Solution behavior of polysiloxanes

In: Recent Developments in Silicone-Based Materials ISBN 978-1-61668-624-6

Editor: Maria Cazacu, pp. 33-75 © 2010 Nova Science Publishers, Inc.

Chapter 2

SOLUTION BEHAVIOR OF POLYSILOXANES

Maria Bercea, Simona Morariu, Cristina-Eliza Brunchi and Maria Cazacu

Petru Poni Institute of Macromolecular Chemistry, 41-A Grigore Ghica Vodǎ Alley,

700487 Iaşi, Romania

ABSTRACT

The thermodynamics of flexible polymers in solution have attracted the interest of

many investigators. Because of its unique properties (low viscosity even at high

molecular weight, high solubility in non-polar solvents, high volatility at low molecular

weight, low surface tension, high refractive index, etc.), poly(dimethylsiloxane) has been

the subject of various studies with respect to its solution properties. Several theories have

been put forward in an effort to explain the various phenomena occurring when very

flexible polymer molecules are dissolved in solvents of different qualities.

The aim of this chapter is to review briefly the background of thermodynamic and

rheological properties for different polysiloxanes in solution and to provide the recent

achievements in this area. The applicability of the theories explaining the various

phenomena that occur when very flexible polymer molecules are dissolved in solvents of

different qualities was critically discussed for the particular case of the polysiloxanes.

The extension of the Flory-Huggins theory by using the new concept of dimensional

relaxation developed recently by Wolf [1,2] enables the modeling of several hitherto

unexplainable anomalous phenomena, as for example the uncommon molecular weight

dependencies of second virial coefficient of poly(dimethylsiloxane) in dilute solutions

[3]. Rheological and optical properties of solutions of polysiloxanes can be regarded in

correlations with their interest for practical applications.

LIST OF SYMBOLS

AP-PDMS -bis(3-aminopropyl)-poly(dimethylsiloxane)

H3C-PDMS -bis(trimethylsilyl)-poly(dimethylsiloxane)

H-PDMS -bis(H)-poly(dimethylsiloxane)

Maria Bercea, Simona Morariu, Cristina-Eliza Brunchi et al.

HO-PDMS -bis(OH)-poly(dimethylsiloxane) known as

poly(dimethylsiloxane)--diol

MEK methyl ethyl ketone

PDMS poly(dimethylsiloxane)

PDMPS poly(dimethylsiloxane-co-diphenylsiloxane)

2A second virial coefficient

c polymer concentration

*c critical concentration that separate the dilute/semidilute regions

**c critical concentration that separate the semidilute/concentrated regions

c polymer concentration at which the dimensions of the polymer coils

are considered to have shrunk to their unperturbed dimensions

c Flory’s characteristic ratio

d fractal dimension

D , D translational diffusion coefficient in perturbed and unperturbed state

aE flow activation energy

'G storage modulus (elastic)

"G loss modulus (viscous)

Bk Boltzmann constant, 1.380650310-23

m2kg/(s

2 K)

Hk Huggins dimensionless constant

k unperturbed dimensions parameter

l average main chain bond length

m molecular weight of the mer

M molecular weight of the polymer

eM entanglement molecular weight

LM stiff factor

nM number average molecular weight of the polymer

wM weight average molecular weight of the polymer

nw M/M polydispersity index

n relaxation exponent

2n refractive index of the polymer

N number of segments

AN Avogadro’s number, 6.0221023

cn number of clusters

r particle radius in colloidal solutions

R ideal gas constant, 8.314 J/(Kg mol)

cR radius of the clusters

HR hydrodynamic radius

uR molar refractivity

Solution Behavior of Polysiloxanes

35

2ofS hypothetical mean square radius of gyration of a chain in which the

internal rotation around the bonds of the main chain is completely free

2S , 2S mean-square radii of gyration in perturbed and unperturbed states

T absolute temperature

tan loss angle tangent

uV molar volume

z excluded volume parameter

a measure of the effect of contact formation between solvent

molecules and polymer segments at fixed chain conformation

(according to the Wolf’s theory which is based on the dimensional

relaxation concept)

H hydrodynamic expansion factor

S static expansion factor

viscometric expansion factor

binary cluster integral for interactions between repeat units

)( Flory-Huggins interaction parameter dependent on polymer

concentration; frequently it is simply denoted

o Flory-Huggins interaction parameter at infinite dilution

H enthalpy contributions to the Flory-Huggins interaction parameter

S entropy contributions to the Flory-Huggins interaction parameter

o Flory's constant, 2.511021

(for ][ expressed in dL/g)

shear rate

][ , ][ intrinsic viscosity in perturbed and unperturbed state

o zero shear viscosity

s viscosity of the solvent

rel relative viscosity

complex viscosity

shear shear viscosity

sp specific viscosity

c/sp reduced viscosity

volume fraction of the polymer

o constant curvature of the characteristic helix (according to the

Yamakawa’s theory, i.e., the helical wormlike touched-bead model) 1

o characteristic stiffness parameter (according to the Yamakawa’s

theory, i.e., the helical wormlike touched-bead model)

intra-molecular interaction parameter (according to the Wolf’s

concept of the dimensional relaxation)


)z( hydrodynamic penetration function

theta condition ( -solvent, -temperature)

coil density

steric factor

long-range relaxation time

o torsion of the characteristic helix (according to the Yamakawa’s

theory, i.e., the helical wormlike touched-bead model)

oscillation frequency

a parameter which quantifies the contributions of the conformational

changes taking place in response to dilution (according to the Wolf’s

concept of the dimensional relaxation)

)z( interpenetration function

1. INTRODUCTION

The increasing interest in polysiloxanes is mainly due to their unique properties, which

are related to their chemical structure and macromolecular architecture, generating a very

important group of products with a wide range of applications.

Poly(dimethylsiloxane) (PDMS) shows some peculiar features in chain construction [4]

because its chain, [Si(CH3)2O]x, has a long SiO bond length, a small van der Waals

radius of the O-atom and a large angle at the O-atom that may reduce the steric repulsion but

does not eliminate the steric conflict for all conformations. The equilibrium flexibility of a

polymer chain, that is the ability of the backbone to rotate, has always been of great interest

for polymer scientists. Differences in physical properties between siloxanes and hydrocarbons

have been attributed to free internal rotation around SiO bond than around SiC bond. The

siloxane chain is flexible in the sense that many configurations are accessible to it. The

inherent rotational barrier around the SiO bond at ordinary temperature is of the order of

RT (where R is the ideal gas constant and T

is the absolute temperature) [5]. Due to their

special properties, the polysiloxanes represent a group of quite unique polymers. They present

very important physical and chemical properties: high chain flexibility, very low glass

transition temperature, very good resistance at temperature, oxidant agents and ultraviolet

radiation, good gas permeability and biocompatibility, but they exhibit rather poor

mechanical properties.

However, the above properties refer mainly to those in the bulk state, so it is not adequate

to conclude that the behavior is similar in the case of isolated polysiloxane chains in dilute

solution, especially regarding the backbone flexibility. Yamakawa and coworkers [6] suggest

that poly(dimethylsiloxane) chains are rather stiff in the static sense. Due to these

considerations, the properties of polysiloxanes in solution are of great interest.

Generally, the classical Flory-Huggins theory [4] was used to describe qualitatively the

behavior of polysiloxanes in solution. However, some inconveniences appear due to several

unrealistic assumptions [2]. In dilute solutions, the segments of the macromolecular coils

cannot distribute among the entire volume of the system due to their chemical bonds (chain

connectivity). Many efforts were carried out in order to find out a better theoretical


37

description. Some sophisticated approaches, such as the excluded volume theory [7] or helical

wormlike chain model [8], were applied to explain different behaviors of polysiloxanes [6,9-

14]. However, even these approaches are incapable to accounting some experimental

findings, e.g., the increase of the second virial coefficient (equivalent to a decrease of the

Flory-Huggins interaction parameter, ) with rising the molecular weight of the polymer

[3,15]. Another discrepancy appears in modeling the minima observed in dependence of

on the volume fraction [16]. These difficulties can be overcome by accounting for the

connectivity of monomers in a macromolecular chains and their ability to modify the

conformation in response to the changes in their molecular surrounding resulting from the

mixing process [1-3]. Some observations concerning the application of this concept to

polysiloxanes solutions will be given in this chapter.

Table 1. Polysiloxanes with different terminal groups and their acronyms

CH3

CH3 CH

3

CH3

CH3CH

3

Si SiO O

Si m

HO OH

HO-PDMS

-bis(OH)-

poly(dimethylsiloxane), usually

known as

poly(dimethylsiloxane)--

diol

CH3

CH3 CH

3

CH3

CH3CH

3

Si SiO O

Si m

CH3

CH3

H3C-PDMS

-bis(trimethylsilyl)-

poly(dimethylsiloxane)

CH3

CH3 CH

3

CH3

CH3CH

3

Si SiO O

Si m

H H

H-PDMS

-bis(H)-


CH3

CH3 CH

3

CH3

CH3CH

3

Si SiO O

Si HH2

m

H2N

AP-PDMS

-bis(3-aminopropyl)-


Si HO O

SiOH

m

n

C6H

5

C6H

5

CH3

CH3

PDMPS

poly(dimethylsiloxane-co-

diphenylsiloxane)


Depending on the synthesis procedure, the poly(dimethylsiloxane)s can possess different

terminal groups (Table 1), which influence the properties of their solutions, especially in the

region of low molecular weights.

