# Natural layer silicate as a modifier for polymeric nanocomposites/Naturalus silikatas kaip modifikatorius polimeriniams nanokompozitams.

1. IntroductionIn the building industry as a functional material for the manufacture for elements of different constructions (windows and doors, transport water and gas pipelines, finishing components such as baseboards, mouldings, flooring) and finishing the residential and industrial buildings and constructions used compositions based on polymeric, oligomeric and mixtures of matrix filled with components of different dispersibility, compound and mechanism of the modifying effect.

For a proper choice of a polymer composite with certain parameters of service characteristics (strength, heat-temperature resistance, wear resistance, resistance to burning, etc.) it is necessary to establish mechanisms of interaction of components, ensuring the formation of an optimal structure.

Among the most widespread types of composite materials used in the building industry are silicate-containing nanocomposites, in which as functional modifiers are used natural components-mica, clay, tripoli, zeolites.

Despite the rapidly developing scope of silicate-containing nanocomposites, many physico-chemical aspects of their formation and processing into products remain unclear. This fact hinders the process of expanding production of functional nanocomposite materials based on polymeric and oligomeric matrices with set parameters of service characteristics. The purpose of this work was to analyze the physical aspects of modifying macromolecular compounds of nano-sized silicate-containing particles.

2. Investigation

In modelling composite systems, which consist of a binder and a filling agent, it is possible to allocate three characteristic types of substances (Fig. 1): substance of a particle (1), binder (3) and a part adjoining a binder particle (a boundary layer, 2).

[FIGURE 1 OMITTED]

Let's consider the elementary case, when nanoparticles and the areas modified by them have spherical forms. Let the volume of system is equal to V, the number nanoparticles--to N, radius of a particle--to [r.sub.j], thickness modified surface layer--to [t.sub.y]

Hence the volume of a particle is equal to

[V.sub.j] = 4/3 [pi] [r.sup.3.sub.j]. (1)

Modified volume [W.sub.j] is

[W.sub.j] = 4/3 [pi]([r.sub.j] + [h.sub.j]). (2)

If N--number of particles, [V.sub.j]--volume of j, particles, then ratio

[C.sub.V] = [N.summation over (j)] [V.sub.j].

Defines the relative volumes of all nanoparticles, or parking factor. The ratio

[C'.sub.V] = <k> [N.summation over (j-1)] [V.sub.j]/V (4)

represents the relative modified volume, <k>--factor of overlapping of the sites, modified by a filler particles.

3. Results

It is known from experiments that even at small concentration nanomeasure particles of the modifier (up to 0,1 mass %) the properties of a composite on the basis of polymer can essentially change. In particular for details made from a modified thermoplastic wear resistance and strength characteristics can increase by 20-30 % ([TEXT NOT REPRODUCIBLE IN ASCII] 2007; Kittel 1956; Liopo 2003, 2005, 2007; Narai-Sabo 1969; Ouense, Pool 2). For an explanation of this experimentally fixed fact it is possible to use the following model.

Let mass concentration of particles filler [C.sub.m], mass and density filling matter [m.sub.f] and [[rho].sub.f] accordingly, [m.sub.b], [[rho].sub.b] is the same for binder agent. Then

[C.sub.m] = [(1 + [m.sub.b]/[m.sub.f]).sup.-1] (5)

From here, the volumetric concentration filler (3) is equal to:

[C.sub.V] = [(1 + [m.sub.b]/[m.sub.fb] x [[rho].sub.f]/[rho]).sup.-1]. (6)

If the volumes (and radiuses) particles of the modifier are identical, then

[C.sub.V] = [V.sub.1] x n = 4/3 [[pi].sup.3]n. (7)

Let the thickness of the modified layer be equal to h. Then for achieving a full modifying performance of a condition the necessary condition is

4/3 [pi][(r + h).sup.3] nk = 1, (8)

where k is the factor considering overlap and compactness of modifying areas. It follows from conditions (7) and (8):

