Effect of cationic polyelectrolyte and surfactant on cohesion and friction in contacts between cellulose fibers

Effect of cationic polyelectrolyte and surfactant on cohesion and friction in contacts between cellulose fibers

Colloids and Surfaces A: Physicochemical and Engineering Aspects 167 (2000) 215 – 227 www.elsevier.nl/locate/colsurfa Effect of cationic polyelectrol...

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Colloids and Surfaces A: Physicochemical and Engineering Aspects 167 (2000) 215 – 227 www.elsevier.nl/locate/colsurfa

Effect of cationic polyelectrolyte and surfactant on cohesion and friction in contacts between cellulose fibers E.A. Amelina a, E.D. Shchukin a,b,c,*, A.M. Parfenova a, V.V. Pelekh a, I.V. Vidensky b,c, A.I. Bessonov b, G. Aranovich c, M. Donohue c a

Department of Chemistry, Moscow State Uni6ersity, Leninskie Gory, 119899 Moscow, Russia b Institute for Physical Chemistry, RAS, 31 Leninskii Prospect, 117915 Moscow, Russia c Johns Hopkins Uni6ersity, Baltimore, MD 21218, USA Received 30 November 1998; accepted 4 June 1999

Abstract The methodics and devices are presented for quantitative study of the characteristics of interaction in contact between individual fibers: friction force F in shear test, and cohesion force, i.e. contact strength p in rupture test. In experiments with cellulose fibers in various liquid media, the friction coefficient m has been estimated, and the molecular component of friction force related only to attraction of fibers, in the absence of any external normal load has been found. The specific free energy of interaction U has been evaluated in measurements using model samples with the nature of surface similar to that of cellulose fibers. The effects of cationic polyelectrolyte and surfactant: polyethyleneimin and tetrabuthylammonium iodid on these parameters have been quantitatively determined. Complicated, non-monotonic (with several extrema) dependence have been estimated between values F, m, p, U and surfactant concentration C. Comparison of these data with the z-potential measurements of cellulose fibers in the same surfactant solutions allows one to propose an explanation of the mechanisms of these polyelectrolyte and surfactant influence on fiber interactions. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Fibers; Cohesion; Friction; Cationic polyelectrolytes and surfactants

1. Introduction The rheological, i.e. structure-mechanical characteristics of the highly disperse fiber materials are  This article was originally submitted to the Per Stenius Special Issue. * Corresponding author. Tel.: + 1-410-3586270; fax: + 1410-5168996. E-mail addresses: [email protected] (E.A. Amelina), [email protected] (E.D. Shchukin)

determined by the interactions in contacts between individual fibers and by the rules of summation of contact strength. The control of cohesion of fibers (or threads) by means of surfactant additives is a basic physical–chemical approach in operating properties of these materials both in processes of their manufacturing and using [1]. This concerns a broad variety of fiber materials: both natural and synthetic, including those in paper/pulp industry. At the consecutive

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steps of the paper sheet formation, transitions must be provided from the minimal cohesion between cellulose fibers in pulp during its homogenizing and casting, to the contact strength which is sufficient for maintaining connectness of the system in the course of dewatering, and to maximal cohesion of fibers in a final product. Studies in this area are devoted mainly to the viscousplastic behavior of paper fiber suspensions, flocculation, flow character [2 – 13], i.e. properties depending on collective behavior of fibers, their 3-dimensional structure formation. As a possible model of flocculation, the entanglement (interlocking) of fibers is considered assuming sufficient fiber flexibility [11 – 13]. The problems of individual fiber interactions and their direct measurements are considered in rather few works [14–18]. The peculiarities of fiber systems are determined, on the one hand, by inhomogeneous (mosaic) character of fiber surface, and, on the other hand, with the participation of a fiber, due to its anisometry, in the formation of a number of local bonds. Rheological properties of fiber structures reflect the resistance of inter-fiber bonds both to their rupture under the effect of normal stresses, and to shear, under tangential ones. This means that friction forces play significant role in contact interactions of fibers. Normal loads on fibers may be small, or absent at the stage of homogenization of paper pulp. Under such conditions, the friction force is caused by the molecular attraction of fibers, and depends essentially on their surface properties. Changing of these fibers surface properties in corresponding direction with the use of various surface-active additives allows to control the rheological behavior of pulp, to obtain effective adhesion between paper fibers and particles of a filler, and also to achieve optimal conditions for textile fibers spinning, etc. [19]. A small radius of curvature of contacting areas of fibers results in very low cohesive forces. This implies the necessity to develop special, highly precise methods and devices to measure these small forces in contacts between individual fibers, in the broad range of conditions, including both normal rupture and shear, and tests in various surfactant solutions. These measurements should