2. THERMODYNAMIC ASPECTS OF POLYSILOXANES IN SOLUTION

The thermodynamic properties of linear polymer solutions are usually discussed from the

point of view of their dependence on two parameters, polymer concentration, c , and

molecular weight M . Generally, polymer solutions can be divided into three regions: dilute,

semidilute and concentrated, separated by the critical concentrations *c and **c ,

respectively [17]. In dilute solution the concentration is sufficiently low ( c < *c ), so the

macromolecular chains conserve their individuality and the intermolecular interactions are

ignored. The semidilute concentration regime is characterized by intermolecular interactions

and eventually entanglements; segment concentration is still low ( *c < c < **c ) but

polymer coils begin to overlap. In concentrated domain, the segment concentration and the

degree of coil overlapping are high ( c > **c ). The macromolecules lose their individuality

due to the formation of an infinitely large network of overlapping molecules. In view of the

fact that the expressions dilute and concentrated are only qualitative and therefore rather

arbitrary, the state of polymer solutions is defined in terms of the so-called chain overlap

parameter, which is defined as the product of the intrinsic viscosity of the polymer in a given

solvent and its concentration in the solution. A solution is considered as dilute if the chain

overlap parameter remains below 1–2 and as concentrated if it assumes values larger than 6–

10 [3].

According to well established thermodynamic concepts, the influences of chain length on

the thermodynamic properties of polymer solutions should vanish as soon as polymer

concentration exceeds a critical concentration c ( *c <

c < **c ) at which the dimensions

of the polymer coils are considered to have shrunk to their unperturbed dimensions. At higher

concentrations, including **c , the dimensions remain unchanged [18].

Poly(dimethylsiloxane) is one of the most thoroughly studied polymers and there is a

relative abundance of data for various PDMS/solvent systems. However, there is a dispersion

of the parameters calculated from the experimental data even for the same thermodynamic

conditions [19], so it becomes difficult to discuss the basic parameters that characterize its

macromolecular chain in solution.

Cyclic and linear PDMS chains have distinct properties in dilute solutions due to the

differences of the spatial distributions of segments. For linear polymers, the behavior of chain

ends contributes less to overall properties as chain length increases. In concentrated systems,

the individual molecular identity is less important as chain length increases. The

predominance of intermolecular interactions rather than intramolecular ones, even through

individual chains adopt unperturbed conformations, was discussed in terms of segmental

behavior over sections of chains. A comparative study of linear and cyclic PDMS in the bulk

state in the limit of M illustrated the segmental nature. In the two types of chain there

is an increase in segmental flexibility with chain length tending to the same value at infinite

chain length [20].


39

The heat of mixing to infinite dilution for PDMS in various solvents and their mixtures

was discussed in different papers [21-25]. Morimoto [23] summarized and discussed

calorimetric results for mixtures of PDMS with a large number of organic solvents. The

thermodynamic properties were also investigated above the usual dilute range of PDMS

solutions [25-28].

Summers et al. [27] have used PDMS as the stationary phase and in gas-liquid

chromatography in order to determine the Flory-Huggins interaction parameter from the

retention volumes at high PDMS concentrations. They used as solvents linear and branched

alkanes as well as aromatic hydrocarbons and the determined values of were in good

agreement with those obtained for the same systems from equilibrium vapor-absorption

experiments.

Flory and Shih [29] analyzed the thermodynamic properties of PDMS solutions and they

found that the entropies of dilution and excess volumes are abnormally low compared with

theoretical calculations. They assume that the discrepancies between experiment and theory

can be explained through the irregularity of the form of PDMS chain having CH3 pendant

groups spaced by comparatively long SiO and SiC bonds. Possibly the irregularity of the

cross section of the chain obstructs efficient packing of the polymer chains in bulk. Effects of

this nature could be ameliorated by using nonpolar solvents which easily fit into irregularities,

determining a decrease of entropy and excess volumes.

The partition function for a solution of PDMS gives rise to an important effect on the

residual free energy of mixing. The thermodynamic functions for the mixing of PDMS

molecules with solvent molecules contain contributions from the exothermic orientation of

the solvent molecules in cooperation with PDMS segments and from an endothermic effect

arising from the penetration of the macromolecular chains into the solvent [30]. During

dissolution of the polymer, a change in dimensions occurs (depending on the solvent quality).

This process is accompanied by a change in intermolecular conformational energy, in

addition to the creation of a certain number of polymer-solvent interactions. The change of

conformational energy in the macromolecular chain influences the heat of mixing of a

polymer-solvent system [31,32]. These results were interpreted with respect the large radius

of the PDMS segment, the existence of the oxygen atom in the PDMS backbone chain and

chain flexibility [4].

The Flory-Huggins polymer-solvent interaction parameter has been traditionally

associated with the heat of mixing of polymer and solvent liquids and with difference in

contact energies. Usually, is mainly entropic and associated with the difference in free

volume between polymer and solvent [33].

A series of papers reported the polymer-solvent interaction parameter for PDMS

solutions [25-28,34-36]. This parameter contains two terms: the first term is due to the

difference in the contact energy between segments of PDMS and the solvent molecules; the

second one is so called structural effect, principally due to the difference in chain length or

bulkiness between the chains [33].

The macromolecular chain of PDMS is able to take a variety of spatial configurations

[29]. It was ascertained [37] that the interaction sites for a PDMS molecule in solution are

assumed to be in peripheral methyl groups and oxygen atoms of the chain, while the terminal

methyl groups may exert the intermolecular forces differing from those of mid-chain


repeating units. The proportion of the former to the interaction energy probably decreases

with the molecular weight of PDMS.

2.1. Polysiloxanes in Unperturbed State

In a poor solvent, the polymer-solvent interactions are not favored, and therefore

attraction forces between chains predominate, consequently the random coil adopts a

contracted conformation. The situation when the second virial coefficient, 2A , is zero is

known as - (theta) state and depends on the polymer-solvent system. In this state, the

polymer chains behave as ideal ones, the interactions of monomer units which are far from

each other along the chain are neglected. Any polymer can reach its -state, either choosing

the appropriate solvent (named -solvent) at constant temperature or adjusting the

temperature (named -temperature or Flory temperature) in a given solvent.

The unperturbed dimensions of PDMS chains appear to be affected by the solvent

medium to a much greater degree than for polymethylene chains or other nonpolar polymers.

The polarity of the SiO bond, and perhaps also of SiC, may render this chain more

sensitive to the influence of the medium [38]. The configuration of PDMS chain in

concentrated solutions and in the bulk (in absence of the solvent) was approximated that of

the unperturbed chain in dilute solution [4,39]. For PDMS solutions in bromocyclohexane

there is an uncertainty in temperature: 28C, as determined from viscosity measurements

[40] and 29C [41] or 29.5C, as determined from light scattering measurements [6].

In a series of papers [6,10,11,42], Yamakawa and coworkers investigated the properties

of dilute solutions of PDMS in perturbed and unperturbed states. They explained

quantitatively the dependences of thermodynamic and hydrodynamic parameters on the

molecular weight on the basis of the helical wormlike touched-bead model with a proper set

of values of the model parameters, i.e., the constant curvature, o , and torsion, o , of the

characteristic helix, the characteristic stiffness parameter, 1

o , and the stiff factor, LM .

The parameter 1

o gives a measure of static stiffness of PDMS chains. The high

flexibility of PDMS chains was widely accepted due to the extremely low glass transition

temperature and small bulk modulus of PDMS chains. However, for single isolated PDMS

chain in dilute solution of bromocyclohexane at 29.5C (theta) a value of 31Å was found

for1

o . Thus, it was concluded that PDMSs have the dynamic stiffness of the same order of

magnitude as the atactic polystyrene chains for which 1

o = 23.5Å in cyclohexane at 34.5C

( conditions), although the chemical structure of PDMS is different from those of vinyl

polymers. It appears that PDMS chain is not so flexible in solution as expected from the bulk

properties, e.g., the glass transition temperature and the bulk modulus. According to helical

wormlike touched-bead model [6,11], these quantities reflect the mobility of rather small

portions of polymer chains in the bulk, so that they depend not only on the kinetics of those

portions, but also on the interactions with the surrounding chains. The behavior of a single

PDMS chain can be explained from the correlations between static and dynamic stiffness and

can be due to the so-called draining effect which was found for typical flexible polymers like


41

PDMS. In order to explain the smallest values of the intrinsic viscosity reported for siloxane

oligomers, Yamakawa and coworkers [6,43] have considered that the nonslip boundary

conditions on the bead surface may break down for these chains. This suggests that the

intermolecular interactions are rather weak for polysiloxanes, influencing the glass transition

temperature and the bulk modulus.

The transport properties of PDMS in the unperturbed state, i.e., the intrinsic viscosity,

][ , and the translational diffusion coefficient, 1

D

, was considered to be influenced by

the draining effect when ][ becomes negative in the region of oligodimethylsiloxane in

bromocyclohexane [6]. If the draining effect exists in PDMS unperturbed Gaussian chain, the

total friction force exerted by the chain on the surrounding solvent becomes smaller than that

in the nondraining limit. Thus, the values of some parameters, such as: the intrinsic viscosity

][ and the hydrodynamic radius, ,HR (determined from the translational diffusion

coefficient, 1

D

, ,HR1

D

), become smaller than the respective values in the

unperturbed state [44]. The relations 5.0M][ and 5.0

,H MR hold only

asymptotically in the limit of large M (nondraining effect) and the exponents of M become

larger than 0.5. The quantities 5.0M/][ and 5.0M/D for PDMS in bromocyclohexane at

29.5C depend appreciably on the molecular weight, even for large value of M for which the

ratio M/S2 is independent (Figure 7 of the reference [6]), being attributed to the

draining effect.