[(1 + h/r).sup.3] = 1/k[C.sub.V]. (9)

As [m.sub.b] [much greater than] [m.sub.f], the condition (6) can be presented in the form of

[C.sub.V] = [C.sub.m] [[rho].sub.f]/[[rho].sub.b]. (10)

Then the expression (9) will become:

h/r = [[[[rho].sub.f]/[[rho].sub.f][C.sub.m]k].sup.-1/3]. (11)

For a limiting case when particles settle down in the points corresponding to the most dense packing of spheres with radius (r + h) and an overlap is absent, k = 0,74. When [r.sub.f]/[r.sub.b] = 4 (typical case) and [C.sub.b] = 0,1%, we shall receive:

h [much greater than or equal to] 15r. (12)

Naturally, the application of the offered model is restricted, because, first, it is necessary to prove that a condition (12) takes place, and, secondly, it is necessary to consider that at the manufacture of a composite it is difficult to reach a uniform distribution of modifying particles in volume binder matter. It is shown really that according to the argotic theorem at each point of substance of a composite at its hashing fluctuation changes of density occur; and there are divergent streams that cause occurrence and disappearance structures. Thus it is possible not only a formation but also destruction of clusters.

Many lower measure particles possess their own not compensated charge with a greater time of relaxation (Avdejchik et al. 2003; Kittel 1956; Belov 1976; Gusev 2005). If the modified volume in a composite to consider as a molecular cluster, its formation around of the charged particle of the modifier can be described as follows. The increase of the cluster's sizes occurs as a result of interaction of the polarized molecules of an environment region. From the theoretical analysis of processes of creation of a composite within the limits of various approximations the conclusion always follows that the process of developing a cluster in composite polymeric systems is inevitable. For modelling this phenomenon the use of the representations stated in (Avdejchik et al. 2003) is possible.

It is known ([TEXT NOT REPRODUCIBLE IN ASCII] 2007) that electric convention in poor conduction liquids arises at action of forces on a volumetric charge of a liquid. Then considering the ionic nature of conductivity, it means that the formed charges (ions or electrons) carry away plenty of neutral molecules of a liquid. But only when the relative concentration of charges in a liquid is small ([10.sup.-6] / [10.sup.-12]). The mechanism of such a result is not absolutely clear. However, it is possible to offer a model of its realization. According to it, even a small size of relative concentration of charges allows to explain the movement of plenty of neutral molecules of a liquid ([10.sup.-6] / [10.sup.-12] molecules in one charge). Neutral molecules in an electric field can be polarized and enter into interaction with a charge forming a structure "charge-layer" of dipoles. The external environment of this structure develops around itself a new layer of dipoles and so on, before some equilibrium formation which can be called "charging cluster".

The number of the molecules entering the charging cluster can be estimated by the following approximations:

1. The interaction of polarized dipole molecules of a liquid around of the central kernel is described by spherical symmetry.

2. The distribution of corners P(a) between the radius-vector which is starting with a charge, and dipole moment of a molecule submits to Gauss law with a dispersion [sigma].

3. The distribution of corners between dipoles of n-th and n+l-th layers are similar to distribution of corners for 1st layer.

Let's define the distribution of corners between dipoles of n-th layer and a radial direction. Let [[alpha].sub.n] is a corner between dipoles of n-th and (n-l)-th spherical layers. For the first layer distribution ([[alpha].sub.1]) looks like

P([[alpha].sub.1]) = 1/[(2[pi]).sup.1/2][sigma] exp(- [[alpha].sup.2.sub.1]/2[[sigma].sup.2]). (13)

For the second layer:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

when

[a.sub.21] = [a.sub.2]--[a.sub.1], [sigma] [much less than] [pi], P[([alpha]).sub.[absolute value of [alpha]]=[pi]] = 0, (15)

the expression (14) can be written down as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

Thus, distribution of molecules dipoles corners of the second layer of environment concerning a radial direction is defined by expression:

P([[alpha].sub.2]) = 1/[(2[pi]).sup.1/2] [[sigma].sub.2] exp(- [[alpha].sup.2.sub.2]/2[[sigma].sup.2.sub.2]], (17)

where [[sigma].sub.2] = [sigma][square root of 2].