allow to reveal the contribution of molecular attraction to friction forces and to present also a general characteristic of interactions in a given medium, invariant with respect to the specimen geometry, i.e. thermodynamic value of the free energy of interaction. In this paper, the technique for such experiments with individual fibers is described, and the results of studies of cationic polyelectrolyte and surfactant effect on fiber interaction are considered. In further studies, these data will be used for the development of physical–chemical models of structure formation, transformations and fracture in paper pulp and other fiber systems, i.e. establishing connection between microscopic and macroscopic, rheological characteristics.

2. Technique and materials

2.1. The de6ice for studying cohesion of indi6idual fibers under conditions of shear The scheme of apparatus is presented in Fig. 1. The rotated (tilted) P-like frame 1 serves as the main element. The frame is rotated by an electromotor and a reducer 2, 3 to which it is fastened with a rigid holder 4. The tilt angle a of the frame is shown with a pointer 5 and scale 6. Samples 7 and 8 are attached to the frame. Either fibers or thin threads may be used as samples. One sample,

Fig. 1. The scheme of device for studying friction forces between individual fibers under conditions of shear.

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fiber AB is fixed between tips A and B of the frame; the second one, fiber CD is connected with frame in point C and bent over AB fiber at an angle of 90°. The free end D is connected with a weight P providing compressive force N between fibers in point O of contact. (This loading system is shown in Fig. 1 with a dashed line.) For the initial, horizontal position of the frame, N= P. The rotation of the frame, i.e. the tilt with respect to horizontal orientation at an angle a creates shear force F =P sin a; corresponding normal force equals N =P cos a. The critical value of a is registered at which fiber CD begins to move along AB. This initial shift is observed with horizontal microscope 9. Cup 10 is used for measurements in liquid media. The principle of such measurements of contact strength between fibers was proposed by Yakhnin [14], and later used in studies carried out in the Department of Colloid Chemistry at Moscow University [15 – 17]. Recently, some essential modifications have been introduced in this method. In the previous model, fibers were attached to the frame with glue; the weight was immersed into the liquid together with the frame. The glue joints and weight were in contact with the liquid medium during measurement time. Such contact should be avoided in studies of surfactant small additives to prevent possible influence of soluble components of glue and contaminations from weight. These undesirable factors are eliminated in the new construction of the device. Instead of glue, the mechanical fixation of fibers is used, and the weight P is placed out of the cup with solution. The lengthening threads are connected to the ends of fibers by special knots (e.g. similar to the 8-like, or some other bends known in marine practice) which do not damage fibers. The threads connected with fiber AB are attached to the frame by special, tiny, fork-like clamps. The thread connected with the C end of fiber CD is fastened to the frame; the thread 11 connected with the opposite end D is put over block 12 (which has a very small friction moment), and is placed above a cup filled with liquid. The weight 13 is attached to the free end of the thread. All working parts of the device are arranged on platform 14 preventing vibrations. In

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Fig. 2. The scheme of device for studying cohesive forces between individual particles (fibers), i.e. rupture under conditions of normal tension.

this new model, the shift of fibers is also achieved by rotation of frame 1. Thread 11 may be connected with sensitive torsion scales, instead of weight. This allows to extend significantly the range of loads P, down to 10 mN. In another model of the device, the frame remains immobile; the shift is provided by the tilt of the block holder, and the corresponding tilt of vertical part of the CD fiber. In this case, the reducer of electromotor is firmly fastened to a vertical block holder 12; during rotation, it is parallel to the thread going over block.