The intrinsic viscosity becomes negative for PDMS with very small molecular weight in

bromocyclohexane (Figure 4 of reference [6]). Negative viscosity was also reported for

polyisobutylenes in isoamyl isovalerate and in benzene [43]. Such unusual behavior was

regarded by the authors as arising from the specific interactions between polymer and solvent

molecules, being impossible to explain it theoretically within the framework of classical

hydrodynamics. They have converted the negative ][ value to the corrected intrinsic

viscosity which was directly compared with the polymer classical hydrodynamic theories, by

subtracting from the ][ value the negative contribution from the specific interactions

between solute and solvent molecules. For a given polymer, the quantity depends on the

solvent [6, 11], even in the range of large values of wM . This suggests a dependence of the

unperturbed chain dimensions also on the limiting value for the Flory-Fox factor, .

We note that such unusual negative values of the intrinsic viscosity were obtained by

using Huggins and Fous Mead equations [6,9,11]. For many polymer solutions, the Huggins

plots change the slope as a function of polymer concentration, making more difficult the

extrapolation of the experimental data to zero polymer concentration. The turning down of the

specific viscosity in the region of very low concentrations could be responsive for the

negative values of the intrinsic viscosity for oligomers of dimethylsiloxane. It appears now

interesting to evaluate the intrinsic viscosity by using a new method, recently published in the

literature (see section 2.3.2.), which gives linear dependences both for polyelectrolytes [45-

48] and neutral polymers [49].


The steric factor, , represents a measure of the hindrance to internal rotation around the

bonds of the backbone of a flexible chain in the unperturbed state. It can be calculated

according to:

2of

2

S

S (1)

where 2ofS is the hypothetical mean square radius of gyration of a chain in which the

internal rotation around the bonds of the main chain is completely free, any type of

interactions are absent ( M/S2of = 3.872 10

-18 [19].

In unperturbed state, the flexibility of macromolecular coils is also determined by the

Flory’s characteristic ratio, c , defined through the equation:

22

nNl/)S6(limc

(2)

where N is the number of bonds, l is the average main chain bond length.

Dilute solutions of poly(dimethylsiloxane)s with different terminal groups were

investigated extensively [8-10,50-53]. It was found that introducing amino end groups the

chains become stiffer as compared to PDMS. One exception was observed for H-PDMS,

when the volume of the terminal group (hydrogen) is lower than the volumes occupied by the

other terminal groups, determining an increase of the flexibility in the unperturbed state

(Table 2).

The unperturbed dimension parameter, k , was determined for polysiloxanes by different

methods (Table 3):

from the Mark-Houwink dependence in theta conditions (theta solvent, theta

temperature):

5.0Mk][ (3)

from the ][ – M dependence in the region of oligomers, when the behavior is

similar with those observed in theta conditions [14,52].

from the relation between k and the unperturbed dimensions 2S through the

average value M/S2 :

2/32o

2/3 M/S6k (4)

where o is Flory's constant, o = 2.511021

(for ][ expressed in dL/g).


43

from the viscometric data obtained in good solvent conditions, ][ . The intrinsic

viscosity in unperturbed state, ][ , can be determined according to [18,54]:

*)c/cexp(*c/77.0

*)c/cexp(1][[][

(5)

where *c is the critical concentration at which the polymer coil begin to overlap

each other, is the coil density.

Table 2. Unperturbed dimensions, M/S 2 , and steric factor, , reported for

poly(dimethylsiloxane)s with different end groups

Polymer/solvent system

at a given temperature M/S2 10

18

(cm2)

Literature

PDMS/MEK, toluene (25C) 5.40 1.39 [19]

H-PDMS/toluene/acetone (30C)

nM = (0.2 – 2.5)104 g/mol

5.34 1.38 [50]

AP-PDMS/toluene/acetone (30C)

nM = 0.23104 g/mol,

toluene : 0.3, 0.46, 0.54, 1.7

8.69 2.44 [13,50]

AP-PDMS/toluene/nitromethane (30C)

nM = (1.27 – 5)104 g/mol

toluene : 0.811, 0.9

8.69 2.44 [50]

H-PDMS/toluene (25C)

nM = (3.1 – 4.94)104 g/mol

6.97 1.80 [53]

OH-PDMS/toluene (40C)

nM = (1.53 – 4.3)104 g/mol

6.27 1.62 [55]

OH-PDMS/toluene (40C)

wM = (5.4 – 10.9)105 g/mol

7.82 2.02

[55]

H-PDMS/toluene (25C)

nM = (0.2 – 2.5)104 g/mol

6.12 1.58 [53]

AP-PDMS/toluene (25C)

nM = (0.23 – 10)104 g/mol

7.00 1.81 [53]

CH3-PDMS/bromocyclohexane (28C)

wM = 3.72104 – 8.8610

5 g/mol

8.66 2.24 [56]


Table 3. k Values reported for polysiloxanes in different experimental conditions

Solvent, temperature Molecular weight of

PDMS

(g/mol)

k 104

(dL/g)

c Literature

MEK, 20C ( ) 9.3104 – 6.8510

5 7.5

[15]

MEK, 20C ( )

3105 – 1.110

6 8.07 [3]

MEK, 20C ( )

7.5104 – 810

5 7.11 [58]

MEK, 20C ( )

and C8F18/CCl2F

(33/67, w/w) 22.5C ( )

5.5105 – 1.210

6 10.6 7.6 [59]

bromocyclohexane, 28C

( )

> 2105 7.8

6.3 [40]


( )

4104 – 910

5 7.95 [56]


( )

3.3104 – 1.0610

6 7.45 [41]

bromocyclohexane, 29.5C

( )

3.3104 – 1.0610

6 8.6 [6,9,11]


( )

7.5104 – 810

5 6.79 [58]

toluene/nitromethane and

toluene, 25C

(OH-PDMS, CH3-PDMS)

0.23104 – 10

5 5.42 – 9.4 [52]

toluene, 25C 2.8104 – 6.310

4 4.85 [57]

different solvents 7 – 8 [19]

From Tables 2 and 3 one observes that the unperturbed dimensions are influenced by the

solvent and temperature, on the one hand, and by the end group of the polymer, on the other

hand. The amino terminal groups determine the stiffness of the polysiloxane short chains, as it

is illustrated by the increase of the steric factor, , or unperturbed dimension parameter, k .

Also, the method of the determination can influence the values of the unperturbed

dimensions and chain flexibility. As for example, for OH-PDMS and CH3-PDMS samples,

the ][ values obtained by using equation (5) are independent on concentration and

temperature. The resulted value of 4.8510-4

dL/g for k is lower than the values obtained in

theta conditions [57] (Table 3).

The uncertainty observed in the -temperature determination for PDMS in solution of

bromocyclohexane influences the accurate determination of the unperturbed dimensions.


45

Thus, the value of 28C for theta temperature, which has been determined from viscosity

measurements [40], is somewhat lower than the value of 29C [41] or 29.5C [6,9,11],

determined from light-scattering measurements.

2.2. Excluded Volume Effects

The behavior of dilute polymer solutions, expressed by different parameters (the second

virial coefficient, the mean dimensions, the intrinsic viscosity) and influenced by temperature,

solvent quality, molecular weight domain, can be discussed through different excluded

volume theories. The theoretical approaches mutually differ in the used mathematical

methods and approximations, but all of them relate the excluded volume effects to measurable

quantities, by considering different possible interactions (polymer-solvent, short- and long-

range, intra- and intermolecular interactions).

The solvent quality plays an important role in determining the type and magnitude of

polymer-solvent interactions. Thus, in a good solvent, the attraction forces between the chain

segments are smaller than the polymer-solvent interactions, so the random coil adopts an

extended conformation. The excluded volume interaction is responsible for the swelling

behavior of the overall chain dimensions in a good solvent, and the polymer is dissolved over

a wide range of temperatures.

Theoretical investigations have established different equations in which the second virial

coefficient, 2A , and the expansion factors ( ) are functions of short-range and long-range

interactions through the interpenetration function, )z( . Thus, for flexible polymers in dilute

solution, some dimensionless parameters, such as the linear expansion factor

22S S/S (where 2S and 2S represent the mean square radii of gyration

in perturbed and unperturbed states, respectively) and the interpenetration function, )z( ,

are universal functions of a single variable, z , called the excluded volume parameter. This

parameter is defined as:

2/12/32o

2/3 M])M/S/(B[)4/1(z (6)

where 2m/B , – the binary cluster integral for interactions between repeat units, m –

molecular weight of the mer.

The interpenetration function, )z( , is defined as:

2/32A

2/3

22

SN4

MA)z(

(7)

2A is the second virial coefficient and AN – the Avogadro’s number.

