Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
2135420
FIELD OF lNV~NllON
The invention relates to defoamer emulsions based on
organofunctionally modified polysiloxanes. More particularly, the
invention relates also to those emulsions which contain finely
divided silica.
BACKGROUND INFORMATION AND PRIOR ART
The use of methylpolysiloxanes for defoaming liquids is
one of the first areas in which these products were used. There
exists a large number of publications and patents wherein the mode
of action of the siloxanes is described, and advice is given for
selecting suitable siloxanes and the forms in which they are
prepared .
It was already recognized earlier that the use of
mixtures of different polysiloxanes can be advantageous. For this
purpose, a large number of different organofunctionally-modified
polysiloxanes have also been developed. A typical organo-
functional group, which modifies the properties of the
polysil oxanes, is the polyether group with oxyethylene and/or
oxypropylene units. In the course of further development,
polysiloxanes, with combinations of polyether groups of different
hydrophilicity, were used for the modification. Finely divided,
mostly pyrogenic silica, which is optionally used in the
hydrophobized form, is an important component of such defoamer
emulsions based on polysiloxanes.
Y2-21438. -2-
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From the large number of O~enlegungsschriften and
patents relating to defoamers based on polysiloxanes, the
following publications are cited as examples:
U.S. patent 3, 984, 347 relates to a preparation, which
consists essentially of:
1. 50 to 98.9% by weight of a basic oil, which is a
polyoxypropylene or a polyoxypropylene-polyoxyethylene polymer
with a molecular weight of 500 to 6,000, or a siloxane glycol
polyme-; of the general formulae
(a) (RaSi (OSiMe2) n (OSiMeG)bOSiMe2G) 4-a~
(b) (RaSi (OSiMe2) n (OSiMeG) rOSiMe3) 4-a~
(c) GMe2Si(OSiMe~) n (OSiMeG)bOSiMe2G),
(d) Me3Si(OSiMe2) n (OSiMeG)rOSiMe3
wherein
R is a hydrocarbon with 1 to 10 carbon atoms,
free of olefinic double bonds,
Me is a methyl group,
~IY2-21438.
~13~
G is a group having the formula -D(OR')mA, in
which D is an alkylene group wlth 1 to 30
carbon atoms and R' is an alkylene group-with
2 to 10 carbon atoms, m has a value of at
least 1 and A is a capping group,
a has a value of 0 or l,
n has a value of at least 12,
b has a value of 0 to 50,
and
c has a value of 1 to 50;
2. 1 to 40~ by weight of a defoamer, which is obtained
essentially from 88 to 95 parts by weight of a liquid poly-
dimethylsiloxane with a viscosity of at least 20 cSt at 25C,
S to 10 parts b-y weight of silica and 0 to 20
parts by weight of a siloxane resin, which
consists essentially of the units SiO2 and
(CH3)3SiO1/2 in the ratio of 1 : 0.4 to 1 : 1.2;
and
~`~'2-21438.
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3. 0.1 to 10~ by weight of a dispersant, which
disperses component 2 in component 1 and is a siloxane copolymer,
which either is
i) a polydimethylpolysiloxane-polyether
copolymer, in which the molecular weight of
the polysiloxane is at least 2,000, and the
polyoxypropylene polymer has a molecular
weight of at least 800, or a polyoxyethylene-
polyoxypropylene copolymer with a molecular
weight of 1,500, the polyether being linked
over an SiC bond to a silicon atom of; the
siloxane,
or
ii) a polydimethylpolysiloxane-polyether polymer,
which is obtained by heating a mixture of a
methyl-hydrogenpolysiloxane having a
molecular weight of at least 1,500, and a
polyoxypropylene glycol having a molecular
weight of at least 800, or a polyoxyethylene-
polyoxypropylene glycol having a molecular
weight of at least l,S00.
!~Y2-21438.