Let's show, that if for (n-1)-layer fairly:

P([[alpha].sub.n-1]) = 1/[[sigma].sub.n-1][square root of 2[pi]] exp(- [[alpha].sup.2.sub.n-1] / 2[[sigma].sup.2.sub.n-1]], (18)

where

[[alpha].sub.n-1] = [(n--1).sup.1/2] [sigma]. (19)

That for n-th layer fairly condition:

P([[alpha].sub.n]) = 1/[(2[pi]).sup.1/2][[sigma].sub.n] exp(- [[alpha].sup.2.sub.n]/2[[sigma].sup.2.sub.n]], (20)

where

[[sigma].sub.n] = [n.sup.1/2][sigma]. (21)

Really, considering that an [[alpha].sub.n,n-1] = [[alpha].sub.n]--[[alpha].sub.n-1] and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] we obtain:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

Or

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

But

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

Then

P([[alpha].sub.n]) = 1/2[[pi].sup.1/2][sigma][n.sup.1/2] exp(-[[alpha].sup.2.sub.n]/2[[sigma].sup.2]n (25)

and

P([[alpha].sub.n]) = 1/[(2[[pi]).sup.1/2][[sigma.sub.n] exp(-[[alpha].sup.2.sub.n]/2[[sigma].sup.2.sub.n]), (26)

where

[[alpha].sub.n] = [n.sup.1/2][sigma]. (27)

If to accept, that the last n-layer is characterized by a dispersion of corner [[sigma].sub.n] = [pi], then the number of molecular layers in charging cluster is defined by expression:

n = [([pi]/[sigma]).sup.2]. (28)

In approach of the spherical form it allows to estimate and number of molecules in the cluster (N) equals to

N = 4[pi](nr).sup.3][rho]/3m. (29)

Where [rho] is density of substance, m is mass of one molecule, r its effective radius (in the considered case it is the dipole size).

The size of the dispersion [sigma] is defined by two opposite operating factors. The factor of the order stabilization of the polarized molecule at an electric charge is energy of communication of molecules of next two layers (u). And the factor disordering is energy of thermal movement (E). Root square the deviation of a corner a1 from zero ([sigma]) is defined by the ratio:

[sigma] [approximately equal to] [E.sub.T]/u = kT/2u. (30)

When calculating the energy of communication (u), it is possible to consider only axial interaction of the next molecules. It reduces u and increases [sigma]. Thus,

u [greater than or equal to] [[mu].sub.1][[mu].sub.1+1]/2[pi][epsilon][[epsilon].sub.0][r.sup.3], (31)

where [[mu].sub.i] is a dipole moment molecule on i-th 1ayer, r--the 1inear molecule size of contacting with surface substance, e is a relative dielectric permeability of environment. Dipole moment of the polarized molecule of non-polar dielectric is defined by relations

[chi] = 3([epsilon]--1)/[epsilon] + 2, (32)

[mu] = [epsilon][chi] E/[n.sub.0], (33)

where [chi] is polarizability of volume unit, [n.sub.0]--quantity of molecules in unit of volume, E--intensity of the electric field created by a charge.

For molecules of cluster we shall receive:

[mu] = 3([epsilon]--1)q/[n.sub.0]([epsilon] + 2)4[pi][epsilon] [R.sup.2], (34)

where q--the central charge of cluster, R--the distance from the charge central to a molecule.

An average value of communication energy <u> is defined by average value the dipole moment <[mu]>, when R = r/2.