2.2. The de6ice to measure cohesi6e forces between indi6idual fibers under condition of rupture caused by a normal load The apparatus constructed earlier [20] in the Colloid Chemistry Department of the Moscow University to measure cohesive forces between macroscopic (several millimeter in size) particles was used as a basic one. It was essentially modified to allow measurements of very small cohesive forces between thin fibers. The sensitivity of a dynamometer was improved, and a special scheme for fastening fibers was elaborated. The magnitoelectric microampermeter 1 serves as a highly sensitive dynamometer, the principal element of this device (Fig. 2). In this case, a microampermeter for 5 mA was used. Due to the

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extreme pliability of this system, it allows to measure small forces, down to 10 nN, and even to a few nano-newtons. The fiber samples (a and b) are attached to two holders 2 and 3. Holder 2, with a bent end is adjusted to the frame of microampermeter, and can rotate around vertical axis when electric current passes through the frame. The other holder, 3 is connected with manipulator 4 allowing the sample to be moved in three mutually perpendicular directions. For measurements in liquid medium, the horizontal parts of holders with fiber samples attached to them are immersed in a cup 5 filled with a liquid. Reliable defense against vibrations is achieved by using a heavy metal platform placed on thick foam-polyurethane. The samples are brought in contact by a manipulator. Touching is observed with a long-focus microscope as the first deviation of sample b from the initial position. Passing a current through the microampermeter frame, one applies a compressive load f to samples. The direction of the current is then changed; this results in a tensile (rupture) force p. The value of the current is measured at which rupture of contact occurs, observed also with a microscope. A special electrical dividing scheme is used for operating direction and value of the current through the frame; it consists of a power source (12 V), milliampermeter, and a system of potentiometers and resistances. For calibrating this device, the correlation is established between current value I in the frame, torque moment M= kI, and force f =M/l =kI/l provided by this moment; k is the constant of apparatus, l is the length of horizons part of the L-shaped holder 2. The accuracy in measuring compressive force f and rupture force p is of 1% to several % in the range from 10 mN to 100 nN, and of 10% for small forces p of the order of 10 nN, and down to a few nN. The fiber samples with the length of 3 mm are attached to the holders by means of special clamps shown in Fig. 3. Fiber 1 is put across the tip of a miniature polystyrene cylinder 2, and fixed by a thin compressing polystyrene ring 3. Tiny grooves are made at the edges of the cylinder tip for better positioning of the fiber. The cylinders with fiber samples are attached, by

polystyrene clutches, to holders so that, after approaching each other, fibers are crossed at the angle of 90°.

3. Materials Samples of different types have been used: 1. The cellulose fibers were those taken from the bleached cotton fabric (presented by BASF) and from unbleached commercial paper, with rough surface, and also from bleached sulfite pine pulp. The diameter of fabric fibers was of the order of 10 mm, and of the paper ones — approximately 20 mm. In pure water, fibers were negatively charged, with z-potential of about − 24 mV. 2. The viscose (rayon) fibers and threads (The Khimvolokno Res. Inst., Moscow), with rather smooth surface, 30 mm in diameter. Initially, these fibers were noticeably hydrophobic; after their washing in alcohol and water, this hydrophobicity lowered a little. 3. The spherical molecularly smooth particles (fused glass), 3 mm in diameter, covered with acetylcellulose (AC) (Sigma [900-35-7], 40% degree of substitution). In aqueous medium, that powder AC showed small negative charge (z-potential about − 4 mV). AC films 50 mm thick were deposited with the varnish method, from the 10% acetone solution. The chemical composition of AC films and cellulose fiber surfaces is not fully identical, and

Fig. 3. The scheme of holders for fibers.

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films are less hydrophilic. Nevertheless, their surface properties are sufficiently alike to allow the qualitative comparison of the trends in cohesion and friction changes caused by various active component in the ambient medium, such as cationic polyelectrolyte or surfactant. Using of such smooth macroscopic particles, with known (and rather small) curvature of the surface allows one to establish, on the basis of measurements of cohesive forces p in particle contact, the invariant thermodynamic characteristic, the free energy of interaction U of surfaces which properties are alike to those of fibers. For this purpose, Derjaguin’s equation is used [21]: p= pKU, where K is a geometrical parameter dependent on curvatures of contacting areas of surfaces. For two spherical particles of the same size, K equals their radius R. The following surface-active additives have been used: 1. Cationic polyelectrolyte polyethyleneimine, PEI (presented by BASF, non-modified, molecular weight 60 k), with relatively low surface activity, widely used as an additive in paper industry, and 2. low-molecular cationic surfactant — highly surface-active tetrabuthylammonium iodid (TBAI) (Aldrich [311-28-4]).

4. Results and discussion Three series of experiments have been carried out: 1. Measurements of friction forces F in point contacts between crossed individual fibers; 2. Direct measurements of cohesive forces (contact strength) p between individual fibers under conditions of rupture; 3. Measurements of cohesive forces (contact strength) p between macroscopic particles covered with AC, allowing to estimate the free energy of interaction of acetylcellulose surfaces. All three series were performed in air, in water, and in PEI and TBAI aqueous solutions.