The hydrodynamic penetration function, )z( , can be expressed as:

][)( 2

MAz (8)


For the perturbed Gaussian chain, Douglas and Freed [60-62] have developed the

renormalization group theory (RTP) which predicts that both (the viscometric expansion

factor) and H (hydrodynamic expansion factor) have smaller values in draining limit than in

the nondraining limit for large excluded volume parameter, z . According to the RTP

predictions, and H as a function of z (that takes into account the effects of the

excluded volume and chain stiffness on the basis of the helical wormlike chain [63]) depends

on the degree of draining. Thus, and H plotted against z do not give respective single-

composite curves. The validity of RTP theory was examined for PDMS dilute solutions in

toluene at 25C by comparing the dependences of and H as a function of z with the

simple composite curves obtained for polyisobutylene, atactic polystyrene, atactic and

isotactic poly(methyl methacrylate) [11]. The results showed that there is no draining effect

on and H for PDMS as in the case of others flexible polymers, despite the fact the

draining effect is significant for PDMS in the unperturbed state [6]. The experimental results

were found in a semiquantitatively agreement with the Yamakawa-Yoshizaki theory [64]

which takes into account the possible effect of fluctuating hydrodynamic interactions on H .

The hydrodynamic, static and viscometric expansion factors, H , S and ,

respectively, were investigated as a function of z for PDMS in toluene at 25C [11]. Because

the hydrodynamic radius in toluene is larger than in bromocyclohexane at theta temperature,

even in the region of low molecular weights, the dimensions of the PDMS chains depend

appreciable on the solvent. As it was discussed above (chap. 2.1), due to the specific

interaction between the polymer and solvent molecules, the intrinsic viscosity is also changed

in good and theta solvent [6]. These facts make impossible to evaluate H and for PDMS

in toluene by using the values of ,HR and ][ directly measured in theta conditions.

Horita et al. [11] estimated 0,HR and 0][ for PDMS chains in toluene at 25C by

multiplying the values of ,HR and ][ measured in a theta solvent at theta temperature

(bromocyclohexane at 29.5C) by proper factors that represent the effect of the solvents. By

plotting H as a function of S calculated in this way from the experimental data obtained

for different PDMS samples [11,55], a single composite curve was obtained (Figure 1a). Also,

3 against 3

S form a single composite curve if the values of and S are correctly

evaluated. With increasing the molecular weight (or S ), the draining effect found for PDMS

in the unperturbed state can cause a progressive decrease of 3 from the single composite

curve (Figure 1b).

Yamakawa and coworkers [65,66] predicted a regularity of )z( values in the low

excluded volume region by changing either the solvent quality, either the molecular weight of

the polymer. Starting from the thermodynamic parameters (chain dimensions, second virial

coefficient and intrinsic viscosity data), the excluded volume effect was investigated for

different polysiloxanes [12-14,53]. Negative excluded volume effects ( )z( < 1 and )z( <

0) were obtained for oligomers of dimethylsiloxanes with amino end groups (AP-PDMS) in

toluene and toluene/acetone solvent/non-solvent mixtures at 28C.


47

log S

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4

log H

(a)

log S3

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8

log 3

(b)

Figure 1. Double logarithmic plots of: (a) H against S and (b) 3 against 3

S for HO-PDMS in

toluene at 25C: (o) [11]; (■) [55].

In contradiction with the behavior observed for long flexible chain oligomers of HO-

PDMS and AP-PDMS, the proportionality 5.0M][ presents some deviations. The

viscosity of AP-PDMS in toluene and toluene/nitromethane mixture (volume fraction of

nitromethane of 0.9) shows upward deviations for nM < 104 [52]. These deviations increase

with increasing the solvent quality and molecular weight. Thus, short chains of PDMS exhibit

anomalous characteristics in dilute solution, the excluded volume effects do not disappear

and 5.0M/][ is not independent on M . This behavior was considered as a consequence of

the non-Gaussian character of flexible chains in good solvents (this state vanishes by

decreasing the solvent quality). Furthermore, in mixtures of solvents, cosolvency and

preferential adsorption phenomena can appear. Preferential adsorption for AP-PDMS in


toluene/nitrometane mixture was observed to be relatively independent on the molecular

weight, both components of the solvent mixture having low affinity for the polysiloxanes

[67].

2.3. Thermodynamic Parameters

2.3.1. Hydrodynamic Radius

Dynamic light scattering technique provides the translational diffusion coefficient, D ,

from which HR can be calculated according to:

D6/TkR sBH (9)

where Bk is the Boltzmann constant, T is the absolute temperature, s is the viscosity of the

solvent.

Edwards and coworkers [68] used the classical boundary-spreading technique to

determine the diffusion coefficients of cyclic and linear oligo- and poly(dimethylsiloxane)s

with 444 g/mol < nM < 4.8104 g/mol in toluene at 25C. Mean square radii of gyration,

2S , was calculated from the diffusion data for both cyclic and linear

poly(dimethylsiloxane)s assuming Gaussian statistics, and it was found to be in good

agreement with the corresponding values obtained by neutron scattering. For short PDMS

chains, the HR values were not in agreement with those calculated according the rotational

isomeric state model [69]. This discrepancy was attributed to deviations from Gaussian

behavior, and a better agreement between experiment and theory was achieved by using

appropriate values of the interpenetration function, which relates radii of gyration and

impermeable hydrodynamic diffusion radii.

The hydrodynamic radius ( HR ) in good (toluene, 25C) and theta (bromocyclohexane,

29.5C) solvent for oligo- and poly(dimethylsiloxane)s was determined and discussed by

Yamakawa and coworkers [11]. Figure 2 shows double logarithmic plot of 5.0H M/R ( HR in

Å) as a function of M for PDMS in toluene at 25C [11,57,68] and bromocyclohexane at

29.5C [6].


49

log(R H /M w0.5

)

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

2 3 4 5 6 7log M

TL

BCH

Figure 2. Double logarithmic plot of 5.0H M/R as a function of M for PDMS in toluene (TL) at 25C

(o) [11], (Δ) [68] and () [57] and bromocyclohexane (BCH) at 29.5C (▲) [6] and (■) [11].

For all range of molecular weights, the hydrodynamic radius of PDMS in toluene is

larger than in bromocyclohexane at theta temperature. A significant difference is observed

even in the region of low molecular weights ( M < 103 g/mol) where the excluded volume

effect may be negligible.

2.3.2. Intrinsic Viscosity

Generally, the viscosity of dilute polymer solutions depends on the nature of polymer

and solvent, the concentration of the polymer, its average molecular mass and molecular mass

distribution, the temperature, and the shear rate. Very often, the intrinsic viscosity, ][ , is

determined through the Huggins equation:

c][k][c/ 2HHHsp (10)

Hk is referred as the Huggins dimensionless constant and relates to the size and shape of

polymer segments, as well as to hydrodynamic interactions between different segments of the

same polymer chain. The values of Hk are in the range of 0.3 (for good polymer-solvent

interactions) to 0.5 (for poor polymer-solvent interactions). Other equations and their

applicability limits were recently reviewed [70].

Figure 3 presents a classical way to analyze the viscometric data by following the

dependences of the reduced viscosity ( c/sp ) as a function of concentration ( c ) for

solutions of the five H3C-PDMS and HO-PDMS samples in toluene at 20C, 40C and 60C.

It can be observed a difference of temperature influence on viscometric behavior for the

solutions of H3C-PDMS (samples 2 and 5), on the hand, and HO-PDMS (samples 1, 3 and 4),

on the other hand.


c (g/dL)

0.1

0.3

0.5

0 2 4 6 8

sp /c

(dL/g) 1

2

3

4

5

20oC

2

0.1

0.3

0.5

0.7

0.9

0 2 4 6

1

345

sp /c

(dL/g)40

oC

c (g/dL)

60oC

0.0

0.2

0.4

0 2 4 6

sp /c

(dL/g)2

c (g/dL)

1

5

34

Figure 3. c/sp vs. c dependence in toluene at 20C, 40C and 60C, for PDMS samples with

different terminal groups: 1 (HO-PDMS): wM = 6.2104 g/mol, nw M/M = 1.44; 2 (H3C-PDMS):

wM = 8.2104 g/mol, nw M/M = 1.36; 3 (HO-PDMS): wM = 4.710

4 g/mol, nw M/M = 1.52; 4

(HO-PDMS): wM = 2.4104 g/mol, nw M/M = 1.57; 5 (H3C-PDMS): wM = 2.510

4 g/mol,

nw M/M = 1.43 [55,71].


51

At 20C, high values of the reduced viscosity can be observed and a change in slope at

very low PDMS concentration for samples 1, 3 and 4 (HO-PDMS) is depicted. According to

different papers, this change in slope corresponds to the transition from extremely dilute to

dilute regimes at a critical concentration, 'c [70,72]. At very low polymer concentration, only

the intramolecular interactions exhibit and the appearance of cyclic structures is possible.

A decrease of the hydrodynamic dimensions of the macromolecular coils occurs above

'c , in the dilute regime, as shown by the deviation of c/sp vs. c dependences. This

deviation is not evident for H3C-PDMS samples at a higher temperature (e.g., 60C). By

increasing the polymer concentration, in the semidilute regime, the reduced viscosity changes

the slope because intra- and intermolecular interactions are in competition. With increasing

the temperature, the c/sp vs. c curves are significantly different. At 40C the intrinsic

viscosity of HO-PDMS samples is lower than at 20C and, at very low concentration, the

change in slope is not evident. One can suppose that possible associations formed at 20C are

destroyed with increasing temperature. For H3C-PDMS samples, viscosity increases with

increasing the temperature. At 60C, the associated structures are destroyed by thermal

motion and the viscosity of HO-PDMS samples decreases.