<[mu]> = 3([epsilon]--1)q/[pi] [n.sub.0][epsilon]([epsilon] + 2)[r.sup.2]. (35)

Hence <u> is defined:

<u> = 9[([epsilon]--1).sup.2] q / 2[[pi].sup.3][n.sup.2.sub.0][[epsilon].sup.3] ([epsilon] + 2)[[epsilon].sub.0][r.sup.2]. (36)

Thus for [sigma] we shall receive:

[sigma] = kT[[pi].sup.3][n.sup.2.sub.0][[epsilon].sup.3] [([epsilon] + 2).sup.2] [[epsilon].sub.0][r.sup.7]/9[([epsilon]--1).sup.2][q.sup.2] (37)

For poorly conduction liquids (hydrocarbonic series of type [C.sub.n][H.sub.n], [C.sub.n][H.sub.2n], [C.sub.n][H.sub.2n+2] where n = 6 / 16), the entering into conditions constants have values: [epsilon] = (2-3), R [approximately equal to] 10[Angstrom], T [approximately equal to] 300K, [n.sub.0] [approximately equal to] 5 x [10.sup.26] ([C.sub.8][H.sub.16]).

Hence:

[sigma] = 1,38 x [10.sup.-23] x 300 x 31 x 25 x [10.sup.52]/9 x 4 x [(1,96).sup.2] x [10.sup.-38]

27 x 25 x 8,85 x [10.sup.-12] x [10.sup.-63]/9 x 4 x [(1,96).sup.2] x [10.sup.-63]. (38)

It means that we receive [sigma] [approximately equal to] 0,15, or n [approximately equal to] 400. Hence, within the limits of considered model thickness of the modified layer of a polymeric matrix substance has a size of about 400 nm. In this case for full modifying all volume of polymer radius of spherical modifier particles should be equaled to about size r > 25 / 30 nm. Such sizes of particles can be received in various technological ways of dispersion. At reduction of radius of particles in S time concentration of the modifier can be also reduced in S time at preservation of modifying effect. Thus, the considered model explains the action on a polymeric matrix including.

Charging clusters arise either in plasma, in gas or in a liquid, in high-molecular or other environments, but they can collapse both due to external influence and under the internal electric fields. If clusters may be simulated as a drop, and it is possible to use Rayleigh approach, according to which stability of the charged drop is defined by configuration action superficial (Fs) and Coulomb ([F.sub.c]) forces:

[F.sub.n] = 4[pi] [r.sup.2][gamma], [F.sub.c] = [(Ze).sup.2]/2r], (39)

where r is cluster radius, Z--number of not compensated electrons, [gamma]--factor of a superficial tension.

At small deformations drop cluster for describing of its stability, we can take the inequality

[Z.sup.2][e.sup.2] [less than or equal to] 16[pi][gamma][r.sup.3]. (40)

If filling agent particles consist of spherical atoms, it is possible to apply the theory of spherical packing for describing the structure with short-range force of interaction between particles. An internal atom in such a particle is surrounded by 12 neighbouring ones forming the first coordination sphere. If it is determined, N coordination spheres and radius of the first coordination sphere to accept for unit, then the radius of N-th coordination sphere ([r.sub.N]) is equal to:

[r.sub.N] = [square root of (N)]. (41)

The quantity atoms (k) on N-th coordination sphere is in Table 1. It means that the most dense spherical packing as for cubic face-centered crystals. The nanoparticles after grinding of crystals may have this cell.

The quantity atoms in these particle (QN) is determined by formula

[Q.sub.N] = 1 + [N.summation over (i=1)] [k.sub.i]. (42)

The considered models allow to understand the modifying action of doping small mass concentration nanodimensioned particles. However, for a more strict arguing adequacy of these models it is necessary for real processes to prove an opportunity of charge occurrence on surface particles. For this it is necessary to analyse the process of destruction of crystal after which there are two juvenile surfaces. These surfaces have different energy because of defects composition etc, in crystals with their new surfaces are different. For electric charges (electrons, ions, radicals, etc.) establishment of probability of charging transition we use a barrier model (Fig. 2). There is one-dimensional dependence of potential W=W (x), where the axis x is normal to juvenile surfaces of a crystal resulted.