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Fig. 4. The dependence of friction force F(g) on normal load N(g) for cotton fibers in water.

4.1. Friction of fibers Fig. 4 presents the results of measurements of friction forces of cotton fibers in water as dependence F= F(N). For similar loads P, and for the same fibers, the values of angle a reveal broad scatter. The large scatter takes place, correspondingly, for values F= P sin a and N= P cos a. Values F and N related to a given load P are located in Fig. 4 at inclined segments a–d. For each load P, the histograms of distribution of values F and N were plotted. Maxima in these histograms correspond to the largest density of data at segments a–d; these areas are denoted by circles. Data presented in Fig. 4 show that the dependence F(N) may be approximated, in the range of loads PFseveral 10 − 4 N, as a straight line crossing the initial of co-ordinates. The tangent of its slope characterizes the friction coefficient m. Significant scatter of m values is observed for different couples of fibers. The data on measurements in the air and in the cationic additive solutions were treated similarly. In all cases, proportionality between F and N was observed which allows considering the tangent of slope of F(N) line as an invariant parameter, the friction coefficient in a given media. The accuracy in measuring this coefficient m is of 5–10%. It is remarkable that high values of friction coefficient of cotton fibers, of 0.5 and more, both in the air and aqueous medium are found, which exceed significantly commonly known engineering values of 0.3 and less [22].

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If the friction coefficient of fibers is calculated as a ratio F/N for a given load P, then it reveals a tendency for increasing at small loads P B 10 − 4 N. A similar situation was observed in study [18] using different paper and synthetic fibers. High values of m for cellulose fibers and increase in m at small loads P can be related to the roughness of fiber surface. The similar conclusion may be drawn from the fact that the highest m values are observed in the very first measurements of a given couple of fibers; during the consequent tests, some decrease in m takes place, probably, due to the smoothening of fiber surface after repeated shears. For viscose fibers, essentially smoother ones, such increase in m is small, and appears only at significantly low loads. The average value of m for cotton fibers in air, both for repeated tests with a given couple, and for different samples, is of 0.6. In pure water, this coefficient for cotton fibers is a little less, maintaining, however, the high mean value of about 0.5. This behavior may be related to a number of factors. In the first place, these fibers are very hygroscopic; the absorbed moisture causes hydration and, possibly, swelling of surface. Thus, a contribution to the high value of friction coefficient may be made by gluing swelled surfaces together. In the second place, some geometric inhomogeneity, nappiness of fiber surface was found to develop in aqueous medium. Microscopic observations show that a number of teasels on fiber surface increases in water, and they are oriented more rectangular with respect to fiber. For elucidation of this factor, special studies are planned of the influence of the duration of fibers immersion in water before bringing them into contact, of the role of consecutive changes in the shear direction, etc. The values of friction coefficient estimated between individual fibers can be compared with data on macroscopic friction between papers and its dependence upon smoothness and humidity [31]. For the smooth fibers of viscose (rayon), friction coefficient in the air is much lower, of the order of 0.3. In pure water, the m values for these fibers grow strongly, up to 0.8. This increase can be related to the essential hydrophobicity of the

fiber surface, that may be inherited partially from oiling in process of fabrication Microscopic observation shows, indeed, poor wetting and strong aggregation of such fibers in water. Careful washing of those viscose samples in ethanol and water before tests resulted in some lowering of the m value, down to 0.6, nevertheless, significantly higher than in air. Alike to this, increase in the friction of viscose fibers in water was observed also in [18].

4.2. The influence of PEI and TBAI additi6es on friction of fibers The data on friction of cellulose fibers in the cationic polyelectrolyte and surfactant solutions show that the dependence of friction force or friction coefficient on concentration is not monotonic. Fig. 5 illustrates the dependence of friction force (in relative units) on PEI concentration (MW 30 k) in aqueous solutions obtained earlier [16,17] in our laboratory for cellulose fibers taken from paper. Fig. 6 presents the curve m(C) estimated recently, with the method described above, for cotton fibers in PEI solutions (different brand, MW 60 k). The character of two dependences is very similar; both curves reveal consequently a maximum at the smallest concentrations, a sloping region in a rather broad range of higher concentrations, and then a steep fall of F and m values caused by further increase in concentration up to C\ 10 − 5

Fig. 5. The dependence of friction force F (in relative units) on concentration of PEI solutions for cellulose fibers [16,17].