Acid terminated poly(dimethylsiloxane)s form supramolecular associations in low

polarity solvents due to the hydrogen bonding interactions of chain ends [73,74]. FTIR

spectroscopy and viscometric data obtained in dichloromethane, carbon tetrachloride and

hexane were used to characterize the supramolecular structures. At high concentrations, chain

extension leads to high viscosity values due to intermolecular hydrogen bonding interactions,

whereas at low concentrations, low viscosity cyclic species are formed by intramolecular

hydrogen bonding interactions. The authors used a quantitative model based on Jacobson-

Stockmayer theory in order to describe the competition between the chain extension and

macrocyclization, by taking into account the variation of the free acid fraction with

concentration in non-polar solvents.

According to literature, Hk can be considered as a measure of the solvent quality: values

around 0.3 are usually obtained in good solvents and 0.5 – 1 in theta solvents [19]. For PDMS

in toluene, the values of Huggins constant ( Hk ) are lower than 0.5 and they increase with

increasing the molecular weight in the range 0.31 – 0.41. The temperature influence is not

significant; there is a small decrease of Hk from 20C to 60C [75]. For PDMS in methyl

ethyl ketone (MEK) at 20C the values tend to be higher than 0.5.

As it was observed for many polymer solutions, in the region of very low concentrations,

the Huggins plots change the slope, making more difficult the extrapolation of the

experimental data to zero concentration. Many efforts were made in order to obtain linear

dependences from the viscometric data in the region of very low polymer concentrations. A

new alternative method was developed very recently for the determination of ][ of

polyelectrolytes [45], according to the following equation:

w

w2

wrel

][Bc1

][][Bc][cln

(11)


where B represents a system specific constant ( B = 0.5 - Hk ) which holds true for the range

of pair interactions between the solute [46]) and ][ is the characteristic specific

hydrodynamic volume.

The equation (11), successfully verified for different polyelectrolyte solutions [46-48,76],

and neutral polymers in solution [49], thus it can be applied for polysiloxanes in solution. As

for example, from the initial slope of the dependence relln as a function of c at sufficiently

low shear rates and polymer concentrations we can have access to the intrinsic viscosity of

high molecular weight HO-PDMS (Figure 4). For the same polymer sample, the influence of

the solvent quality can be observed as in the case of Huggins plots [3]. n-Octane (n-O), a very

good solvent for PDMS, induces strong polymer-solvent interactions, determining a higher

viscosity as compared with toluene (TL) solutions. Methyl ethyl ketone, which is a theta

solvent for PDMS at 20C, acts as a marginal solvent at 40C, the polymer-polymer

interactions are more favored for this solvent.

c (g/dL)

0.0

1.0

2.0

0 0.4 0.8 1.2 1.6

ln reln-O

TL

MEK

Figure 4. Plot of relln vs. c for HO-PDMS with wM = 1.09106 g/mol, nw M/M = 1.43, in methyl

ethyl ketone, toluene and n-octane at 40C, according to Wolf’s model (eq. (11)).

The viscometric behavior also depends on the chemical structure of siloxane unit. For a

small content of diphenylsiloxane in the copolymer structure, the macromolecular coil is

more extended and the intrinsic viscosity increases (Table 4), despite the fact that the

molecular weight of the copolymer is smaller as compared with HO-PDMS sample [77].

Figure 5 shows clearer the limitation of the Huggins equation in the data evaluation,

especially in the region of very low concentrations.


53

Table 4. The number average molecular weight ( nM ), polydispersity index ( nw M/M ),

the intrinsic viscosity values ( H][ , w][ ), and Huggins constants ( Hk ) of HO-PDMS

and two copolymers of dimethylsiloxane with diphenylsiloxane samples in toluene at

25C

Sample

code

Diphenyl

siloxane

units

(%)

nM 10-4

(g/mol)

nw M/M H][a

(dL/g)

Hk a w][ b

(dL/g)

HO-PDMS 0 18.6 1.56 0.90 0.4 0.83

PDMPS1 5.95 14.45 2.28 1.38 0.39 1.20

PDMPS2 47.83 6.88 1.80 0.69 0.25 0.64 aDetermined by using equation (10).

bDetermined by using equation (11).

0.5

1.0

1.5

2.0

2.5

0.0 0.4 0.8 1.2c (g/dL)

sp /c (dL/g)

HO-PDMS

PDMPS1

PDMPS2

Figure 5. Huggins plot (eq. (10)) for HO-PDMS and copolymers of dimethylsiloxane with

diphenylsiloxane (Table 4) in toluene at 25C [77].


The w][ values determined from the initial slope of relln vs. c dependence

(according to Figure 6) and those determined by applying Huggins equation to the

experimental data for which 1.2 < rel < 1.9 (from Figure 5) are given in Table 4. A decrease

of the flexibility of the chains and an increase of the intrinsic viscosity can be observed by

introducing of the diphenylsiloxane units in the polymer structure (HO-PDMS and PDMPS1).

For PDMPS2 the lower value of the intrinsic viscosity is attributed to a lower molecular

weight of the copolymer.

c (g/dL)

0

0.4

0.8

1.2

1.6

0 0.4 0.8 1.2

ln rel PDMS

PDMPS1

PDMPS2

Figure 6. Liniarization of the experimental data by plotting relln vs. c according to the Wolf’s model

(eq. (11)) for HO-PDMS and PDMPS samples (Table 4) in toluene at 25C.

The dependence between intrinsic viscosity and the molecular weight is known as the

Mark-Houwink-Sakurada equation:

aMK][ (12)

where K and a are constants for a given polymer/solvent system at a constant temperature.

The values of parameters K and a are determined experimentally from the dependence

of ]log[ as a function of Mlog using low polydispersity polymer fractions. Table 5

summarizes the literature data concerning the viscometric behavior of PDMS solutions in

different thermodynamic conditions (solvent, temperature). It can be observed that the

exponent a is 0.5 in conditions or for very short chains, and tends to 0.85 in good solvent

conditions.


55

Table 5. The parameters K and a , according to eq. (12), for PDMS solutions in

different thermodynamic conditions

M Solvent, temperature K

(dL/g)

a Literature

< 1.7104

MEK, 20C 0.580 [78]

5104 – 4.710

6 MEK, 30C 8.1510

-4 0.550 [15]

3105 – 1.110

6 MEK, 40C 6.0110

-4 0.565 [3]

7.5104 – 810

5 Bromocyclohexane,

26C (bellow theta

temperature)

1.1110-3

0.430 [58]

2103 - 10

4 Toluene, 25C 0.500 [79]

2103 – 1.3810

6 Toluene, 25C 2.1510

-4 0.650 [80]

> 2105

Toluene, 25C 8.2810-5

0.720 [40]

2.6103 – 6.2510

5 Toluene, 25C 1.3410

-4 0.690 [81]

3103 – 310

5 Toluene, 25C 1.8710

-4 0.658 [82]

1.9104 – 1.310

5 Toluene, 25C 0.840 [83]

0.32104 –

21.73104

Toluene, 25C 2.5110-4

0.623 [52,53]

0.32104 –

21.73104

Toluene/Nitromethane

(90/10), 25C

2.6310-4

0.615 [14,51]

3105 – 1.110

6 Toluene, 25C 4.3310

-4 0.786 [75]

7.5104 – 810

5 Toluene, 30C 1.6510

-4 0.670 [58]

2104 – 910

5 Toluene, 35C 1.2510

-4 0.703 [56]

3105 – 1.110

6 Toluene, 40C 5.3110

-4 0.633 [3]

3105 – 1.110

6 n-Octane, 40C 410

-3 0.787 [3]

1.7104 – 910

5 Cyclohexane, 35C 1.0210

-4 0.735 [19]

The differences observed in Mark-Houwink parameters determined in the same

experimental conditions for a large domain of molecular weights can be due to

measuring/estimating ][ and M , or to differences in chain behavior. For M 104, the

value of ][ in good solvents (as for example toluene) becomes larger that those of ][

determined in theta conditions (as for example bromocyclohexane at 29.5C or MEK at

20C). This suggests that the specific interaction between the polymer and solvent molecules

has a significant effect above this molecular weight.

2.3.3. Polymer-Solvent Interactions

In the polymer solutions, the contributions to the excluded volume depend on the actual

volume of the chain unit as well as on its interaction with the solvent molecules. A measure of

these interactions is the second virial coefficient ( 2A ). In theta conditions, 2A = 0 because the

polymer-solvent interaction vanishes.


From the second osmotic virial coefficients the Flory-Huggins interaction parameter at

infinite dilution, o , can be calculated according to:

2212o VA5.0 (13)

o also offers the possibility to quantify the solvent power. From this dependence, it can

be observed that o = 0.5 in theta conditions, o < 0.5 for good solvent conditions and o >

0.5 when the polymer-solvent interactions are unfavorable.

Generally, the thermodynamic particularities of polymer/solvent systems at any

compositions are normally quantified in terms of Flory-Huggins interaction parameter, .

According to experimental evidence and theoretical considerations, does not only depend

on temperature and pressure, but also on the composition of the mixtures and – at least in

dilute solution – on the chain length of the macromolecules. The behavior of dilute solution

properties has been predicted by applying renormalization group methods [7,84,85].

