Using self-consistent field theory we investigate the properties of interfaces and of bubbles that nucleate in response to a pressure change. We use a simple phenomenological equation of state for a compressible mixture of two polymers. The parameters are chosen as to mimic the behavior of a polymer in a supercritical solvent and the phase behavior in the bulk corresponds to class III in the classification of Konynenburg and Scott. At low pressure, the density of the volatile solvent is small and the interface and nucleation properties are similar to a one-component fluid. At higher pressure, however, there is a triple point at which the polymer coexists with a vapor of the solvent and a mixed solvent-rich liquid. The vicinity of the triple point alters the interface and nucleation behavior: There is a thick wetting layer of the (metastable) solvent-rich liquid at the interface between polymer and vapor, and the solvent condenses into a solvent-rich liquid inside small bubbles. We explore the dependence of the nucleation barrier on temperature, pressure and molecular weight dispersity of the polymer and relate our findings to the binodal and spinodal of the bulk.

1.
M.
Blander
and
J. L.
Katz
,
AIChE J.
21
,
833
(
1975
).
2.
J. W.
Tom
and
P. G.
Debenedetti
,
J. Aerosol Sci.
22
,
555
(
1991
);
P. G.
Debenedetti
,
AIChE J.
36
,
1289
(
1990
).
3.
Nucleation and Atmospheric Aerosols, edited by N. Fukuta and P. E. Wagner (Deepak, Hampton, 1992).
4.
R. C.
Reid
,
Adv. Chem. Eng.
12
,
105
(
1983
);
R. C.
Reid
,
Science
203
,
1263
(
1979
).
5.
J. H.
Han
and
C. D.
Han
,
J. Polym. Sci., Part B: Polym. Phys.
28
,
711
(
1990
).
6.
S. K.
Goel
and
E. J.
Beckman
,
Polym. Eng. Sci.
34
,
1137
(
1994
);
S. K.
Goel
and
E. J.
Beckman
,
Polym. Eng. Sci.
34
,
1148
(
1994
).
7.
C. M.
Stafford
,
T. P.
Russell
, and
T. J.
McCarthy
,
Macromolecules
32
,
7610
(
1999
).
8.
B.
Krause
,
H. J. P.
Sijbesma
,
P.
Münüklü
,
N. F. A.
van der Vegt
, and
M.
Wessling
,
Macromolecules
34
,
8792
(
2001
);
B.
Krause
,
R.
Mettinkhof
,
N. F. A.
van der Vegt
, and
M.
Wessling
,
Macromolecules
34
,
874
(
2001
).
9.
P. H.
Konynenburg
and
R. L.
Scott
,
Philos. Trans. R. Soc. London, Ser. A
298
,
496
(
1980
).
10.
H.
Reiss
,
J. Chem. Phys.
18
,
840
(
1950
).
11.
G.
Wilemski
,
J. Chem. Phys.
80
,
1370
(
1984
);
G.
Wilemski
,
J. Phys. Chem.
91
,
2492
(
1987
).
12.
X. C.
Zeng
and
D. W.
Oxtoby
,
J. Chem. Phys.
95
,
5940
(
1991
).
13.
D. W.
Oxtoby
and
D.
Kashchiev
,
J. Chem. Phys.
100
,
7665
(
1994
).
14.
V.
Talanquer
and
D. W.
Oxtoby
,
J. Chem. Phys.
104
,
1993
(
1996
).
15.
I.
Napari
and
A.
Laaksonen
,
J. Chem. Phys.
111
,
5485
(
1999
).
16.
R. P.
ten Wolde
and
D.
Frenkel
,
J. Chem. Phys.
109
,
9919
(
1998
).
17.
S.
Yoo
,
K. J.
Oh
, and
X. C.
Zeng
,
J. Chem. Phys.
115
,
8518
(
2001
).
18.
V.
Talanquer
and
D. W.
Oxtoby
,
J. Chem. Phys.
102
,
2156
(
1995
).
19.
V.
Talanquer
,
C.
Cunningham
, and
D. W.
Oxtoby
,
J. Chem. Phys.
114
,
6759
(
2001
).
20.
M.
Srinivasarao
,
D.
Collings
,
A.
Philips
, and
S.
Patel
,
Science
292
,
79
(
2001
).
21.
K.
Binder
and
D.
Stauffer
,
Adv. Phys.
25
,
343
(
1976
).
22.
H. M.
Tanaka
,
J. Phys.: Condens. Matter
12
,
R207
(
2000
);
H. M.
Tanaka
,
Prog. Theor. Phys.
101
,
863
(
1999
).
23.
G.
Debregeas
,
P. G.
deGennes
, and
F.
Brochard-Wyart
,
Science
279
,
1704
(
1998
).
24.
W.
Klein
,
T.
Lookman
,
A.
Saxena
, and
D. M.
Hatch
,
Phys. Rev. Lett.
88
,
085701
(
2002
).
25.
M.
Volmer
and
A.
Weber
,
Z. Phys. Chem., Stoechiom. Verwandtschaftsl.
119
,
227
(
1926
);
R.
Becker
and
W.
Döring
,
Ann. Phys. (Leipzig)
24
,
719
(
1935
).
26.
J. W.
Cahn
and
J. E.
Hilliard
,
J. Chem. Phys.
31
,
688
(
1959
).
27.
M.
Müller
,
Phys. Rev. E
65
,
030802
(R) (
2002
).
28.