In Fig. 2 function W (x) looks like

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (43)

[FIGURE 2 OMITTED]

Let's consider the movement of a particle from left to right from area 1 to 3. The wave equations for three considered areas look like:

[[PSI]".sub.j] = [k.sub.j] [[PSI].sub.j] = [0=.sub.=1,2,3], (44)

where

[k.sup.2.sub.1] = 2mE/[[??].sup.2], [k.sup.2.sub.2] = 2m(E--U)/[[??].sup.2], [k.sup.2.sub.3] = 2m(E--V)/[[??].sup.2]. (45)

For the solution, we take search in the form of:

[[PSI].sub.j] = [A.sub.j] exp(i[k.sub.j]x) + [B.sub.j][(-i[k.sub.j]x).sub.j=1,2,3. (46)

Without breaking a generality it's possible to consider [A.sub.1] = 1, [B.sub.3] = 0 because in the field 3 there is no wave moving from right to left, if the charge moves from 1 region to the 2.

It follows from a condition of a continuity of wave function and its derivative:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (47)

The factor of transparency (D) barrier U to a considered case is equal:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (48)

[A.sub.3], as one of roots of system (48), is described by the formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (49)

At the particle movement from area 3 through a barrier to area 1 at the same function W(x) (see 43), the system of the equations is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (50)

It which follows, then:

[B.sub.1] = 4[k.sub.2][k.sub.3]/([k.sub.1] + [k.sub.2])([k.sub.2] + [k.sub.3]) exp(-i[k.sub.2]l) + 4[k.sub.2][k.sub.3]/([k.sub.1]--[k.sub.2])([k.sub.2]--[k.sub.3]) exp(i[k.sub.2]l). (51)

The factor of a barrier transparency at the movement of a particle from area 3 to the left is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (52)

Hence, the ratio of factors of a transparency is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (53)

Thus, distinction of a deficiency degree in both parties of juvenile surfaces lead to development on it electrical charge sites with the sizes of much greater atomic power (Avdejchik et al. 2003, Ajayan 2004, Bragg, Claringbull 1967, Narai-Sabo 1969, Lopio 2007, Lopio 2005, Ouense, Pool 2, Lopio 2007, Gibson, Schultz 1993).

4. Conclusions

The physical basis of the implementation mechanism of the modifying effect of nano-sized particles of geosilicates in high-molecular matrices caused by the uncompensated charge with a large relaxation time is established. The presence of the charge promotes activating the adsorption interaction of polymer macromolecule with the modifier and forming in the periphery of the nanoparticle an ordered quasicrystalline layer that reinforces the composite.

Methods of forming the charge state in silicate-containing nanoparticles (thermal, mechanical, mechanochemical, etc) are determined by the composition of composite material and its functionality.

These results allow for an informed choice of components and technologies of manufacturing and processing the polymer nanocomposite materials used in the building industry.

doi: 10.3846/skt.2010.01

Received 14 12 2009; accepted 09 03 2010

Reference

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Avdejchik, S. V.; Liopo, V. A.; Struk, V. A. 2003. Bull. GrSU, Grodno, Belarus.

Bragg, U.; Claringbull, G. 1967. Crystalline structure of minerals. Moscow. 390 p. (in Russian).

Belov, N. V. 1976. Structural mineralogy essays. Moscow. 344 p.

Gibson, G. A.; Schultz, S. J. 1993. Appl. Phys. 73, 9, 4516.

Gusev, A. I. 2005. Nanomaterials, nanostructures, nanotechnologies. Moscow: Physmathlit. 416 p.

Kittel, Ch. 1956. Introduction to solid state physics. N.-Y. Chapman & Hall. LTD. 683 p.