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The p~2blishea ~:uropean patent application 0 354 016
relates to a tex~ile detergent which contains raw detergents,
builders and at least one material for controlling the foam,~ with
the distinguishing feature that a dispersable preparation of a
silicone defoamer is contained in the detergent and consists of a
non-aqueous emulsion of a primary and a secondary defoamer, the
primary defoaming ingredient being a mixture of:
a) a liquid or organopolysiloxane with at least one
hydroxyl and hydrocarbon group,
b) a silicone resin or a compound producing a
silicone resin,
c) a finely divided filler,
and
d) a catalyst for the reaction between a) and c), the
secondary defoaming ingredient being a mixture of
a liquid methylpolysiloxane, at least one nonionic
silicone surfactant, a first organic dispersant
and a second dispersant, based on a nonionic
difunctional block copolymer with terminal primary
hydroxyl groups.
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~13542~
Finally, reference is made to the published European
patent application 0 427 263, in which a silicone-based defoamer
preparation is described, which contains (i) a polydiorgano-
siloxane, (ii) silica, and (iii) 4 to 2500 parts by weight, based
on 100 parts by weight of the sum of components (i) and (ii) of a
modified silicone oil, the molecule of which has at least one
functional organic group which is linked to a silicon atom, a~
well as at least one epoxy, amino, amide, carboxyl, alkoxyl or
'.~ydroxyl group, and at least one optionally substituted
polyoxyalkylene group which is linked to a silicon atom.
Even though these known defoamers can be iused
advantageously to prevent or eliminate foam in aqueous systems,
unfulfilled or inadequately fulfilled requirements, nevertheless,
remaln .
One of these requirements is to prepare defoamer
emulsions which are as concentrated and stable as possible and can
be diluted by the user to the desired concentration, while
.etaining the stability of the emulsions. This is possible with
simple stirring equipment without requiring expensive stirring
technology or special precautions. At the same time, the diluted
emulsions must satisfy high stability requirements and should
exhibit high stability particularly when subjected to temperature
changes and to shaking. It is, therefore, an object of the
invention to solve this technical problem.
~'Y2 21438.
~13~
OBJECT OF THE lN V l':N l lON
An object of the present invention is a defoamer
emulsion based on organofunctionally modi~ed polysiloxanes.
SU~IARY OF THE lNV~;NllON
Such a defoamer can be obtained by mixing together
(a~ O to 90 parts by weight of an organopolysiloxane of
the general formula
ICH3 CH3 CH3 ICH3
Rl-SiO- SiO- '-iO- SiRl
CH3 CH3 a O CH3
CH3- i-CH3 b
--1 c
~ hereinafter referred to as Formula I)
in which
Rl can be the same or di~erent in the average
molecule and represents an alkyl group with 1 to 8
carbon atoms, or the -Z-(CnH2nO-)mR2 group, wherein
R2 is a hydrogen group or an alkyl group with 1
to 8 carbon atoms,
~IYt-2 1 438 .
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s~
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Z is a divalent group having the formula -O-,
-(CH2)p-O- or -CH2-CH(CH3)-CH2-O- with p = 2 or
3,
n has an average numerical value of 2.7 to 4.0,
m has an average numerical value of 5 to 130,
a has an average numerical value of 4 to 1,500,
b has an average numerical value of 0 to 100, and
c has an average numerical value of 0 to 50;
(b) 0 to 90 parts by weight of an organopolysiloxane of
the general ormula
CH3 fH3 fH3 CH3
R3-Sio- SiO- SiO- iR3
CH3 CH3 d O CH3
CH3 - 51 _ CH3 e
(referred hereinafter as Formula II)
in which
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R3 can be the same or di~erent in the average molecule
and represents a hydroxyl group or alkoxy group with
1 to 4 carbon atoms,
d has an average numerical value of 4 to 1,500,
e has an average numerical value of O to 100,
and
f has an average numerical value of O to 50;
(c) O to 90 parts by weight of an organopolysiloxane of
the general formula
CH3
R5-o- [CXH2xO] -y -iO- ~CxH2xO] -Y Rs
CH3 w
(referred to hereinafter as Formula III)
in which
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Rs can be the same or different in the average molecule
and represents an alkyl group with 1 to 4 carbon
atoms, with the proviso that at least 90~ of the Rs
groups are methyl groups,
x has an average numerical value of 2.6 to 3.0,
y has an average numerical value of 8 to 80,
w has an average numerical value of 7 to 50,
and
z has an average numerical value of 1.5 to 10,
the sum of the components (a), (b) and (c) being not less
than 10 parts by weight and not more than 90 parts by
weight; and
(d) O to 15 parts by weight of finely divided silica,
and stirring this mixture into a mixture of (e) and
(f) obtained from
(e) 5 to 85 parts by weight of an organopolysiloxane of
the general formula
~ ~ 2 ~t438
2 0
fH3 CH3 fH3 fH,
R4-sio- SiO- SiO- SiR4
I
CH3 CH3 g O CH3
CH3 - S i - CH3 h
R4
(referred to hereinafter as Formula IV)
in which
R4 in the average molecule can be the same or
di~erent and represents an alkyl group with 1
to 8 carbon atoms or the -Z-(CqH2qO-)rR2 group,
wherein
R2 and Z have the meanings already given,
q has an average numerical value of 2.0 to
2.7,
r has an average numerical value of 5 to 120,
g has an average numerical value of 4 to 200,
h has an average numerical value of 0 to 100,
and
j has an average numerical value of 0 to 50;
~'Y2-21438. -l2-
213S~
and
(f) 5 to 50 parts by weight of water with a low-shear
stirrer and thus converting this mixture into a stock emulsion,
which is diluted to the desired concentration subsequently or only
immediately before it is used.