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Fig. 6. The influence of PEI additives on friction coefficient m between cotton fibers.

M. This qualitative similarity allows one to assume that surface properties of these two types of fibers are rather alike, and to use the data about PEI influence on the z-potential of fibers (paper samples) given in Fig. 7 [16] for analysis of complicated dependencies in Figs. 5 and 6. As this is clear from Fig. 7, the PEI additives cause the change of z-potential from initially negative values in pure water to positive one, with the transition through isoelectric state at C: 10 − 8 M. The maximal positive value of about 40 mV is reached at C:10 − 6 M. The following decrease takes place when increasing concentration to C: 10 − 4 M. On this basis, the maximum in F(C) or m(C) can be explained as a result of neutralization of

Fig. 7. The dependence of z-potential of cellulose on concentration of PEI solutions [16].

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the negative charge of fiber surface due to adsorption (still low at this stage) of cationic PEI and decrease in the forces of electrostatic repulsion. The following change in the sign of charge and increase in electrostatic repulsion caused by growing of concentration till 10 − 7 M result in weakening of cohesion and, correspondingly, in the decrease of friction coefficient. In the relatively broad range of high concentrations, both F(C) and m(C) dependencies manifest constant level; this may be connected with reaching the limit adsorption and formation of a dense adsorption layer providing the most effective screening of fibers against cohesion (structure-mechanical barrier [23], or steric stabilization). Electrostatic repulsion due to sufficiently high positive values of z-potential contributes in the same direction. Alongside with this, PEI is a polymer, with relatively high molecular mass, and its influence upon fiber interaction can be considered in terms known for stabilization and flocculation by polymers [24]. In this approach, the steep decrease in F and m at C\ 10 − 4 M may be explained as the depletion stabilization effect and additional weakening of fiber interaction. (Such decrease is absent in Fig. 9; this can be caused by the roughness of fiber surface after long stay in aqueous medium.) In principle, in the range of concentrations corresponding to the right part of the plateau in F(C) and m(C) curves, one could predict arising a minimum and a second maximum, caused by the depletion flocculation effect (disadvantage of polymer molecules presence in the thin gap between fibers due to the loss in configuration entropy) and increase in fiber cohesion. Absence of such extrema may be explained as minor role of these effects with respect to steric stabilization and electrostatic repulsion. However, the second extremum (minimum) in the F(C) dependence does appear if the tests are carried out in solutions of the strongly surface-active, low molecular quaternary ammonium salts, including TBAI (Fig. 8 [15]). In that case, the increase in friction forces is caused by hydrophobization of the surface of fibers and strengthening of their cohesion. The above data relate to experiments in which fibers were kept in PEI solutions for several

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E.A. Amelina et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 167 (2000) 215–227 Table 1 The values of friction coefficient m of fibers in water at different pH pH m

Fig. 8. The dependence of friction force F (in relative units) on concentration of TBAI solutions for cellulose fibers [15].

hours; this time is believed to be enough for achieving adsorption equilibrium. Increase in this time to 1–2 days results in some changes (Fig. 9). In the range of smallest concentrations, the maximum in m(C) curve still exists. At higher concentrations, in the broad range of C= 4× 10 − 7 – 10 − 4 M, the friction coefficient of fibers in PEI solutions remains practically the same as in pure water; values of m for all these concentrations are remarkably higher than in the previous case (Fig. 6). Such increase in friction coefficient after durable stay of fibers in solution may be related to the swelling of fibers and in-

Fig. 9. The dependence of friction coefficient m between cotton fibers on concentration of PEI additives after durable (1 – 2 days) stay of fibers in solution.