However, these approaches are not able to account the experimental finding that the second

virial coefficients, 2A , may increase with increasing the molar mass of the polymer. In

contrast to the original assumption, the Flory-Huggins interaction parameter ( ) does not

only depend on temperature and pressure, but also on composition and - even in the region of

high polymer concentrations - on the chain length of the polymer. Numerous attempts have

been done to incorporate these features into the theory [6,9-11,25,86].

The experimental information showed that the individuality of macromolecules

survives in thermodynamically good solvents up to almost the pure melt. In order to explain

this behavior, Wolf [1] developed a new concept of dimensional relaxation. This approach

treats the dilution process (the basis for determination of Flory-Huggins interaction

parameters) in two steps: a separation of intersegmental contacts by the insertion of the

solvent, keeping constant the chain conformation; an expansion of the macromolecular coil

(the system rearrange) in order to minimize its Gibbs energy. The following expression was

proposed for the Flory-Huggins interaction parameter at infinite dilution, o :

o (14)

The Wolf concept considers the parameter as a measure of the effect of contact

formation between solvent molecules and polymer segments at fixed chain conformation; this

parameter does not depend on M . is an intra-molecular interaction parameter, which

raises the chemical potential of the solvent in the solution up to the value of the pure solvent.

The parameter quantifies the contributions of the conformational changes taking place in

response to dilution and becomes zero for theta conditions. The sign and extent of the

molecular weight dependence of 2A depends on . For the majority of solutions, 2A

decreases with increasing M and, thus, < 0 explains why solvents are favorable from

thermodynamic point of view. In some rare cases 2A increases with rising M and this is not

in agreement with classical thermodynamic concepts. According to Wolf’s theory, the

increase of 2A with increase of M corresponds to > 0 and expresses the fact that the


57

conformational relaxation needs not necessary to be favorable. For sufficiently dilute polymer

solutions, there is the only difference between this new approach and the original Flory-

Huggins theory consists in the second term of eq. (14). According to the theoretical and

experimental considerations, becomes zero under theta conditions (where the coils assume

their unperturbed dimensions) and the conformational relaxation does no longer contribute to

o 2].

By considering the experimental data reported for different polymer-solvent systems,

there is a linear dependence between and .

The influence of the molar mass is included in , a parameter defined as:

)a1(N5.0 (15)

where N is the number of segments and 2NK , a112N ]M)/[(KK , where 1

and

2 represent the density of the solvent and polymer, respectively, and 1M is the molecular

mass of the solvent.

According to the Wolf’s theoretical approach [1,2], the dependence of the second virial

coefficient, 2A , as a function of polymer chain length can be expressed as:

)a1(

122

22 NV

AA

(16)

where:

V2

21A

22

2

(17)

and 1V is the molar volume of the solvent.

For theta solvents 2A = zero and = 0, resulting = 0.5. The sign of

2A depends on

the magnitude of and . An increase of the chain length determines either a decrease

(usually) or an increase of 2A , as a function of the sign of which gives information on the

conformational response of the segments to dilution. and can be evaluated from the

chain length dependence of 2A . We can examine the plot of 2A as a function of )a1(M

and, according to the relation (16), the second virial coefficient is not always zero for infinite

long chains.

Figure 7 is a representation of the experimental data in the traditional way, i.e. in a

double logarithmic plot of the second virial coefficient as a function of number average

molecular weight ( nM ) of PDMS in two thermodynamic situations: good (TL) and poor

(MEK) solvents. [3]. Different qualitative behavior can be depicted in Figure 8: 2A decreases

with increasing the molecular weight for good solvent (TL), when o increases, whereas for

poor solvent (MEK), 2A rises with increasing the molecular weight, thus o decreases for


poor solvents. This aspect can not be described theoretically with the well known theories of

thermodynamics [7] according which the second virial coefficient should decrease with

increasing the molecular weight. This discrepancy can be now explained with the new

concepts of dimensional relaxation developed recently by Wolf [1,2].

log A 2

-5

-4

-3

5.4 5.5 5.6 5.7 5.8

log M n

(cm3mol/g

2)

TL

MEK

Figure 7. Double logarithmic plot of 2A as a function of nM for HO-PDMS in TL and MEK at 40C

(data from [1,3]).

104A 2

0

1

2

3

0 2 4 6 8M n

-(1-a)

(cm3mol/g

2) TL

MEK

Figure 8. 2A vs. )a1(

nM

for HO-PDMS in TL and MEK at 40C according to eq. (16) (data from

[1,3]).


59

Figure 9 represents the conformational response ( ), as a function of for a fixed

conformation for PDMS [3]. The straight line which is obtained, like for others polymers [1],

shows that, from thermodynamic point of view, the solvents are qualitatively good if the

conformational response is favorable, when the reduction of the Gibbs energy is associated

with the conformational rearrangements, dominated by the entropic contribution.

-1

1

3

5

7

0 1 2 3 4

Figure 9. Parameters of the new Wolf’s approach, as a function of , for a fixed conformation for

HO-PDMS [1,3].

The Gibbs energy of dilution at fixed conformation (dominated by enthalpy) remains low

because the effect must be distributed on the many segments involved in the opening of

intermolecular contacts. The conformational response, , passes zero for 2A = 0,

independent of chain length. Thus, the linear interrelation between the two characteristic

parameters, covering the entire range of solvent quality for PDMS, shows that increases

and decreases as the solvent becomes worse [1,3].

2.3.3.1. Composition Dependence of

The generalization of the Wolf’s approach to arbitrary polymer concentrations yields the

relation:

1(2)q1/()( 2 (18)

where: is the volume fraction of the polymer and q is an additional parameter obtained

from the measured concentration dependence of the interaction parameter.

Thus, only one additional parameter ( q ) is required to incorporate the concentration

dependence in the Flory-Huggins interaction parameter. By using the experimental data


obtained for a given polymer-solvent system, for which it is known the o value (limiting

value of for 0 ), the expression can in good approximation be simplified to:

)21(q)q1)(()( 2o (19)

This relation is able to describe the concentration dependence for the Flory-Huggins

interaction parameter for PDMS solutions [2].

2.3.3.2. Enthalpic and Entropic Contributions to

By analyzing how the solvent quality is reflected in concentration and temperature

dependent Flory–Huggins interaction parameter, the enthalpy ( H ) and entropy ( S )

contributions to were evaluated for PDMS in various solvents [25]:

)T/1(T

1H

(20)

HS (21)

where T is the absolute temperature.

Thus, it was possible to obtain information on the enthalpy and entropy parts by plotting

as a function of inverse temperature for different constant concentrations. At infinite

dilution, H is negative for toluene, which is a good solvent (exothermal heat of dilution)

and increases with increasing the polymer concentration, presenting an inversion in the heat

effects. For n-octane, which is a very good solvent, it was also observed a change in sign of

the heat dilution, but, in this case, from an endothermal behavior at low polymer

concentration, to an exothermal one at high polymer concentration. S dependence results as

a mirror image because entropy and enthalpy changes are dependent each other. Thus, the

concentration dependence of the H and S for PDMS in solvents with different

thermodynamic quality is very complex. The noncombinatorial entropy part associated with a

certain heat effect becomes less favorable as the solvent deteriorates. The H values

associated with the combinatorial behavior of the solutions ( S = 0) is largest for the worst

solvent, MEK. These behaviors can result from the arrangements of the solvent molecules and

polymer chains for very different compositions [25].

3. RHEOLOGICAL BEHAVIOR OF

DIFFERENT POLYSILOXANES IN SOLUTIONS

The use of poly(dimethylsiloxane) solutions in many industrial applications (for example

in coating processes) depends on the knowledge of their rheological properties. The

measurements in dynamic regime provide more substantial information than those


61

accomplished in stationary regime, especially with regard to the viscoelastic behavior of the

materials, in general, and of multiple phase systems, in particular, in a close connection with

the structure of these systems. The most common way to qualify the fluid properties consists

of the measurements of the complex elasticity modulus components: storage modulus

(elastic) 'G and the loss modulus (viscous) "G , the complex viscosity ( ) and the loss

angle tangent ( tan ) [87,88].

The rheological properties of two linear poly(dimethylsiloxane)s with closed molecular

weights but differing by the end groups were investigated in solution (by using toluene as

solvent) at different temperatures [89]. Samples of CH3-PDMS, with nM = 1.5104 g/mol,

and HO-PDMS with nM = 1.62104 g/mol, respectively, were investigated in continuous and

oscillatory regime of shear. Figures 10 and 11 show the variation of the viscoelastic

parameters as a function of oscillation frequency ( ) for CH3-PDMS and OH-PDMS

solutions in toluene (30 g/dL) at 20°C. The curves are very similar for both samples, the

dominant modulus being the viscous modulus "G and the moduli variation with the

frequency is typically for viscoelastic Maxwellian fluids, that is, "G scales with 1 and 'G

with 2 .

0.0001

0.001

0.01

0.1

1

10

100

1000

0.1 1 10 100 1000 (rad/s)

G'

G"

tan

G'=G"

Figure 10. Curves of 'G , "G , and tan as a function of for OH-PDMS (30 g/dL in toluene) at

20°C [89].


0.0001

0.001

0.01

0.1

1

10

100

1000

10000

0.1 1 10 100 1000 (rad/s)

G'

G"

tan

G'=G"

Figure 11. Curves of 'G , "G , and tan as a function of for CH3-PDMS (30 g/dL in toluene)

at 20°C [89].