In Formula I, R1 preferably represents a methyl group or a
polyether group, in which Z is -o- or -(CH2) 3-0- . In this case,
the polyether group has the formula -(CH2)3-O-(CnH2nO-)mR2.
The average numerical value of n is 2.7 to 4.0, a nume~ical
value of 2.7 to 3 being preferred. This average numerical value
is obtained during the block-wise synthesis of the polyether or
random addition reaction of corresponding amounts of ethylene
oxide and propylene oxide. Optionally, higher alkylene oxides can
also be used.
The average numerical value of m is 5 to 130. It indicates
the average number of oxyalkylene units in the polyether group.
Preferably, m has an average numerical value of 6 to 50.
R2 is a hydrogen group or an alkyl group with 1 to 8 carbon
atoms. Especially preferred is an alkyl group with 1 to 5 carbon
atoms, particularly the butyl group. The subscripts a, b, and c
preferably have the following values: a = 4 to 800, b = 0 to 50,
c = 0 to 30.
-l3-
~1~5~0
The secon~ polysiloxane component corresponds to the
general Formula II. In this polysiloxane, R3 represents a
hydroxyl group or a lower alkoxy group with 1 to 4 carbon atoms.
The hydroxyl group is preferred and the alkoxy group is to be
regarded as a precursor, which can be converted into the hydroxyl
group under hydrolysis conditions.
Admittedly, the values of d, e and f are to be regarded as
independent of the subscripts a, b and c. However, they
correspond to the given and preferred ranges but need not be
identical in the two formulas.
The third polysiloxane component corresponds to the general
Formula III. In this polysiloxane, Rs represents an alkyl group
with 1 to 4 carbon atoms, however, with the proviso that at least
90~ of the Rs groups are methyl groups. The subscripts have the
following average values:
x = 2.6 to 30, preferably 2.8 to 3.0;
y = 8 to 80, preferably 20 to 60;
w = 7 to 50, preferably 13 to 30;
and
z = 1.5 to 0, preferably 1.5 to 5.
~iY2-21438.
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~1~5~20
The polyslloxanes of Formulas I, II and III can be present
in the inventive defoamer emulsion in amounts of, i~ each case, 0
to 90 parts by weight. However, the condition that the sum of the
two polysiloxanes constitutes at least 10 parts by weight but does
not ex-eed 90 parts by weight, must be fulfilled. For example,
the following combinations (aside from other combinations) are
possible:
Siloxane Type Parts by Weight
Siloxane I 90 0 0 30 20
Siloxane II 0 90 0 30 45
Siloxane III 0 0 90 30 25
Component d is a finely divided silica which is customarily
used in defoaming emulsions as an action-enhancing substance. In
general, pyrogenically produced silica is used which can also be
hydrophobized by treatment with silanes. Preferably, amounts of
0.2 to 5 parts by weight are used.