6.5 0.55

7 0.55

8 0.6

9–10 0.78

14 0.85

crease in their roughness (surface nappiness, microscopically observed), say, due to the increase in pH of solution caused by PEI. The measurements showed that variation of PEI concentration from 10 − 9 to 10 − 4 M changed pH of the medium from 6.5 to 9. So, the data on measurements of F and m in PEI solutions presented above relate to media with different pH, — and the problem arises, how strong could be the effect of pH changes on the character of m(C) dependence in various ranges of PEI concentrations. The special measurements of m carried out with cotton fibers in aqueous media with different pH confirm the significance of such influence. Increase in pH values was obtained by the KOH additives, with corresponding monitoring. Results for one series of tests with the same couple of fibers are given in Table 1. Probably, the differences in kinetics of water and polyelectrolyte penetration have also to be taken into account in the detailed explanation of such observations. The significant growth of friction coefficient is observed in the range of pHF9, i.e. in solutions with the high PEI concentrations (F 10 − 4 M). But just in this area the drop in m values takes place. At low PEI concentrations, the pH values remain practically unchanged. This confirms that the increase in m at low concentrations and the decrease at high ones (Fig. 6) is related namely to the effect of PEI adsorption. After durable stay of fibers in PEI solutions (Fig. 9), the influence of high pH manifests in the absence of decrease in friction coefficient at concentrations of C:10 − 4 M and some above. The results described above illustrate the opportunities to use the methodics and techniques elaborated in this work for measurements of the friction coefficient in the unit (point) contact between individual fibers, and for the quantitative characterization of the dependence of this parameter upon ambient medium and other con-

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ditions taking place in dispersions of fiber materials. The influence of surface properties of fibers on friction coefficient, the effects of cationic additive on this coefficient are complicated, manifold and diverse. The role of surface properties can be particularly great when the normal component of the load is either small or absent. In this case, the force of friction is defined (only) with the cohesive force caused by molecular attraction of fiber surfaces, particularly, its dispersion constituent. This component of friction force controls mainly macroscopic, rheological properties of paper pulp in processes of homogenizing. In accordance with the Derjagin’s molecular theory of friction [21,25], the friction force is defined by equation F =m(N + N0), where N is the normal component of applied load, N0 is the sum of molecular attractive forces. In the absence of external loads, the friction force is caused only by the force of molecular attraction N0, i.e. Fm = mN0. In aqueous media, in ionic surfactant solutions, the fiber interaction includes an electrostatic (repulsion) component caused by electric double layers, and the value of N0 is the balance of all surface forces; for simplicity, this value and corresponding components of friction force are described here as molecular forces. Because of the small radius of curvature of fibers, values of N0 appear to be much less than minimal normal loads N used in the described above method of measuring friction force F and coefficient m. This does not allow to distinguish the molecular component of friction force by the simple linear extrapolation of the F =F (N) dependence down to N = 0. However, the evaluation of this component of friction force of fibers is essential for understanding of the mechanism of surfactant effects on fiber friction and, correspondingly, on rheological characteristics of fiber aqueous dispersions. This evaluation can be obtained from the direct measurements of cohesive forces p = N0 in contact between two crossed fibers, in the normal rupture tests. Using values of friction coefficient m found in the above described experiments, one can estimate molecular component of friction forces as Fm = mp.

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4.3. The PEI and TBAI effects on cohesi6e force p between fibers and molecular component of friction Measurements of cohesive force p in contact between individual fibers in the normal rupture tests were carried out with the precise apparatus described above. These experiments were provided with cellulose fibers taken from paper, in air and in aqueous solutions of cationic surface-active PEI and TBAI. In a series of tests used here as an example, the cohesive force in a point contact between fibers was found in air as of 0.18 dyne (1.8× 10 − 6 N); this is rather high value, at the level of cohesive forces in phase contacts, e.g. those arising between crystals during their bridging [20]. The paper and cotton fibers occur sufficiently similar in their nature. This allows one to use the same value of friction coefficient m: 0.6 for evaluation of the molecular component of friction forces in both systems. In such approach, one finds for this component of friction force at a point contact in air the value about f: 10 − 6 N. As mentioned above, friction coefficient has a tendency to some increase at the smallest loads. Thus, the true value of the considered friction force can be even more. High values of p and F in the air are probably caused by the interaction of hydrophilic parts of contacting surfaces which are capable of forming hydrogen bonds; this is in accordance with the high hydrophilicity of paper fibers. Arising of the large number of these point contacts which accompanies the formation of textured fiber structure can provide significant strength of blotting paper (i.e. unglued structure with coagulation contacts only) reaching several tens of MPa (: 1 kG mm − 2) [26]. The high hydrophilicity of cellulose is responsible for the abrupt, close to two orders of magnitude, reduction of the cohesive force p of paper fibers in water at the expense of hydration of their surface that makes impossible any attraction of hydrophilic parts. Direct measurements show that cohesive force p in water is about 4× 10 − 8 N; correspondingly, the molecular component of friction force at a point contact evaluated as Fm =mp occurs to be of (2–3)× 10 − 8 N.

