nevertheless, the DLP theory does provide a strong start towards synthesizing an explanation of interac­tions occurring over a wide range of distances.

Concluding comments The behavior of suspensions of cellulosic fibers

and the performance of paper both depend upon basic intermolecular interactions in the cellulose-water system. The overall effect of these interac­tions results from a complex interplay of material properties and geometry. For interactions at long distances (i.e., the behavior of colloids), this com­plex interplay of properties and geometry will eventually be understood and described in a quantitative fashion by the DLP theory of van der Waals interactions. The material properties functioning in the short-range interactions are dominated by the hydrogen-bonded natures of cellulose and water. The complex geometry of the solid phase is best understood in terms of a micro-and mesoporous lamellar structure, the characteristics of which depend upon its in­stantaneous moisture content. The complex in­terplay of this geometry and the intermolecular interactions between the hydrogen-bonded struc­tures of water and cellulose determine the proper­ties of paper. It would seem that in the coming years considerable effort might be devoted to a synthesis of views that would explain both the long-range and short-range interactions in the cellulose-water system, for clearly these interac­tions form the foundation of the papermaking process and are the underlying reasons for the properties of paper.

Swanson Thank you very much, Dan. We have time for

questions.

Richard W. Perkins, Jr. Would you comment on that layer-expansion of

fibers to give that beautiful fiber structure that you showed at the beginning? Is that critical... ?

Caulfield That was a cross section of a high-yield, kraft

pulp fiber that was prepared by the layer-expansion technique that is used at the Southern Regional Laboratory. It’s an exaggeration of the water-swollen characteristics. It is made by im­pregnating the fiber with the polymer butyl methacrylate and then removing the polymer later on.

Swanson As you well know, the sorption of water by

cellulose is exothermic and, therefore, at higher temperatures the cellulose takes on less water. Have you examined the lamellar structure of fibers by gas adsorption techniques after critical-point drying of a specimen, a virgin fiber, perhaps, that has been soaked in water until it was more or less in equilibrium and then heated to the boiling point to maximize this effect of temperature on the pickup of water? Do you know what happens to the lamellar structure under those conditions? This is not a strange phenomenon to the paper industry. While we don’t often heat stock to the boiling point we may heat it to 160°F and this has a very detrimental effect on the bonding strength of such pulps; wondered whether this showed up in the lamellar separations.

Caulfield No, I don’t. A lot of the complicating effects

have been ignored in my talk. I didn’t mention anything about what might happen to the distri­bution of hemicellulose at those high tempera­tures. There would be marked changes that have nothing to do with the lamellar structure.

Alfred H. Nissan John, I believe that where you heat stock, you

free it, you reduce slowness. . . . If you free it, you are reducing specific surface and specific volume and, therefore, would be closing up some of the surfaces. . . .

Swanson The question involves the freeing of stock after

it has been heated to a higher temperature. Yes, this should show up in gas adsorption studies us­ing the critical-point drying method. It should show up as a difference in the lamellar surface area, I should expect. Someone should look into this.

Question Would you comment on the persistence of the

hysteresis right down to very low relative humidities? I always thought that this was a reflection of the fact that the water clustered, rather than formed monolayers.

I

Caulfield Yes, at the very lowest relative humidities

there can't be any multiple layer formation. There still has to be access to individual molecules at the very lowest level. And this type of low-pressure hysteresis has been observed in other materials that are not cellulosic. Carbon black that is present as lamellar surfaces shows a low-pressure hysteresis with non-polar, gaseous ad­sorbates too. One of the proposed explanations is that of Everett and his group; it applies specifically to the case of charcoal and non-polar molecules, but it seems equally applicable to cellulose. This involves an irreversible change in the free energy of the solid substance, because of the separation, a prying apart, by the entering molecule – an actual non-equilibrium change.

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