As polysiloxane e with the general Formula Iv, siloxanes
are preferably ! used in which the R4 groups represent an alkyl
group with 1 to 4 carbon atoms and/or groups having the formula
-(CH2)3-O-(CqH2qO-)2H. In distinction from the polyether siloxanes
of Formula I, the polyether group of the polyethersiloxanes 5 is
more hydrophilic, that is, the average value of q, ranging from
2.0 to 2.7, is lower than that of the siloxanes I. This is
brought about by a higher proportion of ethylene oxide in the
synthe~is of the polyether. A range of 2.3 to 2.6 is particularly
preferred.
~'Y2-21438.
2135420
-
From the values of the subscripts g, h and j, it is evident
that the polysiloxanes of Formula IV generally have a lower
molecular weight than the polysiloxanes of Formula I. , The
following average numerical values are preferred for the
subscripts: g = 4 to 100, h = 0 to 20 and j = 0 to 25.
The inventive defoamer emulsion can be obtained by mixing
together components (a) = siloxane I, (b) = siloxane II, (c) =
polysiloxane III and (d) silica and stirring into this mixture the
components (e) = polysiloxane of Formula IV and (f) water by means
of a low-shear stirrer.
A procedure is preferred in which the components (a), (b),
(c) and (d), to begin with, are heated in the presence of an
alkaline equilibrating catalyst for 0.5 to 10 hours at 50C to
200C. An alkaline equilibrating catalyst, preferably an
e~ective amount, about 0.5 to 2 parts by weight, of an alcoholic
solution of an alkali or ammonium hydroxide or carbonate, such as
an ethanolic solution of potassium hydroxide, is used.
Preferably, the equilibration is carried out for 3 to 6
hours at 90C to 150C. It can be assumed that, during this
reaction, there are also reactions between the polysiloxanes and
reactive centers at the surface of the finely divided silica.
~IY2-21438.
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The mixture, so obtained, is now emulsified with the
mixture of components (e) and (f) to form a stock emulsion. The
latter can then be diluted to the desired concentration
immediately or at a later time, if necessary, on the location
where the defoamer is to be used. The concentration for use is
generally 5 to 20~ by weight of dispersed phase.
Despite the low water content, the stock solution, which
can be diluted pursuant to the invention, has a low viscosity and
can be converted in any convenient manner, for example, simply by
stirring-in water into the desired, dilute emulsion used for the
defoaming.
The stability of the diluted emulsions can be increased
even further by diluting the stock emulsion with water, which
contains a stabilizer and/or thickener. Stabilizers and/or
thickeners based on a carboxyl group-containing polyacrylate are
particularly preferred. For this stabilization, the pH of the
aqueous solution is adjusted to a value of about 7. Such
stabilizers or thickeners are commercially available and
described, for example, in the German O~enlegungsschrift 39 25
220 .
The stock emulsions, obtained pursuant to the invention,
and the emulsions, diluted to the desired concentration, have the
required stability when subjected to temperature changes and/or
shaking as shown in the following Examples, it being understood
that the Examples are provided by way of illustration and not by
way of limitation.
~Y2-21438. -17-
21~5~2~
EXAMPLE 1
A siloxane of Formula I (31 parts by weight, a = 80, c = 7,
b = 0 and Rl = CH3- and -Z-(CnH2nO-)mR2 in the ratio of 2 : 7,
wherein Z = -(CH2)p-O- with p = 3 and n = 2.9, m = 15, R2 = -H),
are mixed with 5 parts by weight of a siloxane of Formula II
(d = 300, f = 0 and R3 = -OH) and treated with 2 parts by weight
of a finely dispersed silica. After the addition of 0. 5 parts by
weight of a 10~ methanolic solution of potassium hydroxide, the
mixture, so obtained, is heated for 3 hours at 100C.
The heated product (37 parts by weight), is added'to a
mixture of 30 parts by weight of a siloxane of Formula IV (g = 18,
h = 6, j = 2 and R4 = -Z- (CqH2qO) rR2 with Z = -O-, R2 = C3H7-
and q - 2.6, r = 40) and 33 parts by weight of water, and stirred
with a low-shear stirrer.