The curves corresponding to elastic and viscous moduli are crossing at a value of

frequency, "G'G , that is inversely proportional with the long-range relaxation time,

(Table 6). The long-range relaxation time for OH-PDMS sample decreases with increasing

the temperature, whereas for H3C-PDMS sample there is a tendency to increase when the

temperature is raised (Figure 12). The higher values obtained below 40°C for HO-PDMS

sample could be explained by the stronger interactions between the polar -OH terminal

groups, comparatively with those corresponding to the -CH3 terminal groups of H3C-PDMS

sample.

The shear viscosity ( shear ) is independent of the shear rate ( ) at all temperatures

showing a Newtonian behavior for both samples. Moreover, the complex viscosity vs.

frequency dependence overlaps with the shear viscosity ( shear ) vs. shear rate ( ) curve

validating the Cox-Merz rule for HO-PDMS and H3C-PDMS samples, according to the

following relationship:

)()(* shear (22)

Thus, the zero shear viscosities, o , were determined by the extrapolation of the complex

viscosity to zero oscillatory frequency, according to the equation:

*)(lim0

o

(23)


63

Table 6. The complex viscosity ( ) and the crossover value of ( "G'G ) determined

at different temperatures for solutions of 30 g/dL in toluene

Sample Temperature

(°C)

(Pa·s)

"G'G

(rad/s)

OH-PDMS

nM = 1.62104 g/mol

10

20

30

40

60

80

0.1244

0.0895

0.1124

0.1538

0.2346

0.3449

127

143

142

150

197

218

CH3-PDMS

nM = 1.5104 g/mol

10

20

30

40

50

60

0.0727

0.1189

0.0968

0.0928

0.1486

0.1566

1175

313

201

163

153

90

The flow activation energy ( aE ) of HO-PDMS and H3C-PDMS samples was calculated

using an Arrhenius type relation:

)RT/Eexp(A ao (24)

where: R – the universal gas constant (8.314 J/Kmol), T – the absolute temperature (K).

0

4

8

12

0 20 40 60 80t (

oC)

.103(s

)

Figure 12. Dependence of the long-range relaxation time ( ) as a function of temperature for

HO-PDMS (○) and H3C-PDMS (■).


From the plots of *ln on ( T/1 ) (Figure 13) one observes that the dependences are

linear in the temperature range from 20°C to 80°C. The higher value of the activation energy

calculated for HO-PDMS sample (19.53 kJ/mol) as compared with the sample H3C-PDMS

(7.66 KJ/mol) can be attributed to the intermolecular interactions of –OH end groups in a

nonpolar solvent.

-4

-3

-2

-1

0

2.75 3 3.25 3.5

103/T (1/K)

ln(Pa·s)

Figure 13. Dependence of *ln on T/1 for the samples HO-PDMS (●) and H3C-PDMS (▲).

The evolution of linear viscoelasticity during cross-linking of poly(dimethylsiloxane)s

was investigated by Winter and coworkers [90-93] by small amplitude oscillatory shear. The

network junctions were assumed to be due to chemical cross-links and not due to others

association phenomena, crystallization or phase separation.

At the gel point, the relaxation modulus, )t(G , follows a power law which is denoted as

gel equation:

nSt)t(G (25)

where S is the gel stiffness and n is the relaxation exponent.

Stoichiometrically balanced PDMS gels gave the specific exponent value of n = 1/2,

whereas for stoichiometrically imbalanced PDMS samples 1/2 < n < 1. Transformation of

the data from the frequency to time domain required the hypothesis that the power law

behavior extends over the entire frequency range, 0 < < . For the imbalanced gels

)('G)("G and a higher rate of the stress relaxation was observed. Because the gel point

was found to occur before the crossover point between )('G and )("G , the authors firstly

proposed a new method to localize the gel point, i.e., the detection of a loss tangent

independent of the frequency [94,96]. The final modulus of PDMS network scales with


65

concentration at a power close to 2. Both gel stiffness and relaxation exponent are strongly

composition dependent. Relaxation exponents between 0.19 and 0.92 and variations of gel

strength over 5 decades were found for PDMS, depending on the entanglement molecular

weight, eM . Thus, prepolymers with the molecular weight below eM produce critical gels

with lower n values, in the range of 0.4 to 0.7, whereas above eM , critical gels with lower

n values (0.2 – 0.4) were obtained, depending on the stoichiometry. Addition of a diluent

affects the relaxation exponent and near the overlap concentration n approaches the limit of

1 [92].

The static and dynamic properties of cross-linked poly(dimethylsiloxane) clusters near

the gelation threshold have been studied also by Adam et al. [94] starting from PDMS

samples with 1.78·105 g/mol < wM <2.06·10

7 g/mol in toluene. In the vicinity of the gelation

point, the mass distribution of the polymer clusters is described by the following power law

[95]:

M

M2.2c fMn (26)

where cn is the number of clusters with mass M and

M

Mf is the cutoff function that

indicates that there is no mass larger than M in the system.

For all clusters of size cR one can write the following relation:

dcRM (27)

where d represents the fractal dimension that depends on the polymer environment: a) in the

reaction medium (without solvent) 5.2d and b) in dilute solution (where the polymer

clusters swell) 2d .

The weight average molecular weight ( wM ), the z-average square radius of gyration

z2S and the z-average diffusion coefficient ( D ) of polymer clusters determined by static

light scattering experiments were found to be linked by the following relation:

d)3(

zw RM

(28)

where zR is either the radius of gyration z2S determined by static light scattering

measurements, or the hydrodynamic radius, HR , deduced from the diffusion coefficient, D

(equation (9)).

The experimental value of d)3( obtained from the wM – zR dependence was 1.71

0.07 in agreement with the theoretical prediction ( 6.1d)3( ) corresponding to the

percolation model.


The interaction parameter, wB , was found to depend on the weight average molecular

weight according to the relation:

X

ww M47.0B (29)

where 03.035.0X and wB is determined from the following dependence:

w2/12

H

B

][

S

R

(30)

X exponent obtained by experimental measurements has also a value close to the value

expected by the percolation model ( 375.0X ).

These observations allow concluding that the static properties of cross-linked

poly(dimethylsiloxane) clusters near the gelation threshold are well described by the

percolation model. The rheological data obtained for this chemical system showed that the

local dynamic properties are independent of the distance to the threshold, allowing real

exponents to be evaluated.

Mixtures of PDMS with CO2 were studied in the entire range of compositions at

pressures between 100 bar and 700 bar and temperatures in the range of 30 – 70C [96]. The

volumetric and the viscometric behavior of PDMS solutions in condensed gases have

demonstrated that these systems behave very much like in the ordinary low molecular weight

liquids. Bellow the entanglement point, the viscosity of the mixture is less than those

calculated by additive rule, on the basis of the volume fractions of the components

( 2,1i,i ). If the chains are entangled, the deviations become positive and this effect

increases with increasing the molecular weigh. Large negative excess volumes were obtained

for high volatile solvents. The concentration dependences of the activation energies and

volumes exhibit pronounced sigmoidal shapes. The chain entanglements play an important

role for the occurrence of the inversions in the excess viscosities. This complex behavior was

described quantitatively by means of one ajustable parameter independent of the molecular

weight. The concentration dependence of both excess volume and excess viscosities can be

described quantitatively by a simple relation on the form: 212211 )kk( , in which 1k

and 2k are theoretical parameters, their meaning is explained in ref. [96].

Liquid-crystalline polymer (LCP)/low molar mass nematic (LMMN) composites have

attracted attention due to its application in electrooptic devices. The rheological properties of

LCP solutions are changed dramatically when a small amount of LCP is dissolved in LMMN.

For these composites, both aligning-to-tumbling and tumbling-to-aligning transitions have

been evidenced [97-100]. These changes in the rheological properties are in agreement with

the Brochard theory which affirms that the dissolved polymer can influence differently the

system viscosity, depending on its chain conformation (specifically a prolate vs oblate shape)

[101]. The hydrodynamic theory of Brochard predicts that the dissolution of an oblate side-

chain LCP in a flow-aligning nematogen will produce a transition to tumbling flow and the

dissolution of a prolate main-chain LCP in a flow-tumbling nematogen will produce a

transition to aligning flow. Others investigations concerning of the rheological and


67

viscometric properties of dilute solutions of a liquid crystal polymer based on polysiloxane in

a nematic solvent (4’-pentyl-4-cyanobiphenyl and 4,4’-n-octylcyanobiphenyl) were reported

[102,103]. Certain inconsistencies between prediction of the hydrodynamic model of

Brochard and experimental observation of stress transients and electrorheological responses

of side-chain liquid crystal polymer/low molar mass nematic solutions were been observed

and a modification of this theory was been proposed. The modification of Brochard’s theory

supposes that an elastic torque between director rotation and LCP orientation produces

additional viscous dissipation. By application of the modified Brochard’s theory to the

polysiloxane/nematic solvent system a good agreement between theory and experimental data

was obtained.

Tailored poly(dimethylsiloxane) ionomers, which possess highly flexible polysiloxane

backbone, were synthesized and the theoretical predictions of the scaling of viscosity with

polymer volume fraction by both Rubinstein and Semenov theory were compared with the

experimental results [104,105]. This theory predicts a number of regimes of viscosity

dependence on polymer volume fraction based on parameters linked to the solvent quality and

associating polymer structure, for example the length between stickers, overall molecular

mass, strength of interactions and entanglement molar mass of the polymer. The solution

viscosities of poly(dimethylsiloxane) sodium and zinc ionomers with tailored number of

monomers between ions and number of ions per chain in good and in theta solvent conditions

over a broad range of concentrations were reported [106]. For these poly(dimethylsiloxane)

ionomers, the dynamics in both the entangled and unentangled semidilute regimes can be

modeled by intermolecular bonds with renormalized lifetimes.