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Fig. 10. The influence of PEI on cohesion force (attraction) p between paper fibers under conditions of normal rupture.

The data on the effect of cationic additives on cohesive force p between fibers are presented in Figs. 10 and 11. Like in the case of friction forces and coefficient measurements, the dependence p(C) is also non-monotonic one, with the maximum in the area of the same low concentrations at which the maxima in curves m(C) and F(C) are observed (Figs. 5, 6 and 8). For the further growth of additive concentrations, there is a tendency for the appearance of the second extremum, a minimum. In TBAI solutions, this is in the range of concentrations corresponding to those at which similar minimum is presented in curves F(C). In PEI solutions, such minimum in p(C) takes place at concentrations corresponding to the

Fig. 11. The influence of TBAI on cohesion force (attraction) p between paper fibers under conditions of normal rupture.

constant level in F(C) and m(C) dependence. The biggest additives of PEI, CF 10 − 4 M did not cause any significant decrease in cohesive force p; this behavior is different from that of m and F (after short time of keeping fibers in solution, Figs. 5 and 6). However, the dependence p(C) was found completely identical to that of m(C) when the m values were measured for fibers kept in solution long enough time (Fig. 9). The similarity in concentration dependence of values p, and F, and their comparison with measurements of z-potential in PEI solutions (Fig. 7) allow one to consider the effect of cationic polyelectrolyte on cohesive forces p in the same manner as presented above, when discussing dependences m(C) and F(C). The growth of cohesion force p (with respect to pure water), with passing a maximum in the area of small concentrations of surfactant, can be related to decrease in the surface charge of fibers (initially-negative) and achieving isoelectric point when electrostatic repulsion is depressed, and conditions of maximum cohesion are provided. Decrease in p during consequent growth of concentration is caused by the increase in surface charge, now positive one, due to the increase in adsorption of cationic component; the role of electrostatic repulsion is growing. The trends of the next extremum appearance in the case of PEI may be connected, as considered earlier, with cohesion increase due to depletion flocculation; for TBAI, more probable reason for such behavior is the surface hydrophobization and strengthening of cohesion, prevailing electrostatic repulsion. As mentioned above, measurements of cohesive forces p in contacts between crossed fibers in water and in surface-active substance solutions allow one to characterize quantitatively the additive effects on molecular component of friction forces in the point contact. This component may be calculated as Fm = mp, using values of m found in studies of fiber shear in PEI solutions (Fig. 6). Fig. 12 presents the dependence between value of Fm = mp and PEI concentration. It reveals possibility of several times changes in friction forces from growth to decrease and to increase again. The small additives of PEI, C :10 − 9 –10 − 8 M

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for other disperse (porous) materials using data on the number of contacts and their strength [27,28].

4.4. E6aluation of surfactant influence on the free energy of interaction as a thermodynamic characteristic of the cohesion in contact between cellulose surfaces

Fig. 12. The influence of PEI additives on molecular component of friction force Fm = mp between cellulose fibers.

may cause two-fold and more growth of friction force (comparing with water). On the contrary, the high concentrations of PEI, C F 10 − 5 M, result in two-fold decrease in friction force. It should be stressed that the values of friction force found in such approach are related to an individual (point) contact between fibers crossed at 90° angle. In a real fiber dispersion, particularly, in textured one, e.g. during homogenizing of paper pulp, a lot of such point contacts emerge between fibers. The summary molecular forces of fiber attraction and friction forces caused by them depend on structure, size and geometry of fibers predetermining number of contacts per unit volume. These summary forces, as product of an individual contact strength and number of contacts reveal themselves in macroscopic, rheological resistance. Thus, the proposed method to measure small cohesive forces allows to estimate micro-characteristics of contact interactions between fibers and to evaluate quantitatively their dependence upon surface-active additives. This direct evaluation of cohesive and friction forces between fibers, particularly, their minimal possible values, is a necessary step in searching optimal surfactant additives to operate effectively properties of fiber systems. The next step planned by the authors in this field is to develop the physical – chemical rheology of fiber systems combining data on contact interactions under various media influence and modern models of fiber structures, as that has been done