Narai-Sabo, I. 1969. Inorganic crystal chemistry. Budapest. Pub. Of Hungary SA. 504 p.

Liopo, V. A. 2008. Micas crystals effect on the surface water films, Grodno, GSU bulletin. Ser. 2. V. 3: 93-100.

Liopo, V. A. 2007. Dimensional boundary between nano- and bulk states: theory and experiment, Grodno, GSU bulletin. Ser. 2. V. 2: 65-71.

Liopo, V A. 2007. Definition of maximum size of nanoparticles, Grodno, GSU bulletin. Ser. 2. V. 1: 50-56.

Ouense, F.; Pool, Ch. 2005. Nanotechnologies. Moscow: Technosphere. 334 p.

Liopo, V. A.; Nikitin, D. A.; Struk, V. A.; Nikitin, A. V. 2003. Nanomeasure mineral modificator of polymeric composite materials, in X-ray diffraction & crystal chemistry of minerals. St. Petersburg, 339-340.

[TEXT NOT REPRODUCIBLE IN ASCII], 2007 / C. B. [TEXT NOT REPRODUCIBLE IN ASCII] B. A. [TEXT NOT REPRODUCIBLE IN ASCII] [Avdejchik, S. V. et al. Polymer silicate machine building materials (ed. V. A. Struk)]. [TEXT NOT REPRODUCIBLE IN ASCII]. 431 c.

Valerij Liopo, Sergey Avdejchik, Alimjon Ryskulov, Vasilij Struk

Grodno State Agrarian University, Tereshkova st., 28, 230008 Grodno, Belarus

E-mail: gffh@mail.ru

Valerij LIOPO. Professor of the Department of Technical Mechanics and Material Sciences of Grodno State Agrarian University, Tereshkova 28, 230008, Grodno, Belarus, telephone (job): +375 152771906

Sergey AVDEJCHIK. Associate Professor of the Department of Technical Mechanics and Material Sciences of Grodno State Agrarian University, Tereshkova 28, 230008, Grodno, Belarus, telephone (job): +375 152771906

Alimjon RYSKULOV. Associate Professor of the Department of Technical Mechanics and Material Sciences of Grodno State Agrarian University, Tereshkova 28, 230008, Grodno, Belarus, telephone (job): +375 152771906

Vasilij STRUK. Professor of the Department of Technical Mechanics and Material Sciences of Grodno State Agrarian University, Tereshkova 28, 230008, Grodno, Belarus, telephone (job): +375 152771906

Table 1. Coordination numbers (k), coordination spheres (N--its number) at the most dense spherical packing with type ... ABCABC ... N k 1 12 2 6 3 24 4 12 5 24 6 8 7 48 8 6 9 36 10 24 11 24 12 24 13 72 14 0 15 48 16 12 17 48 18 30 19 72 20 24 21 48 22 24 23 48 24 8 25 84 26 24 27 96 28 48 29 24 30 0 31 96 32 6 33 96 34 48 36 36 36 36 37 120 38 24 39 48 40 24 41 48 42 48 43 120 44 24 45 120 46 0 47 96 48 24 49 108 50 30 51 48 52 72 53 72 54 32 55 144 56 0 57 96 58 72 60 48 61 120 61 120 62 0 63 144 64 12 65 48 66 48 67 168 68 48 69 96 70 48 71 48 72 30 73 192 74 24 75 120 76 72 77 96 78 0 79 96 80 24 81 108 82 96 83 120 85 144 86 24 86 24 87 144 88 24 89 96 90 72 91 144 92 48 93 144 94 0 95 48 96 8 97 240 98 54 99 120 100 84

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Author: | Liopo, Valerij; Avdejchik, Sergey; Ryskulov, Alimjon; Struk, Vasilij |
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Publication: | Engineering Structures and Technologies |

Article Type: | Report |

Geographic Code: | 4EXBE |

Date: | Mar 1, 2010 |

Words: | 3843 |

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