Aqueous emulsions of linear PDMS have been proposed as a new contrast agent for the

gastro-intestinal nuclear magnetic resonance [107], their use offering some advantages: the

effect of diarrhea and flatulence are reduced; PDMS is an inert photon-rich polymer because

it has two methyl groups in its repeating unit; in 1H-NMR spectrum there is about a 5 ppm

chemical shift from PDMS to water, which is usable for the chemical shift artifact (in

imaging technology, an artifact is a feature appearing on the image which does not

correspond to the properties of the subject in a certain region). Except for this application,

PDMS is widely employed in current researches of new biomedical devices due to its good

hemo- and biocompatibility properties [108]. Crosslinked PDMS colloidal solutions were

proposed as an alternative to emulsions of linear dimethylsiloxane oligomers to avoid

possible absorption by intestine [109]. Emulsions and colloidal PDMS solutions are more

convenient for medical applications because their rheological properties are adjustable. The

rheological properties of colloids are influenced by the volume fraction of the disperse phase

( ), particle radius ( r ), packing effects, the type of surfactant, etc. The rheological

properties changes dramatically above a critical value of the volume fraction, c . For

monodisperse emulsions c 0.635, while for polydisperse emulsions c

0.71 [110]. For

c , the compressed emulsions show predominant elastic behavior and the viscosity

increases abruptly with the increase of the volume fraction. The yield stress appears at low

strain and is proportional to r2/3/1 and it was not observed for c [109].


4. OPTICAL PROPERTIES OF POLYSILOXANE SOLUTIONS

The materials based on polysiloxanes are suitable for optical applications due to their

refractivity and transmittance combined with dielectric and mechanic properties. Generally,

the refractive index of a solution depends on the light wavelength, temperature and the

solution concentration. The variation of the refractive index increment of

poly(dimethylsiloxane) in toluene as a function of the temperature and the light wavelength at

different concentrations from 0.005 g/mL to 0.05 g/mL was determined by Nilsson and

Sundelof [111]. The refractive index increment of the poly(dimethylsiloxane) solution slowly

decreases by concentration and temperature increasing. Moreover, the refractive index

depends on the type of the end groups and the structure of polysiloxanes. Brunchi et al. [112]

studied the optical properties of some polymers containing siloxane units. The experimental

refractive index determined at 435 nm and 25°C for HO-PDMS ( nM = 1.62104

g/mol) and

H3C-PDMS ( nM = 1.5104 g/mol) in toluene were 1.401 and 1.403, respectively. The CH3

end groups determine a slight increase of the refractive index in comparison with the OH end

groups. Additional, this parameter was calculated for poly(dimethylsiloxane) with different

end groups by using the following equation, according to the Lorenz-Lorentz approximation

[113]:

)2n/()]1n(V[R 22

22uu (31)

where 2n represents the refractive index of the polymer according to different

approximations, uR is the molar refractivity and uV is the molar volume.

The refractive index was calculated with above equation based on the assumption that the

molar volume and the molar refraction of the chain repeating unit are additive functions of

composition (eqs. (32) and (33) [114]:

ii

iu VaV (32)

ii

iu RaR (33)

where iV and iR are the group contributions, and ia is the number of groups, i , is the

repeating unit.

The experimental values of the refractive index for HO-PDMS and H3C-PDMS in toluene

differed slightly from those calculated with the Lorenz-Lorentz equation, by considering the

corresponding group contributions to the molar refraction and volume. The calculated

refractive indices were 1.402 and 1.400 for HO-PDMS and H3C-PDMS, respectively.

The refractive index can be adjusted by controlling the composition of the polymer. The

influence of polysiloxane composition on the optical properties was studied for PDMPS

(Table 1) with different concentrations of diphenylsiloxane units, in toluene, the results being

presented in Figure 14 [112].


69

0 20 40 60 80 1001.35

1.40

1.45

1.50

1.55

1.60

Refr

acti

ve in

dex

Diphenylsiloxane content (%)

Figure 14. Influence of diphenylsiloxane content on the refractive index of PDMPS [112].

The refractive index increases from 1.401 for poly(dimethylsiloxane) to 1.577 for

poly(diphenylsiloxane) by increasing diphenylsiloxane content. The silicone polymers with

the diphenylsiloxane content between 12 % and 21 % mol having the refractive indices

between 1.425 and 1.440 could be used in bio-optic applications. The increase of the

diphenylsiloxane content in the copolymers determines the improvement of the optical

properties but the materials becomes more rigid. It is necessary to change the end groups or to

introduce new substituents in the copolymer structure during the synthesis to remove such

disadvantage.

Some copolymers containing siloxane were developed as materials having optical

properties. Thus, new siloxane-modified methacrylate copolymers were synthesized and

characterized [115] in order to their using in contact lens. An increase of the toughness and a

decrease of the tensile strength of these copolymers by increasing the methyl methacrylate

content in copolymer were observed [116]. The refractive index of vinyl polymers

(poly(methyl methacrylate-allyl methacrylate) and poly(styrene-allyl methacrylate)) decreases

by dimethylsiloxane grafting [117].

The behavior of PDMS and PDMPS with different contents of diphenylsiloxane units in

solvent/nonsolvent (toluene/methanol) mixtures was investigated by turbidimetry [77]. The

characteristics of the samples are listed in Table 4. The turbidity of the polymer containing

siloxane units slowly increases by increasing the polymer concentration (Figure 15). Some

conformational changes were evidenced for PDMS in the entire range of solvent/nonsolvent

binary mixture for polymer concentrations between 0.1 g/dL and 0.2 g/dL (Figure 15a). In the

case of copolymers, these phenomena were not observed (Figure 15b,c).

For all samples, it was observed that the turbidity increases by increasing the nonsolvent

amount in the solvent-nonsolvent mixture (Figure 16).


nonsolvent/solvent ratio

0.4

0.6

0.8

1.0

0 0.4 0.8 1.2c (g/dL)

Tu

rbid

ity (N

TU

)

0.11 0.180.250.33

a)

0

1

2

3

4

0 0.4 0.8 1.2c (g/dL)

Tu

rbid

ity (N

TU

)

0.110.180.250.330.43

nonsolvent/solvent ratiob)

0

2

4

6

8

0 0.4 0.8 1.2

c (g/dL)

Tu

rbid

ity (N

TU

)

0.110.18

0.250.330.43

nonsolvent/solvent ratio c)

Figure 15. Variation of turbidity vs. concentration for: (a) PDMS, (b) PDMPS1 and (c) PDMPS2.


71

PDMS

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6

Nonsolvent/Solvent (vol/vol)

Tu

rbid

ity (N

TU

)

PDMPS1

PDMPS2

Figure 16. Turbidity of PDMS (●), PDMPS1 (□) and PDMPS2 () solutions for 0.550 g/dL as a

function of nonsolvent/solvent ratio at room temperature.

The increase of the turbidity is more accentuated for the copolymer having the higher

diphenylsiloxane unit content. This observation was in accord with experimental data

obtained by Brunchi et al. [112] which showed that by increasing the amount of phenyl

groups, the refractive index boosted to the detriment of transmittance and flexibility.

Moreover, the modification of the wavelength from UV to the visible domain determined the

increase of the transparency which remained constant above 400 nm. The PDMS sample is

insoluble in nonsolvent/solvent mixture at ratios higher than 0.4 unlike

poly(dimethylsiloxane-co-diphenylsiloxane)s that are soluble at higher ratios. The turbidity of

PDMS is lower than the copolymers turbidities at the same concentration and

solvent/nonsolvent ratio; the turbidity of the copolymers is more affected by the addition of

the nonsolvent.

5. CONCLUSION

Based on the literature data and also on own studies, it can be appreciated that the

behavior of the polysiloxanes in solution is different from those in bulk. The high interest in

the study of the polysiloxanes in solution comes in special from the observations that the high

flexible polysiloxane chain behaves rather as stiff one when it is seen as an isolated chain.

Beside the polysiloxane polymer characteristics (cyclic or liniar structure, molecular weight,

nature of the substituent to the silicon atoms or the ending groups nature), both solvent nature

as well as concentration have a significant influence on the polymer behavior in solution.

The data on both thermodynamic (unperturbed state, excluded volume effects,

thermodynamic parameters) and rheological behaviors of the polysiloxanes in solution were

reviewed.

The thermodynamic behavior of polysiloxanes in solution can not be entirely described

by using classical theories of thermodynamics [3]. New theoretical considerations [1-2],


which takes into account the chain connectivity and the ability of polymer coils to change the

conformation in response to alterations of their environment, are able to give a better

quantitative description of polysiloxanes in solution.

The results on the investigations of some optical properties (transparence and refractive

index) of the polysiloxanes in solution were also presented and discussed in correlation with

the polymer structure.

ACKNOWLEDGEMENTS

The authors are grateful to Prof. Bernhard A. Wolf from Johannes Gutenberg Universität

Mainz for useful comments and suggestions. The research activity was partially realized in

the framework of an exploratory research project (Contract Number 516/2009, additional

contract nr. 1/2010).

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Solution behavior of polysiloxanes