EXAMPLE 2
A siloxane of Formula 1 (20 parts by weight, a = 18, b = 6,
c = 2 and R1 = -Z(CnH2nO)m-R2 with R2 = C3H7- and n = 3, m = 33) is
mixed with 20 parts by weight of a siloxane of formula III
(x = 3.0, y = 51, w = 15, z = 4). This mixture is added to a
mixture of 20 parts by weight of siloxane of formula IV (g = 48,
h = 0, j = 2 and R4 = -Z- (CqH2qO) rR2 with z = -(CH2)p-O-, p = 3,
R2 = H- and q = 2.6, r = 40) and 40 parts by weight of water and
stirrea together with little shear.
~'Y2-21438.
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2135420
EXAMPLE 3
A siloxane of Formula III (60 parts by weight, x = 2.8,
y = 20, w = 25 and z = 2) is stirred into a mixture of 25 parts by
weight of a siloxane of Formula IV (g = 21, h = 7, j = 2 and
R4 = -Z-(CqH2qO)rR2 with Z = -O-, R2 = C3H,- and q = 2.6, r = 40) and
15 parts by weight of water.
EXAMPLE 4
A siloxane of Formula II (38 parts by weight, d = 70,
e = 10, f = 6, R3 = -OC2Hs) is mixed with 2 parts by weight of a
finely dispersed silica. This mixture is stirred with little
shear into a mixture of 30 parts by weight of a siloxane of
Formula IV (g = 60, h = 0, j = 4 and R4 = -Z-(CqH2qO)rR2 with
Z = -CH2-CH(CH3)CH2-O-, R2 = CH3-, q = 2.5 and r = 40), and 30 parts
by weight of water.
EXAMPLE 5
A siloxane of Formula I (38 parts by weight, a = 500,
c = 0 and Rl = CH3-) is mixed with 2 parts by weight of a finely
dispersed silica and stirred with little shear into a mixture of
30 parts by weight of siloxane of Formula IV (g = 18, h = 6,
j = 2 and R4 = -Z-(CqH2qO)rR2 with Z = -O-, R2 = C3H7- and q = 2.6,
r = 40) and 30 parts by weight of water.
~Y2-21438.
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2135420
EXAMPLE 6
Water (80.1 parts by weight) is added to a stirred vessel
and 2.5 parts by weight of a 30% dispersion of a thickener based
on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5) are
added. 14.9 parts by weight of the emulsion of Example I are then
added. This mixture is stirred with a multi-stage, impulse,
counter-current agitator for 5 minutes at a peripheral speed of 3
m/s. After that, the pH of this emulsion is adjusted to a value
of 7 with 2.5 parts by weight of a 5.6~ sodium hydroxide solution.
EXAMPLE 7
Water (78.3 parts by weight) is added to a stirred vessel,
followed by 2.5 parts by weight of 30~ dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5). After
that, 16.7 parts by weight of the emulsion of Example 2 are added.
This mixture is now stirred for 5 minutes with a multi-stage,
impulse, counter-current agitator at a peripheral speed of 3 m/s.
The pH of this emulsion is then adjusted to a value of 7 with 2.5
parts by weight of a 5.6~ sodium hydroxide solution.
~IY2-21438.
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213~420
EXAMPLE 8
Water (83.2 parts by weight) is added to a stirred vessel,
followed by 2.5 parts by weight of 30% dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5). After
that, 11.8 parts by weight of the emulsion of Example 3 are added.
This mixture is now stirred for 5 minutes with a multi-stage,
impulse, counter-current agitator at a peripheral speed of 3 m/s.
The pH of this emulsion is then adjusted to a value of 7 with 2.5
parts by weight of a 5.6% sodium hydroxide solution.
~XAMPLE 9
Water (80.1 parts by weight) is added to a stirred vessel,
followed by 2.5 parts by weight of 30% dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5). After
that, 14.9 parts by weight of the emulsion of Example 4 are added.
This mixture is now stirred for 5 minutes with a multi-stage,
impulse, counter-current agitator at a peripheral speed of 3 m/s.
The pH of this emulsion is then adjusted to a value of 7 with 2.5
parts by weight of a 5.6% sodium hydroxide solution.