M. W.
Matsen
,
J. Chem. Phys.
110
,
4658
(
1999
).
29.
J.
Noolandi
and
K. M.
Hong
,
Macromolecules
14
,
727
(
1981
),
J.
Noolandi
and
K. M.
Hong
,
Macromolecules
15
,
483
(
1982
).
30.
M. W.
Matsen
and
M.
Schick
,
Phys. Rev. Lett.
74
,
4225
(
1995
).
31.
E.
Helfand
,
J. Chem. Phys.
62
,
999
(
1975
).
32.
G. M.
Schneider
,
Adv. Chem. Phys.
XVII
,
1
(
1970
).
33.
Using experimental data for carbon dioxide and hexadecane we identify ε=5.8⋅10−20J and σ=4.5 Å.
34.
P. Virnau, M. Müller, L. G. MacDowell, and K. Binder, Comp. Phys. Comm. (to be published).
35.
M.
Müller
and
L. G.
MacDowell
,
Macromolecules
33
,
3902
(
2000
).
36.
Fixing the values of bA and bB, we set the length scale of the nonlocal contribution in the SCF theory. For the solvent this length scale should be identified with the range of the interaction potential (which is of the order σ). The values of bA and bB do not influence the bulk phase diagram, but only affect the properties of the inhomogeneous system (e.g., interface tension, nucleation barrier). In order to describe an experimental system, one might adjust the values bA and bB as to match the interface tension for the pure components.
37.
J. S. Rowlinson and F. L. Swinton, Liquids and Liquid Mixtures (Butterworth, London, 1982).
38.
L. G. MacDowell, P. Virnau, M. Müller, and K. Binder, J. Chem. Phys. (to be published).
39.
M. Schick, Les Houches lectures on “Liquids at interfaces” (Elsevier Science, New York, 1990); B. V. S. Dietrich, in Phase Transitions and Critical Phenomena, Vol. 12, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1988).
40.
A.
Werner
,
M.
Müller
,
F.
Schmid
, and
K.
Binder
,
J. Chem. Phys.
110
,
1221
(
1999
);
A.
Werner
,
F.
Schmid
,
M.
Müller
, and
K.
Binder
,
Phys. Rev. E
59
,
728
(
1999
).
41.
J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Clarendon, Oxford, 1982).
42.
S. M.
Wood
and
Z.-G.
Wang
,
J. Chem. Phys.
116
,
2289
(
2002
).
43.
K.
Binder
,
Phys. Rev. A
29
,
341
(
1984
);
K.
Binder
,
Adv. Polym. Sci.
112
,
181
(
1994
).
44.
D. W.
Heermann
,
Z. Phys. B: Condens. Matter
55
,
309
(
1984
).
45.
R.
McGraw
and
A.
Laaksonen
,
Phys. Rev. Lett.
76
,
2754
(
1996
).
46.
V.
Talanquer
,
J. Chem. Phys.
106
,
9957
(
1997
).
47.
V. K.
Shen
and
P. G.
Debenedetti
,
J. Chem. Phys.
114
,
4149
(
2001
).
48.
A.
Laaksonen
,
V.
Talanquer
, and
D. W.
Oxtoby
,
Annu. Rev. Phys. Chem.
46
,
489
(
1995
);
D. W.
Oxtoby
,
J. Phys.: Condens. Matter
4
,
7627
(
1992
);
D. W.
Oxtoby
and
R.
Evans
,
J. Chem. Phys.
89
,
7521
(
1998
).
49.
(1) The nucleation barrier vanishes in the vicinity of the spinodal like ΔG∼(μ−μspin)3/4. (2) If we used the chemical potential μA of the volatile component instead of μB, the data in Fig. 6 (inset) would not scale onto each other.
50.
L.
Granasy
and
D. W.
Oxtoby
,
J. Chem. Phys.
112
,
2410
(
2000
).
51.
R. P.
ten Wolde
,
M. J.
Ruiz-Montero
, and
D.
Frenkel
,
Phys. Rev. Lett.
75
,
2714
(
1995
);
R. P.
ten Wolde
,
M. J.
Ruiz-Montero
, and
D.
Frenkel
,
J. Chem. Phys.
104
,
9932
(
1996
).
52.
W.
Ostwald
,
Z. Phys. Chem., Stoechiom. Verwandtschaftsl.
22
,
289
(
1897
).
53.
R. P.
ten Wolde
and
D.
Frenkel
,
Phys. Chem. Chem. Phys.
1
,
2191
(
1999
).
54.
The gas has a large entropy and, hence, is favored at high temperatures (Ref. 19). Moreover, the interface tension is expected to decrease upon increasing the temperature.
55.
S.
Auer
and
D.
Frenkel
,
Nature (London)
413
,
711
(
2001
).
56.
The parameters of our calculations do not correspond to a carbon dioxide–polystyrene mixture, which was investigated in Ref. 7. The pressure and temperature in the experiment is much higher than the critical values of carbon dioxide (T/TAc≈1.23 and p/pAc≈3). Unfortunately, we do not know the complete phase diagram of the carbon dioxide-polystyrene mixture. Our calculations are performed at T/TAc=1.034 and the loading pressure 3/kBT=0.16 corresponds to p/pAc=0.818.
57.
F. J.
Blas
and
A.
Galindo
,
Fluid Phase Equilibria
4831
,
1
(
2002
).
58.
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1987).
59.
P.-G.
deGennes
,
J. Chem. Phys.
72
,
4756
(
1980
).
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