The above described techniques of measurements of cohesion in contacts between crossed fibers in tests with shear and rupture open ways to evaluate only the force characteristics of fiber interactions. The micro-geometry, the curvature of contacting parts of surfaces is not definite, particularly, due to their roughness. This does not allow one to estimate the principal thermodynamic parameter of contact interaction, i.e. the specific free energy of interaction U (in a reversible, equilibrium contact). This parameter is important for transition from micro- to macro-characteristics of fiber disperse systems and estimations of the level of energy required by the system as a whole, which is necessary for optimizing processes of treatment of such systems at various stages of fiber materials manufacturing. The evaluation of thermodynamical characteristics of contact interaction between cellulose fibers was carried out with the model objectives, macroscopic spherical particles covered with acetylcellulose film. The surface properties of these particles are approximately similar to those of cellulose fibers. The large, about 1.5 mm radius of curvature and high smoothness of the contacting areas of these particles provide rather large, and reliably, reproducibly measured cohesive forces. This allows one to estimate the specific free energy of interaction (of cohesion) U, by use of Derjaguin’s equation, as U= p/pR; R is radius of particles. Like in the case of paper fibers, the forces of cohesion p of such particles decrease more than an order of magnitude in transition from air to water. It is known that acetylcellulose is, generally, less hydrophilic than cellulose (depending on degree of acetylation). However, very similar quantitatively changes in behavior of fibers and these, covered with acetylcellulose particles (AC-

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Fig. 13. The influence of PEI additives on cohesion force p between spherical molecularly smooth particles covered with acetylcellulose.

particles) in air and in water show approximately same level of their hydrophilicity. This gives basis for using the data obtained with smooth spherical particles for the analysis of surface-active components (PEI, TBAI) effects on thermodynamics of fiber interaction. Fig. 13 shows the dependence of cohesive force p between such macroscopic particles (in relative units) versus concentration of PEI solution. In Fig. 14, the concentration dependence is presented of the free energy of interaction U found with Derjaguin’s equation. The values found: 0.05–0.1 mJ m − 2 are in good qualitative agreement with data [29] on molecular adhesion forces between

cellulose films get by the surface force apparatus technique. These dependencies reveal also the complicated, non-monotonic character, with several extrema. The curves p(C) for AC-particles and fibers are alike in many features; the areas of concentrations in which the first (left) maximum and consequent minimum are observed, coincide practically for both types of samples. The analogous picture takes place also for TBAI solutions. Juxtaposition of these results with the data in work [30] on z-potential of acetylcellulose in aqueous solutions of the same additives shows a good correlation between this dependence m(C), and curves p(C) and U(C) for particles covered with AC: the left maximum corresponds to isoelectric state, and the minimum-to the high positive values of z-potential. The second (right) maximum in curves p(C) and U(C) is observed in the area of concentrations where z-potential is rather high, of 18–20 mV. In the case of TBAI, such second maximum can be related to the hydrophobization of particle surfaces, with the predominance of attraction forces over electrostatic repulsion. For PEI, the more probable reasons are changes in conformation of macromolecules in the thin gap and depletion effects. Different values of the minima and secondary maxima for AC-particles and fibers are probably connected with different adsorption activity of additives used as related to these samples (alongside with difference in hydrophilicity).

5. Conclusion

Fig. 14. The dependence of the free energy of interaction U of spherical particles covered with acetylcellulose on concentration of PEI solutions.

The methods and technique considered here allow one to estimate directly microcharacteristics of contact interactions between fibers and to characterize quantitatively the influence of various media and surfactant additives on these interactions. The measurements of cohesive forces in a point contact between fibers open the opportunity to evaluate the molecular component of friction force, i.e. the component related only to attraction force between contacting areas of surfaces, which exists in the absence of significant external normal loads, as this can take place in processes of paper pulp homogenizing.

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These data will be used in the further development of models of structure formation, transformations and fracture in paper pulp and other fiber systems, thus establishing connection between microscopic and macroscopic-rheological characteristics. The role of surface properties of fibers is particularly important in this aspect. The effect of surface-active additives upon these properties allows one to control fiber interactions and to operate rheological behavior of fiber dispersions. The direct estimation of cohesive and friction forces between fibers and, particularly, their minimal and maximal possible values may be useful for the search of optimal polyelectrolyte and surfactant additives providing effective operating of the fiber systems properties in desirable direction.

Acknowledgements The authors thank D. Horn, J. Gullichsen and P. Stenius for useful discussion of this work, and the BASF-for presented materials. This work was supported by the Russian Foundation for Basic Research, project No. 98-03-32754a, and by the TAPPI grant.

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