~'Y2-21438. -21-
2135~2~
EXAMPLE 10
Water (80.7 parts by weight) is added to a stirred vessel,
followed by 2.5 parts by weight of 30~ dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5). After
that, 14.3 parts by weight of the emulsion of Example 5 are added.
This mixture is now stirred for 5 minutes with a multi-stage,
impulse, counter-current agitator at a peripheral speed of 3 m/s.
The pH of this emulsion is then adjusted to a value of 7 with 2.5
parts by weight of a 5.6~ sodium hydroxide solution.
EXAMPLE 11
Water (78.3 parts by weight) is added to a stirred vessel,
followed by 2.5 parts by weight of 30~ dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5). After
that, 16.7 parts by weight of the emulsion of Example 2 are added.
This mixture is now stirred for 5 minutes with a turbine with a
peripheral speed of 5 m/s. The pH of this emulsion is then
adjusted to a value of 7 with 2.5 parts by weight of a 5.6~ sodium
hydroxide solution.
~Y2 21438. -2~- ;
213S4~D
EXAMPL~ 12
Water (78.3 parts by weight) is added to a stirred ve~sel,
followed by 2.5 parts by weight of 30% dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commerctally
obtainable, for example, under the name of Acrysol RM-5). After
that, 16.7 parts by weight of the emulsion of Example 2 are added.
This mixture is now stirred for 5 minutes with a dissolver disk at
a peripheral speed of 7 m/s. The pH of this emulsion is then
adjusted to a value of 7 with 2.5 parts by weight of a 5.6% sodium
hydroxide solution.
EXAMPLE 13
Water (87.3 parts by weight) is added to a stirred vessel,
followed by 2.5 parts by weight of 30~ dispersion of a thickener
based on a polyacrylate containing carboxyl groups (commercially
obtainable, for example, under the name of Acrysol RM-5). After
that, 16.7 parts by weight of the emulsion of Example 2 are added.
This mixture is now stirred for 5 minutes with a spatula. The pH
of this emulsion is then adjusted to a value of 7 with 2.5 parts
by weight of a 5.6~ sodium hydroxide solution.
a) Heat StabilitY
To determine the heat stability, the emulsions of Examples
I to 13 were kept in a 250 mL glass bottle at 60C in an oven and
evaluated every 8 hours. The time after which no destabilization
of the emulsion is detectable, lS noted.
~IY2-21438.
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~135~2û
b) Shakina Stabilitv
The shaking stability was determined by filling 80 mL of
the emulsion to be tested into 100 mL glass bottles and shaking
them in a shaker with a shaking frequency of 240 per minute and a
de~ection of 3 cm. The emulsion was checked hourly for
destabilization. Emulsions with shaking stabilities of less than
2 hours could be harmed during transport. For this reason, longer
shaking stabilities are desirable.
The heat stability of the emulsions of Examples I to 13
exceeded 150 hours.
The shaking stability of the emulsions of Examples I to 13
exceeded 8 hours.
The defoaming action of the emulsions of Example 7 and
Examples 11 to 13, prepared with different peripheral speeds from
the emulsion of Example 2, were checked in order to show that the
defoaming is independent of the dilution method.
~Y2-21438. -24-
213~120
TEST METHOD:
Dilexo AM 15 (a pure acrylate dispersion of the DEA
Company) is mixed with water in a ratio of 8 : 2 (dispersion I).
Dispersion I (100 g) is added to a 250 mL beaker and the
temperature is adjusted to 20C. After that, 1~ of the defoamer
emulsion to be tested is added. This mixture is stirred for 1
minute at 2,500 rpm with a turbine, the diameter of which is 4 cm
and which is clamped in a stirrer in such a manner that it is
0.5 cm above the bottom of the beaker. Directly after the
3tirring, 50 mL of the stirred dispersion I is added to a tared
50 mL measuring cylinder and weighed. From the weight A~and
density of the unstirred dispersion ~ (1.02 g/mL), the air,
stirred in, can be calculated as a percentage by volume using the
following equation:
~ by Volume of Air = 100 - 2A/aD
Defoamer A (g/50 mL)~ by Volume of Air
Without 36.4 28.6
Example 7 46.4 g.o
Example 11 46.5 8.8
Example 12 46.3 9.2
Example 13 46.7 8.4
NY2-21438.
